Hypothesis of dark matter and dark energy with minus mass

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1 Hypothesis of dak matte and dak enegy with minus mass Hyoyoung Choi In 1998 yea, obsevation by The High-z Supenova Seach team, if the cosmological constant is 0, Ω M = 0.38(±0.). The quantity of the matte couldn t be negative value, so as fa as we know, the value is tashed away. We have to know that not the field equation has disposed the value, but ou thought disposed that value. In the wold of plus mass, gound state is a point that enegy is low, but in case of minus mass(negative mass), gound state is a point that enegy is the highest. Accodingly, in the wold of minus mass, enegy level is filled fom the highest to the lowest, and stable state means the highest enegy state, so the catastophe to enegy level of - neve happens even if minus mass spontaneously emits enegy. Assuming that minus mass exists, Newton s Law of motion was deived in between minus and plus masses and also between minus and minus masses. Also, explanation on how minus masses will be distibuted in the cuent state of space with Newton Law of motion. As fo dak mattes and dak enegy, minus mass can poduce an additional centipetal foce in the galaxy o galaxy cluste, which suppots the dak matte, while the plus mass can emege epulsive effects that acceleate the inflation diection and a qualitative intepetation could be possibly made on dak enegy fom minus mass. As a method fo poving the existence of minus mass, an explanation on the evolution velocity of the galaxy though minus mass has been pesented. In this pocess, the existence of spheical mass distibution was given; futhemoe, explanation was done using this, to show obsevation esults whee dak matte effect though minus mass is popotional to distance. If Ω M is -0.38, univese s age is 14.5 Gy. It is in the ange estimated by othe obsevations. Assuming that minus mass and plus mass wee bon togethe at the beginning of univese, it satisfies the vaious poblems that pevious dak matte and dak enegy possess, such as, centipetal foce effects of galaxy and galaxy clustes fom pevious dak mattes, mass effects that is popotional to the distance, epulsive foce needed fo expansion, dak enegy that has plus values, low inteaction between dak matte when collision occus between dak matte, deceleation expansion and acceleation expansion of univese, fomation of void, inflation mechanism, fine tuning poblem of mass density, collision of Bullet cluste, difficulty in obsevation, the eason of that dak enegy seems to has a small and constant value. As a esult, the necessity of obsevation focusing on exact computation and detection of minus mass is stated. PACS numbes: d, x, Cq keywod: minus mass, negative mass, dak matte, dak enegy, inflation, void, bigbang, cosmological constant, fine tuning poblem 7icaus7@gmail.com I. Intoduction Now the obsevation is a vey impotant issue, and seems to detemine eveything in quantum mechanics, but the obsevation is not to detemine existence and nonexistence, it is just local evidence of existence and nonexistence, and the thing that detemines existence and nonexistence in natue is all sots of physical laws, not obsevation. It is necessay to watch caefully the fact that all sot of physical laws such as Law of enegy consevation o Law of consevation of momentum do not deny minus mass. [1] All sots of physical laws do not deny them, thus minus mass can exist! If we conside the situation of antipaticle and antimatte, we can know they exist, although they ae not obseved in common situation. We have must explain the eason why they ae not easily obseved in common situation by thei motion o chaacteistics, suggest explanation of existing phenomenon, and new pediction with thei chaacteistics, and inspect it with obsevation. With the assumption that minus mass exists, in the text, the eseache ties to examine motion of minus mass and plus mass, and motion of minus mass and minus mass, and to suggest that minus mass can povide pope desciption of dak matte and dak enegy. Most of people have stong avesion of minus mass, but no law of physics says thee is only plus mass in natue, and we think that we feel as if ou thought of mass, namely mass that is the a synonym fo the fact something exists denies negative value. Howeve, negative chage and positive chage suggest that something exists does not mean plus value only. The geat achievement of physics in theoy of elativity and quantum mechanics equest us to eview the pevious thought of physical quantities.

2 II. Newton s law of motion of minus mass When an object with mass of +m1 is away fom an object with mass of +m by distance, the foce woked between two objects is descibed as following type. F = G m 1m ˆ (1) When an object with mass of m 1 is away fom an object with mass of m by distance, what type does the foce woked between two objects have? Many people think the foce decides motion of object in gavity, but actually the acceleation decides the motion of object in gavity, and also plays a ole of deciding the moving diection of object which is at the state of stop. We can set up following dynamic equation to descibe the motion of object. That is, the gavity ceated on mass m 1 by mass m is expessed as follows: F 1 = m 1 a 1 = G m 1m ˆ () m 1 a 1 = G m 1m ˆ (3) a 1 = G m ˆ (4) As we can see in the equation above, the tem of acceleation emains only because mass m 1 is eased fom both tems. Now the equation of motion means the equation of acceleation, not the equation of foce, the acceleation povides infomation of motion diection, and decides the diection of motion. 1.The law of motion of plus mass and plus mass Figue 1: Plus mass +m 1 and plus mass +m (initial velocity =0, m 1 > 0, m > 0) m 1 a 1 = G m 1m ˆ (5) a 1 = G m ˆ (6) m a = G m 1m ˆ (7) a = G m 1 ˆ (8) Plus mass and Plus mass : The foce woked between plus mass is attaction, and two objects move towad the cente of mass. The foce is attaction, thus thei potential enegy has minus value. The diection of acceleation is in the diection of ˆ, so the distance between two objects ae educed gadually..the law of motion of minus mass and plus mass Figue : minus mass -m 1 and plus mass +m (initial velocity =0, m 1 > 0, m > 0) m 1 a 1 = G ( m 1)m ˆ (9) a 1 = G m ˆ (10) +m a = G ( m 1)m ˆ (11) a = G m 1 ˆ (1) Minus mass and Plus mass : Minus mass is acceleated in the diection of plus mass, and plus mass is acceleated in the diection to be fa away fom minus mass. The diection of acceleation a1 woked on minus mass m 1 is ˆ, so m 1 moves in the diection of educing distance, and the diection of acceleation a woked on plus mass +m is +ˆ, so plus mass +m is acceleated in the diection that distance inceases, namely the diection of being fa away fom minus mass. If the absolute value of plus mass is bigge than that of minus mass, they will meet within finite time(attactive effect), and if the absolute value of plus mass is smalle than that of minus mass, the distance between them will be bigge, and they cannot meet(epulsive effect). The type of foce is epulsion, so the potential enegy has plus value. 3.The law of motion of minus mass and minus mass Figue 3: minus mass -m 1 and minus mass -m (initial velocity =0, m 1 > 0, m > 0)

3 m 1 a 1 = G ( m 1)( m ) ˆ (13) a 1 = +G m ˆ (14) m a = G ( m 1)( m ) ˆ (15) a = +G m 1 ˆ (16) Minus mass and Minus mass: Both two objects ae acceleated in the diection of +ˆ which extends adius, so as time passes, the distance between them is geate than initially given condition, and the foce between them is attaction, but the effect is epulsive. The foce is attaction( Gm1m/ ), thus the potential enegy between them has minus value. 4.Minus mass cannot fom the stuctue geate than atom As examined the equation of motion fo minus mass, it is maked in fom of F = ma(m > 0), when attaction is applied togethe with nuclea foce(when usually nuclea foce is attaction, but has the fom of epulsive coe []), and assuming nuclea foce has the fom of F = Q()ˆ, Q() is the positive function of distance, thus nuclea foce is in the fom of attaction woked in the diection of -ˆ. Hee, fo the foce woked on minus mass m, F = m a = Q()ˆ (17) a = Q() ˆ (18) m the tem of acceleation is plus, so the effect of inceasing adius, namely epulsive effect appeas. This means that minus mass cannot fom the stuctue like atom(massive nucleon, bayon, paticle consists of multi elementay paticle), because nuclea foce has not binding minus mass when it is applied to minus mass. Also, gavity has not binding minus mass(epulsive) Additionally, fo the poblem of mesons that mediates nuclea foce o weak inteaction, if thee is no meson that delives stong inteaction o weak inteaction, it is doubtful if stong inteaction o weak inteaction can be woked o not. Fo example, nucleon must have intenal stuctue including meson o quak, but in case of minus mass, nuclea foce is epulsive, so it cannot have the intenal stuctue of nucleon fom the beginning. That is, thee is a geat possibility that minus mass cannot include meson o quak which has minus mass in nucleus. The fact that it cannot make nucleon means that it is impossible to fom massive mass stuctue like a sta in addition to atomic stuctue. This povides pope explanation of the fact that minus mass is not seen as it has visible massive mass stuctue. Also geneally it satisfies the nonbayonic [3] mattes equied fo dak matte. If minus mass was bon at the beginning of univese, thee is highe possibility that it exists until now as a cetain basic state bon at the beginning of univese, and that it does not have stong inteaction like nuclea foce, weak inteaction, and electomagnetic inteaction(neutal o has not intenal stuctue(plus mass elementay paticle has a 1/,1/3,/3 chage)). This point is keeping with cuent chaacteistics equied fo dak matte. If minus mass and plus mass wee bon togethe at the beginning of univese, plus mass has attactive effect each othe, so it foms sta and galaxy stuctue now, but minus mass has epulsive effect each othe and nuclea foce cannot fom nucleons by binding minus mass, so they cannot make massive mass stuctue like sta o galaxy. If dak matte is minus mass, non-obsevation of dak matte sta and galaxy can be explained. 5.Minus mass is stable at the maximum point! [1] Natue pefes stable state, and has the tendency to go to stable state. Additionally, this can be expessed in anothe way that natue pefes low enegy state, and has the tendency to go to low enegy state. Such an idea is fequently used as a logic which denies the existence of minus mass. That is, if thee is minus mass and minus enegy level, minus mass spontaneously emits enegy to be stable, and goes to enegy state of minus, so finally it is confonted by catastophe. Is it ight? In case of plus mass, stable state means low enegy state, theefoe it is not necessay to divide which one natue pefes among two states(stable state and low enegy state). By the way, does stable state mean low enegy state also in case of minus mass? We can get an answe, if we examine Hamonic oscillation. Figue 4: When thee is minus mass in potential which has a point of maximum value and a point of minimum value. We begin by consideing the oscillatoy motion of a paticle that is constained to move in one dimension. 3

4 We assume that thee exists a position of unstable equilibium fo the paticle and we designate this point as the oigin. Restoing foce is in geneal some complicated function of the displacement and pehaps of the paticle s velocity o even of some highe time deivative of the position coodinate. We conside hee only case in which the estoing foce F is a function only of the displacement F(x) can be expanded in a Taylo seies, F (x) = F (0) + x 1! F (0) + x! F (0) + x3 3! F (0) + a point of maximum value to be stable, not a point of minimum value which enegy is low. In the wold of plus mass, gound state is a point that enegy is low, but in case of minus mass, gound state is a point that enegy is the highest. Accodingly, in the wold of minus mass, enegy level is filled fom the highest to the lowest, and stable state means the highest enegy state, so the catastophe to enegy level of - neve happens even if minus mass spontaneously emits enegy. + xn n! F (n) (0) + (19) Since the oigin is defined to be the equilibium point, F(0) must vanish, Then, if we confine ou attention to displacements of the paticle that ae sufficiently small, we can neglect all tems involving x and highe powes of x. We have, theefoe, the appoximate elation F (x) = +kx (0) The foce is alaways the opposite diected towad the unstable equilibium position(the oigin), the deivative F (0) is positive and theefoe k is a positive constant. mẍ = +kx (1) ẍ + ω 0x = 0 () (ω 0 = k m ) (3) This fom of diffeential equation is the same as that of paticle which has plus mass. But we have to notice that plus mass caies out hamonic oscillation on a point of minimum value, wheeas minus mass caies out hamonic oscillation on a point of maximum value. Additionally, estoing foce is +kx at this time. F = U (4) U = 1 kx (5) E = T + U = 1 mẋ 1 kx = 1 mω 0A (6) In phase space x ( E k ) + p ( me ) = 1 (7) This equation is ellipses equation, because total enegy E < 0 As examined in the question of Hamonic oscillation, in case of plus mass, a point of minimum value which enegy is the lowest is stable. Howeve, in case of minus mass, stable equilibium is a point of maximum value, not a point of minimum value. So minus mass is towad Figue 5: Hamonic oscillation of minus mass In hamonic oscillation of minus mass E = 1 mẋ 1 kx = E + (8) H + ψ = E + ψ, H ψ = E ψ (9) [x, p ] = [x, p + ] = [x, p + ] = i h (30) [x i, p +j ] = +i hδ ij (31) [x i, p j ] = i hδ ij (3) Hamiltonian H of minus mass (in hamonic oscillation) H = 1 mẋ 1 mw x (33) = ( P + m + 1 mw x ) (34) = hw( mwx h + P + m hw ) (35) mw = hw( h x+i P + mw )( m hw h x i P + ) (36) m hw a (annihilation opeato) and a (ceation opeato) ae defined 4

5 N(a a) is mw a = h x + i P + m hw (37) mw a = h x i P + m hw (38) N = a a = mw h (x + P + m w + i mw [x, P +]) (39) = 1 h [mwx + P + mw ] 1 = 1 h [ H w ] 1 (40) (41) H = hw(n + 1 ) (4) Eigen value of numbe opeato N Theefoe, N n = n n (43) H n = hw(n + 1 ) n (44) = hw(n + 1 ) n (45) = E n n (46) En = hw(n + 1 )(n = 0, 1,, 3, ) (47) Gound state of minus mass is n=0 state. Eigen value is E 0 = 1 hw, fist-excite state E 1 = 3 hw III. Hypothesis of dak matte and dak enegy with minus mass 1. Hypothesis of dak matte and dak enegy with minus mass If negative enegy and positive enegy wee bon togethe at the moment of Big Bang, then negative enegy would ceate minus mass, and positive enegy could exist in univese as the state of positive enegy like plus mass and adiant enegy. Minus mass was disappeaed nea massive plus mass stuctue(such as planet, sta, etc.) afte meeting plus mass because of Newton dynamic motion of minus mass and plus mass, but minus mass which was bon at the beginning of univese still exists out of galaxy, and this minus mass is the oigin of dak enegy, which acceleates plus mass in the diection of cosmic expansion and dak matte, which collects galaxy in Galaxy cluste, o stas in each galaxy 1)At the beginning of univese, assume that the pai of positive enegy and negative enegy was pai poduction and pai annihilation epeatedly when cosmic enegy is 0. E T = (+E + ) + ( E ) = 0 )Fom among (+E + ) and ( E ), the pai of enegy is exists which was not disappeaed 3)E + = m + c +hv(enegy state) Some of them ceated matte and antimatte matte which had mass, but because of the asymmety between matte and antimatte matte, they wee disappeaed each othe, then ceated adiant enegy, and some mattes suvives. 4)But, in case of negative enegy, it cannot ceate paticles that have intenal stuctue, because of essential chaacteistics of minus mass, so it just ceates minus mass E = m c only. 5)Theefoe, most of negative enegy is conveted to m c which is a type of mass as the tempeatue falls down at the beginning of univese, wheeas positive enegy is conveted to m + c and positive enegy state(adiant enegy), so the velocity that it is conveted to mass is elatively slow. Accoding to this, the density of minus mass is consideably geate than that of plus mass at the beginning of univese. 6)At this time, total of potential enegy has minus value(descibed in V-) 7)As the univese is cooled down, positive enegy ceates plus mass and stas moe and moe, thus matte state inceases moe than enegy state. 8)Stating 7 billion yeas ago, the numbe of plus mass eached to fixed ate in popotion to minus mass, and fom this moment, total potential enegy of univese had plus value, thus it enteed in the peiod of acceleating expansion.(descibed in V-) If minus mass and plus mass wee bon togethe at the beginning of univese, plus mass has attactive effect each othe as seen in Chapte, so it foms sta and galaxy stuctue now, and minus mass has epulsive effect each othe, so it cannot fom any stuctue, and may spead out unifomly in the whole aea of univese as minus mass at the point that it was bon. Owing to the effect of minus mass and plus mass, minus mass was disappeaed nea massive plus mass stuctue(such as planet, pemanent sta, etc.) afte meeting plus mass, but minus mass which was bon at the beginning of univese can still exist at the vacuum state out of geneal galaxy as much as the numbe of plus mass. This minus mass geneates the effect of centipetal foce which binding plus mass in galaxy o galaxy cluste..desciption of the effect of centipetal foce and dak matte with minus mass V () = GM()/ (48) M() = M() visible + M() dak (49) 5

6 Figue 6: Revolution velocity of galaxy. The evolution velocity though the total quantity of matte that can be obseved is A, while the actual obseved value is B. Cuently, fom the calculation of total amount of visible mattes duing geneal obsevation of galaxy, it must show the fom of Gaph A that indicates the evolution velocity of sta is deceased as it appoaches to exteio of galaxy, but fom the value accoding to actual obsevation, it shows evolution velocity is almost unifom at both points whethe it is close o fa away fom cente of galaxy as shown in Gaph B, and if stas keep cuently obseved velocity, stas go out without being held in gavity, so geneally scientific cicles insist that invisible matte that cuently holds stas, namely positive dak matte that plays a ole of centipetal foce should exist thee. [3] Fo this phenomenon, this pape ties to explain that minus mass can ceate invisible gavity effect, and exta dak matte effect in galaxy. When minus mass is distibuted unifomly in Fig.7, if we examine the aea of galaxy diamete woking the gavity on the basis of mass m fo the analysis, thee is no minus mass in the space of spial space on the left, so minus mass can exist as much as the size of black and white on the ight. Minus mass on the ight woks the foce on plus mass m on the oigin to the left(plus mass moves afte eceiving the foce that becomes fathe fom minus mass), and this diection will be in keeping with the cental diection of gavity of eal galaxy. Theefoe, finally minus mass which emains on the ight woks the gavity effect on mass m as much as the same sized plus mass exists on the left. Accoding to this, plus mass m on the am of galaxy has eceived additional centipetal foce by minus mass geate than visible plus mass(galaxy mass), so it must have highe velocity V as shown in obsevation to stay in elevant obit. Details ae explained in [V. Method to pove the existence of minus mass.] If we explain the same figue in the diffeent way, if Figue 7: Minus mass effect on ams of galaxy. The actual obseved spial galaxy is on the left. Since epulsive effects occu between minus masses in Newtons dynamics, minus masses will be distibuted all ove space because it cannot fom lage mass stuctues like stas. Minus mass within the galaxy is cancelled out by attaction fom lage plus mass duing the galaxy fomation pocess. Futhemoe, the space, othe that the galaxy, will maintain the distibution state of minus mass. minus mass and plus mass of same size exist togethe in the aea of galaxy on the left that thee is no minus mass(white aea), two mass ae completely offset, so that aea is just same as empty space. Now minus mass is distibuted unifomly in the whole aea aound mass m located on the oigin, so the gavity woked on plus mass m by minus mass is offset each othe. Wheeas, plus mass which is not offset emains in white aea on the left, unifomly distibuted plus mass woked additional attaction, namely centipetal foce on mass m on the oigin. Accodingly, mass m on the am of galaxy eceives centipetal foce by eal galaxy, and centipetal foce by the distibution of minus mass out of galaxy(the same effect as plus mass is distibuted in galaxy). Dak matte, which is equied to explain geate velocity of galaxy as compaed with the gavity of galaxy cluste, and geate sta s velocity in each galaxy, can be descibed not only with plus mass. 3. Desciption of epulsion effect of cosmic expansion and dak enegy with minus mass Minus mass can wok additional centipetal foce on stas in galaxy as descibed peviously, and also minus mass can povide epulsion which is the oigin of cosmic expansion fom Newton dynamics. As consideed the poblem of the gavity at the point placed on abitay adius R of spheical object like the 6

7 4. The diffeence in mass when ceating the pai of minus mass and plus mass If plus mass and minus mass simultaneously epeat pai ceation and pai annihilation micoscopically at the vacuum state which satisfies enegy consevation and momentum consevation, to mateialize enegy and momentum consevation, the size of two mass can be diffeent when ceating a pai of plus mass and minus mass because of the existence of potential enegy, momentum consevation, etc. Figue 8: Expansion of the univese by minus mass distibution. The foce, which is applied to the galaxy and galaxy cluste and located within adius R fom the cente of a 3-dimensional space, when assuming equal distibution of minus mass fom epulsive effects between minus masses acoss space is valid. eath that mass is unifomly distibuted [4], the gavity by mass distibution out of adius R is offset each othe, and thee is only the gavity effect by mass within adius R. If minus mass was bon at the beginning of univese togethe with plus mass, it should be unifomly distibuted in univese by epulsion between minus mass. Of couse, thee can be diffeence in minus mass density owing to the local distibution of massive plus mass. Fo the gavity effect that almost unifomly distibuted minus mass has on plus mass(galaxy o galaxy cluste) located in adius R fom the cente of univese(3- dimensional cente), minus mass within adius R only has the gavity effect on plus mass located within adius R, and at this time, plus mass is acceleated in the diection of begin fa away fom minus mass. The diection that plus mass becomes fathe fom minus mass is in keeping with the diection of cosmic expansion, and also minus mass continuously woks the foce, so finally plus mass is gadually acceleated(expansion velocity becomes faste). As examined in Chapte II, in the desciption of the foce of plus mass and minus mass, the foce is epulsion(the diection of +R), and integated potential enegy is plus value. Theefoe, the assumption of the existence of minus mass can suggest the explanation of epulsive effect equied fo cosmic expansion, and the accompanying positive dak enegy. If thee is diffeence between ( m c )and(+m + c ) owing to momentum consevation and enegy consevation at the state of epeating ceation and annihilation of m and +M + in a vacuum in an instant(enegy consevation can be boken fo vey shot time because of uncetainty pinciple, so it can be ceated by such an enegy as well), two mass ae pai-ceated. If two mass ae pai-annihilated, enegy consevation is mateialized on the whole, but the gavity by (-m) and (+M) can wok on othe objects in ou univese fo vey shot time befoe pai annihilation afte pai ceation This study calculated dynamically the diffeence between two mass in accodance with enegy and momentum consevation below, if minus mass and plus mass ae pai-ceated in a vacuum. If we conside the existence of diffeence in mass when pai ceation Minus mass and plus mass that enegy consevation is mateialized when pai ceation and pai annihilation fom E T = T + U + m 0 c E T = m c M +c + + ( GM +( m )) (50) 1 ( v c ) 1 ( V c ) E T = m c M +c + + GM +m = 0 (51) 1 ( v c ) 1 ( V c ) P T = m v 1 ( v + +M +V = 0 (5) c 1 ) ( Vc ) (initial enegy 0, initial momentum 0, M + > 0, m > 0,) In equation (5), ae define, equation (5) is 1 ( v c ) = a (53) 1 ( V c ) = b (54) m v a = M +V b (55) m = M + ( a b )(V v ) (56) If equation (51) is substituted fo equation (53), (54) GM + m = m c a M +c b (57) 7

8 substituion equation (56) in equation (57) GM + M + ( a b )(V v ) = c a M +( a b )(V v ) M +c GM + Both tem ( b a )( v V ) multiply, ( a b )(V v ) = (c b )(V v ) c b GM + b (58) (59) = c a (1 v V ) (60) In equation (60), the left tem is bigge than 0, thus the ight tem must be bigge than 0, accodingly, V > v (61) and plus mass, the size of absolute value of minus mass is the same as that of plus mass, and minus mass and plus mass of same numbe wee bon, and this study ties to conside the cosmic expansion when the distance between them is simila. 1)Potential enegy when thee is one pai of minus mass and plus mass U U 1 = G(m +)( m ) = + G(m +)(m ) = Gm + (65) (if,m + = m ) )Potential enegy when thee is two pai of minus mass and plus mass U If equation (61) is substituted fo equation (56), ( V v ) = m b M + a > 1 (6) m > a M + b = c v (63) c V Consideing V > v, which is the esult fom equation (61), in equation (63), numeato is bigge than denominato, m > M + (64) so we can get the esult. equation (64) shows that, if minus mass and plus mass ae pai-ceated, thee is the diffeence between minus mass and plus mass when initial enegy and momentum ae 0 in the system that enegy consevation and momentum consevation ae mateialized. This diffeence in mass when minus mass and plus mass pai ceation pesents that, if minus mass and plus mass wee bon togethe at the beginning of univese, minus mass which is not offset fom among them can exist in univese now, and also minus mass which is bigge than plus mass can exist. Accodingly, if minus mass is dak matte, it povides the desciption that total amount of dak matte is bigge than that of matte. The existence of minus mass povides quantitative desciption of the existence of dak matte and dak enegy, it can make it possible that enegy value which is the oigin of initial state of univese can be 0, and this has a vey impotant meaning. 5.The univese expands even if the size of minus mass is the same as that of plus mass In pevious paticle physics, accoding to the case of the bith of antimatte, when pai-ceating paticles symmetical to cetain paticle, thei physical quantities ae the same each othe, accoding to the situation that has opposite specific value, when pai-ceating minus mass Figue 9: Aanges 1 when pais of minus and plus masses exist U = 6 U i = U + + U (66) i=1 U = U + + U = (U 1 + U + U 3 + U 4 ) + (U 5 +U 6 ) = 4 Gm +m = 4 Gm + ( Gm +m + (67) + Gm m ) (68) + ( Gm + ) (69) = (4 )( Gm + ) (70) (m + = m ) Potential enegy has plus value, so thee is epulsion, and the univese expands. We can know that the univese expands at the state that the size of minus mass is the same as that of plus mass, and the numbe was identically bon U = 6 U i = U + + U (71) i=1 8

9 Figue 10: Aanges when pais of minus and plus masses exist U = U + + U = (U 1 + U + U 5 + U 6 ) + (U 3 +U 4 ) = ( Gm +m + Gm +m ) ( Gm +m + (7) + Gm m ) (73) = ( Gm + ) (74) = ( Gm + ) (75) (if, m + = m ) Potential enegy has plus value, so thee is epulsion, and the univese expands. We can see that potential enegy keeps plus value at the state that the size of minus mass is the same as that of plus mass, and the numbe was identically bon, although thee is diffeence in the value of potential enegy accoding to the distibution of each mass. Theefoe, potential enegy is plus, thus the foce is plus, and the univese expands. 3)Potential enegy when thee ae geneally n pais of minus mass and plus mass: n n(n 1) U n = U +i + U j (76) i=1 j=1 (U + :plus potential enegy, U :minus potential enegy) If n pais of minus mass and plus mass ae ceated, geneally the numbe of tem of plus potential enegy is n, the numbe of tem of minus potential enegy is n(n-1), so the numbe of tem of plus potential enegy is geate than that of tem of minus potential enegy by n. Accodingly, even if the absolute value of minus mass is the same as that of plus mass at the beginning of univese, the univese has the value of plus potential enegy, and expands. 6. The effect of gavitational lensing Geneally, it is possible to examine the existence of dak matte with the existence of additional mass with the effect of gavitational lensing. If minus mass is dak matte, so if we ty to examine the effect of gavitational lensing, peviously the gavity between plus mass is attaction, so it has the shape of convex lens to collect within the fom, wheeas the foce between minus mass and plus mass is epulsion, so a set of massive minus mass can make the effect that distots obsevation taget in the fom of concave lens. If existing measuing instument ecognizes the effect of gavitational lens with distoted aspect of galaxy o galaxy cluste, the effect of concave gavitational lensing owing to the existence of minus mass also plays a ole of distoting galaxy o galaxy cluste, so it can be the basis of invisible dak matte. Additionally, in the distibution of dak matte suggested with peviously measued effect of gavitational lens, dak matte may be ceated puely by plus mass, but also it can be ceated by the distibution of dak matte by minus mass. But in the hypothesis of dak matte with minus mass in this study, minus mass is distibuted out of galaxy, not within galaxy. Theefoe, the effect of concave gavitational lensing by minus mass out of galaxy will be pesented to an obseve on the eath in the same fom as the effect of convex gavitational lensing which galaxy woks. Figue 11: Concave Gavitational lensing effect. The left side is the Gavitational lensing effect that occus when the galaxy is suounded by minus mass and the ight side is Gavitational lensing effect that occus when plus mass exists alone No the effect of concave gavitational lensing by minus mass has been obseved. Howeve, we have neve thought about minus mass itself, so we might not have thought about the concave gavitational lensing as well, and it might be difficult to classify the effect of concave gavitational lensing and the effect of convex gavitational lensing. Fo the situation pesented on the left when obseving the light on the eath which passed though galaxy 9

10 suounded with minus mass, this study suggested that thee is invisible dak matte in galaxy, and owing to this gavity it can be happened owing to the effect of convex lens, it means, if thee is any matte on the left and ight side of galaxy that plays a ole of concave lens, it is difficult to classify convex lens and its fom. Accoding to the explanation of the effect of concave gavitational lensing fom the viewpoint of gavity, not geometical optics, thee is the effect of centipetal foce by the distibution of minus mass out of galaxy with the effect of centipetal foce in galaxy as descibed peviously, so thee is eal mass of galaxy + the gavity when filling the whole galaxy with plus mass that has the same density as that of minus mass in galaxy. Theefoe, if the light fom the exteio passes inside of galaxy o nea galaxy, eal gavity of galaxy + gavity of dak matte(by minus mass) is added, and finally it will pesent much geate effect of gavitational lensing. If we conside the situation that we can obseve puely the effect of concave gavitational lensing, that situation is just the same as the situation when thee is single concave lens on the ight in Figue above. Fist, an obseve on the eath must obseve it on Position B and C afte moving by consideably geat distance as compaed with the size of galaxy, but the eath has neve changed the position of obsevation fom the taget fo distant obsevation. second, eal obsevation on the eath is the single B o C situation in Figue on the ight, and if an obseve on the eath pefomed obsevation peviously on C, geneally an obseve of C would descibe the effect of gavitational lensing is geneated because thee is invisible dak matte on the ight of black and white aea(cicle dawn with dotted line on the ight). 7. Desciption of inteaction between dak mattes when colliding with galaxy clustes As shown in the ecent obsevation of dak matte, dak matte seems not to inteact with each othe when colliding with galaxy clustes [5], and it can be pedicted with essential chaacteistics of minus mass. Unifomly distibuted minus mass eceives attactive effect fom massive plus mass, so dak matte which has minus mass is clusteed aound galaxy because of attaction of galaxy. If the type of foce woked between minus mass when colliding with galaxy clustes is epulsive, and minus mass is distibuted almost unifomly without foming massive mass stuctue, the shape of dak matte is not distoted o tansfomed even if dak matte(minus mass) and dak matte(minus mass) pass though simila aea, that is, they will seem not to inteact each othe. Also thee is epulsive effect between dak mattes that ae made up with minus mass, thus thee will be almost no diect collision as well. Repulsive effect that is the natue between minus mass as descibed above povides the pope desciption that existing dak mattes do not inteact each othe, although they inteact gavitationally with plus mass. As the facto that beaks the unifom distibution of minus mass, fist, minus mass eceives the attactive effect fom massive plus mass, thus fo the distibution of minus mass nea massive plus mass such as galaxy o galaxy cluste, the density of minus mass is highe as it is close to galaxy o galaxy cluste, and is lowe as it is fathe. Second, If plus mass(like galaxy) that has stong gavity o intestella cloud that has plus mass pass though existing aea that minus mass is distibuted, minus mass can be disappeaed when meeting plus mass o it can be dawn owing to attactive effect of massive plus mass at this moment, so thee can be the aea that minus mass, namely, dak matte is not unifomly distibuted 8. Solution fo the difficulty in desciption with cosmological constant and vacuum enegy Fom the obsevation of univese, now we know that the univese acceleating expands, and to explain this acceleating expansion, we ty to explain cosmic expansion with the thought of cosmological constant and vacuum enegy, etc., but cosmological constant and vacuum enegy [3] theats the causationism that is the basis of science, and the enegy consevation that is fundamental chaacteistic of ou univese. At least, minus mass obseves enegy consevation and momentum consevation. This means that minus mass is not seious taget moe than cosmological constant o vacuum enegy in physics, although it is moe difficult to imagine the existence of minus mass moe than cosmological constant o vacuum enegy. IV. Explain fo the poblem of non-obsevation with the chaacteistics of minus mass As examined with Newton dynamics of minus mass, attaction woks between plus mass, and they have attactive effect, so they gadually clustes each othe, and then make massive mass like planet o sta. On the othe hand, attaction woks between minus mass, but they have epulsive effect, and nuclea foce cannot fom nucleons by binding minus mass, so they cannot make massive mass stuctue like planet o sta. This explains that existing dak matte is not an inteuption in foming galaxy while the univese is gowing. When matte and antimatte ae pai ceation and pai annihilation, antimatte also had basically plus mass, so gamma ays wee emitted when pai annihilation, and 10

11 with this phenomenon, the existence of antimatte was poved, but pai annihilation of minus mass and plus mass is in the fom of (E) + (+E) = 0, thus geneally gamma ays ae not emitted afte pai annihilation. So it seems to be moe difficult to detect. Bubble box that detects a chaged paticle used in acceleato also is useless when minus mass is not chaged, it cannot be valid means because minus mass cannot daw the tace itself with pai annihilation, and Thought wall of minus mass was too big. Howeve, the essential eason is that enegy value which can pai ceation ceate minus mass and plus mass might be limited at the beginning of univese. The eason why we have not found minus mass on the eath until now is that minus mass exists as the state of mass when it was bon without foming massive mass stuctue which can be easily measued owing to basic chaacteistics of minus mass(epulsive effect) as descibed above, and that minus mass is not obseved because minus mass which exists aound massive plus mass such as eath o the sola system eceives attactive effect fom massive plus mass, and it was disappeaed long time ago when foming galaxy, even if it existed at the beginning of univese. Thee is no obsevation of minus mass until now, but basic chaacteistics of minus mass and aspect of dynamic motion with plus mass stangely povide the pope desciption of dak matte and dak enegy in ou univese. 1. Calculating centipetal foce in galaxy fom minus mass distibuted out of galaxy We obseved not plus mass but gavitation effect. That is, univese has not said that dak matte is plus mass. This study mentioned the effect of centipetal foce descibed peviously, and the effect of centipetal foce of minus mass with the desciption of dak matte(fig.7). The eseache suggests that it is possible to pove the existence of minus mass with the compaison between obseved value and evolution velocity of sta accoding to the distance in galaxy which is calculated fom minus mass distibuted out of galaxy. V () = GM()/ (77) M() = M() visible + M() dak (78) Fom the calculation of centipetal foce in Newton dynamics(efe to Fig.7), the impotant mattes to calculate gavity effect of minus mass ae the size and model of empty space of minus mass by eal galaxy on the left, in case of spial galaxy o oval galaxy, it may be close to oval if we conside the fact that most of mass is placed on galaxy coe, the otation of galaxy, and the gavitational adius of galaxy coe, thus we egad empty space of minus mass as spheical o oval, and pefom calculation to compae with obseved value. The chaacteistics of minus mass unifomly satisfy the effect of centipetal foce which existing dak matte in galaxy o galaxy cluste, the fact that it does not inteupt to fom galaxy even though it has gavitational inteaction, difficult element fo the obsevation, vey low inteaction between dak mattes when colliding with galaxy o galaxy clustes, epulsion enegy equied fo cosmic expansion, epulsive effect on plus mass, etc. On the othe hand, minus mass also has the wall of thought that geneally it is difficult to accept. Howeve, we can say about the wall of thought, minus mass just collides with ou a fixed idea, and it does not collide with enegy consevation o momentum consevation. Some people deny minus mass because it cannot be accepted in the abstact, but it is necessay to efe to the fact that the quantum theoy o the theoy of elativity in 0th centuy is contadicted with existing fixed idea, povide quantitative explanation of dak matte and dak enegy, and then to pefom an expeiment tageting on the obsevation of minus mass. V. Method to pove the existence of minus mass Figue 1: Effective minus mass. The minus mass distibution, whee gavity is applied without cancellation of the oblique field located on the ight side. mv = GM +( + )m GM ( )m (79) (M + ( + ) > 0, M ( ) > 0) Adding the tem of centipetal foce by minus mass to the tem of centipetal foce by plus mass as descibed above, we compae evolution velocity of sta and the density of minus mass, then expand this to apply to othe galaxies, and we can inspect if the intepetation of dak matte distibuted out of galaxy is pope o not. 11

12 The distibution of minus mass that emains without being offset in Fig. 1 is cescent-shaped, so it seems to be difficult to calculate, but if we assume that the white empty space on the left is full with minus mass and plus mass at the same density, hee minus mass is unifomly distibuted ove the whole aea, so the effect of minus mass on mass m is 0. Remaining plus mass is distibuted ove the white aea on the left at the density of minus mass, and the gavity that unifomly distibuted plus mass woks on plus mass m place on adius is woked only by the distibution of mass within adius. equation (83) is applied to abitay spheical o oval galaxy, and in case of nomal shaped spial galaxy, the distance which spheical appoximation can be applied fom the cente of galaxy will be effective. So if we conside that the distibution of minus mass out of galaxy comes unde isothemal, the effect of mass in galaxy by the distibution of minus mass out of galaxy is popotional to as shown in equation (84), and this is in keeping with obseved dak matte. Figue 13: Equal to the degee of gavity that is applied on the equally distibuted plus mass within the adius of the left side. The gavitational effect fom minus mass, which functions at mass m is equal to the gavitational effect fom plus mass within adius. Figue 14: Revolution velocity of NGC 6503 Theefoe, the effect of minus mass that emains out of galaxy without being offset can make it appoximate to the gavity geneated by the distibution of plus mass within the adius R in galaxy In equation(79) M = ρ ()V = ρ ()( 4π3 3 ) (80) v = mv = GM +( + )m + + G(M + + M ) = + v = + GM ( + )m + (81) G(M + + ρ ( + )V ) (8) + GM + + ρ ( + )( 4π ) (83) The mass density of collisionless isothemal sphee is given as ρ() = σ πg [7] in galaxy dynamics. σ is velocity dispesion. M dak = M minus = σ 3G (84) Figue 15: Distibution of plus mass and minus mass on NGC6503. The distibution of the galaxy mass, which is can be obseved, is mostly in the galaxy nuclei, while the effects of minus mass, which is distibuted ove the outside of the galaxy, inceases with the atio of distance. NGC 6503 in Fig.14 is oval galaxy, and the gaph shows the total amount of dak matte with the distibution of minus mass that emains without being offset fom minus mass out of galaxy. Plus mass dak matte distibuted in galaxy does not fom the spheical distibution, and it is boken owing 1

13 to the gavity of galaxy coe, gavitational action with stas, and otation of galaxy, if its shape is not vey intentionally assumed. Futhemoe, thee ae vaious heat souces in galaxy accoding to position, so it cannot be egaded as collisionless Isothemal. Howeve, the effect of centipetal foce that minus mass woks fom the exteio of galaxy can keep the spheical distibution of mass, and make the mass effect that inceases linealy in accodance with distance as seen above because it eceives less influence fom elements such as the gavity of galaxy coe, o otation of galaxy. Also ideal state of collisionless can be achieved by minus mass, because minus mass has epulsive effect each othe. At the sola system, non-obsevation of dak matte is explained. In minus mass hypothesis, dak matte exists at the exteio of galaxy, so dak matte is not obseved at the sola system.. Desciption of cosmic deceleating expansion and acceleating expansion In [III-1] above, the numbe of minus mass was geate than that of plus mass at the beginning of univese, so if we induce how many tems of potential enegy suvive when the numbe of minus mass is geate than that of plus mass, U + :Plus potential (+ GMm ), U :Minus potential ( GMm ), U T :Total potential Focus on the numbe of tems of emaining potential enegy athe than the concete value of potential enegy, *Potential enegy between plus mass and plus mass has value:u = ( Gm +m + ) = 1U *Potential enegy between minus mass and plus mass has + value:u = ( G( m )m+ ) = 1U + *Potential enegy between minus mass and minus mass has value:u = ( G( m )( m ) ) = 1U (if, U + = U ) 1)When the numbe of minus mass is, and the numbe of plus mass is 1 U T = ( G( m )m+ ) + ( G( m )( m ) ) = U + + 1U = 1U + (85) )When the numbe of minus mass is 3, and the numbe of plus mass is 1 U T = 3U + + 3U = 0 (86) 3)When the numbe of minus mass is 4, and the numbe of plus mass is 1 U T = 4U + + 6U = U + (87) 4)When the numbe of minus mass is 4, and the numbe of plus mass is U T = 8U + + 7U = 1U + (88) Figue 16: Deceleation and acceleation of the univese Fig.16 shows cuent cosmic expansion. Cuently expansion velocity of ou univese was educed owing to attaction of matte, but it has inceased again fo last 7 billion yeas. Minus mass woked epulsion on plus mass give an effect of centipetal foce to plus mass in galaxy, and it plays a ole of dak enegy that expands plus mass on the whole of univese. Now this study ties to descibe cosmic deceleating and acceleating with minus mass that expands the univese. Fom [III-5. cosmic expands even if the size of minus mass is the same as that of plus mass] descibed peviously, the fact that potential enegy between two is not 0, even if the size of minus mass is the same as that of plus mass, and it suggests something to pay attention in teating minus mass. 5)When the numbe of minus mass is n, and the numbe of plus mass is n +, total potential enegy is given as follows. U T = (n n + )U + + ( n (n 1) U + n +(n + 1) U ) (89) equation (89) is expessed as follows moe stictly i=n,j=n + i,j=n U T = ( Gm im+j + ij ) + ( Gm im j ij ) i,j i,j=n + + i,j,i>j i,j,i>j ( Gm +im +j ++ij ) (90) U T = (n n + )( Gm m + + ) + ( n (n 1) ( Gm m ) (U + = ( Gm m+ + + n +(n + 1) ( Gm +m + )) (91) ++ ),U = ( Gm m ),U = ( Gm+m+ ++ ) 13

14 + :The mean distance between plus mass and minus mass, :The mean distance between minus mass and minus mass, ++ :The mean distance between plus mass and plus mass) Calculate the value of U = U +, n = 10, n + = 1 10 with equation (89) when thee is a diffeence in the numbe between minus mass and plus mass to examine changes, (n, n + ) (10, 1)U T = 10U U = 35U + (10, )U T = 0U U = 6U + (10, 3)U T = 30U U = 18U + (10, 4)U T = 40U U = 11U + (10, 5)U T = 50U U = 5U + (10, 6)U T = 60U U = 0 (10, 7)U T = 70U U = 4U + (10, 8)U T = 80U U = 7U + (10, 9)U T = 90U U = 9U + (10, 10)U T = 100U U = 10U + We can see the change in total potential enegy in accodance with the diffeence in the numbe of minus mass and plus mass fom 10 samples above. iv)the value of total potential enegy inceases as the numbe of plus mass appoaches to the numbe of minus mass. v)if the numbe of pai of minus mass and plus mass is n, n tems of positive potential emains as shown in equation (76)(U T =nu). Final state of univese. The analysis above can descibe that cuent univese expanded with deceleated speed appoximately 7 billion yeas ago, wheeas it expanded with acceleated speed in last 7 billion yeas [6], and most of negative enegy was conveted to minus mass owing to the chaacteistics of negative enegy and positive enegy pai-ceated at the beginning of univese, wheeas some positive enegy was exist as adiant enegy(pai annihilation of matte and antimatte, adiation) which does not have positive matte and mass, at this time, it expanded with deceleated speed because total potential enegy had minus value, then plus matte gadually inceased as the univese was cooled down and cuently it enteed in acceleating expansion which total potential enegy of univese has plus value afte passing though the point that total potential enegy of univese is zeo. 6)Calculation of basic aangement that thee ae two pais of minus mass and plus mass In basic aangement of Fig.9, calculate total potential enegy by setting m = km +, (k 1:the absolute value of minus mass is geate than that of plus mass) in equation (68), U T = 4 Gm +km + ( Gm +m + + Gk m + m + ) (9) Figue 17: Potential enegy fom atio of minus mass and plus mass - The tendency of total potential enegy in accodance with the numbe of minus mass and plus mass - i)in specific(o Citical) atio of the numbe of minus mass to the numbe of plus mass, the total potential enegy has 0. When the univese is flat.(ex. (n, n + ) = (10, 6)) Hee, we note that total potential enegy does not have 0 when geneal matte comes unde 60% of dak matte. 60% is the popotion by assuming that all tems of potential enegy ae identical, and pescibing that the numbe of n is 10. ii)if numbe of plus mass less than specific numbe, total potential enegy has minus value. Cosmic deceleating expansion iii)if numbe of plus mass ove than specific numbe, total potential enegy has plus value. Cosmic acceleating expansion If U T 0, = [4k ( 1 + k )]( Gm +m + ) (93) (k 4 k + 1) 0 (94) Thee ae thee easons that total potential enegy is geate than 0. Fist, thee ae 4 tems of plus potential, and tems of minus potential. Second, when k=1, total potential enegy is geate than 0 as shown in equation (70). And thid, cuently the univese has expanded with acceleated speed. Conside k > 1, (k ) 7 (95) 7 + k (96) 1 < k (97) 14

15 In m = km +, k= is the value of that total potential enegy U becomes zeo. Now accoding to the esult of obseving WMAP [8], dak matte has enegy as 5.1(±0.4) times as that of geneal matte, and this is simila to k that is geneated when total potential enegy of univese U=0. It is difficult to conside that the aangement(coespondence unifomly distibution) of Fig.9 descibes the state of univese exactly, but ou univese enteed in the peiod of acceleating expansion 7 billion yeas, and it is still nea citical density, so we can conside total potential enegy is close to 0, and suggest something with the fact that k, the popotion of minus mass to plus mass, is simila with the size of mass atio of dak matte to geneal matte. In III-1 above, it descibed that the quantity of minus mass decided at the beginning of univese can explain the effect of centipetal foce in galaxy(v-1), epulsion effect on cosmic expansion(iii-3,v-3), deceleating expansion at the fist half, and acceleating expansion(v-) of univese at the second half(7 billion yeas ago) at the same time. Theefoe, it is necessay to ty to calculate and obseve minus mass moe stictly, laying aside the abstact avesion of minus mass. 3.Dak matte and dak enegy come fom one oigin The hypothesis of dak matte and dak enegy with minus mass insists that dak matte is not diffeent fom dak enegy each othe, dak matte is the effect of centipetal foce by minus mass out of galaxy, and dak enegy is that plus potential tem in total potential enegy, and total potential enegy has plus value at now. so univese has acceleating expansion. Accodingly, if we calculate the distibution and mean density of minus mass that descibes otation velocity within galaxy, and explain acceleating expansion of cuent univese with the size of potential enegy that has positive value by this minus mass, we can pove the hypothesis that minus mass is the oigin of dak matte and dak enegy. It is necessay to conside the meaning of equation (65),(70),(75),(76) in this couse. - Minus mass has obseved, but it was tashed away - In 1998 yea, obsevation by HSS(The High-z Supenova Seach team) team and SCP team(supenova Cosmology Poject team), I have seen a calculation that if the cosmological constant is 0(It is that they got a minus mass density fom inspected field equation duing 70yeas.), Ω M = 0.38(±0.) [9] Howeve, HSS team and SCP team have asset that cosmological constant must be evival. Because Ω M must not be negative value in they thought. They did not know that minus mass is stable at the maximum point! In case of minus mass, gound state is a point that enegy is the highest. Accodingly, in the wold of minus mass, enegy level is filled fom the highest to the lowest, and stable state means the highest enegy state, so the catastophe to enegy level of minus infinity neve happens even if minus mass spontaneously emits enegy.( Refe to II-5) We must to know that not the equation has disposed the value, but ou thought disposed the value. In hypothesis with minus mass, E T = plus mass(4.6) + minus mass(x) + 0Λ(7.1) (minus mass > plus mass, cosmological constant Λ = 0) E T = plus mass( x ) + minus mass( y ) + U T If cosmological constant Λ=0 and mass density of univese is minus valueω M = 0.38, to get the age of the univese. Fom Fiedmann equation, t 0 = 1 H xdx ΩM x + Ω R + Ω Λ x 4 + Ω K x (98) Ω M = 0.38(±0.),Ω R h ,Ω Λ = 0 Use to Ω K = 1 Ω Λ Ω M =1.38, H 0 = 100h km/s/mpc, h=0.701 define to Ω K = a, Ω M = b, Ω R = c, t 0 = 1 H 0 1 t 0 = 0 xdx = 1 1 xdx ΩK x + Ω M x + Ω R H 0 ax + bx + c 1 H 0 [ ax + bx + c a [ ax ] 1 t 0 = 1 +bx+c H 0 a 0 b 1 a 0 0 dx ax + bx + c 1 [ b 1 ln( a ax H 0 a + bx + c + ax + b) a (99) ] (100) ] 1 0 (101) t 0 = 14.5Gy (10) This value is appoach to the t=13.73 Gy calculated in a WMAP.(+3.6% lage) Consideing the vey lage changes(λ=0 and Ω M = 0.38; Λ is a coefficient of x 4 ), it seems to incease existence pobability of minus mass. Additionally, if Ω M = Ω visible (4.6) + Ω dak ( 3.3) = 18.7, we get the t 0 =14.97 Gy 15

16 Univese age by othe method Radioactive decay method : Gy, HR diagam(hetzspung-russel diagam) : 13. Gy The aithmetic mean of two methods is So, it(14.5gy fom minus mass density) is in the ange estimated by othe obsevations. 4. Effect of concave gavitational lensing As obseved the effect of concave gavitational lensing mentioned in III-6. Effect of gavitational lensing, this can be the evidence fo the existence of minus mass. Figue 0: Contaction of plus mass 5.Desciption of fomation of void and galaxy If thee wee plus mass and minus mass at the beginning of univese, and thee was minute cave caused by pai annihilation of plus mass and minus mass, it could gow to the pesent scale though cosmic expansion. It is difficult to explain pesent lage-scale Void only with the unifom distibution of plus mass. Also, as consideed cosmic expansion velocity in the pocess of foming galaxy, it is difficult to fom galaxy stuctue with unifomly distibute plus mass. On the othe hand, fom the unifom distibution of minus mass and plus mass, we can explain the fomation of galaxy owing to the situation that natually beaks unifom distibution of mattes such as attaction effect between plus mass, epulsion effect between minus mass, attactive effect between massive plus mass and minus mass, and Void caused by pai annihilation. Figue 18: Pai ceation Figue 1: Stuctue of univese Making simulation model of the initial state of univese unde the assumption of unifom distibution of plus mass and minus mass, we can pove the fomation of cuent Void and galaxy stuctue and on the basis of this, we can pove the possibility of the existence of minus mass. 6. Fine tuning poblem and inflation mechanism Pai ceation of minus mass and plus mass seems to povide the pope explanation of homogeneity, local nonhomogeneity, and flatness of ou univese without sepaate assumption with basic chaacteistics of Newton dynamics. With efeence to the flatness of univese, the calculation of cosmic citical density with pevious plus mass leads to the poblem that pesent density should be close to citical density, the cosmic density at the beginning should be close to citical density, and initial condition should be set delicately. [3] Howeve, accoding to the hypothesis of minus mass, potential enegy of univese is not single potential when thee is only plus mass(potential that has both + and -), and the density of univese close to citical density was fom basic mechanism of pai ceation, namely 1:1 coespondence of minus mass to plus mass, and fom of potential enegy. Figue 19: Plus mass absence egion by pai annihilation o gavity effect If we ty to explain the stat and natual end of inflation with minus mass fo inflation mechanism, and 16

17 phase tansition which the gavity is sepaated was geneated at the beginning of univese when vacuum state was E T = (E ) + (E + ) = 0, the sepaation of gavity means the existence of mass, E = m c, E + = m + c so we can conside that both minus enegy and plus enegy wee conveted to mass. - Bigbang hypothesis - As seen in equation (76) and (V-.) above, total potential enegy has the biggest positive value when the numbe of plus mass is simila o equal to that of minus mass, if all enegy was conveted to mass when the gavity was bithed o sepaated, it can explain that thee was vey big plus potential value at that time, and it can explain the eason of the stat of Big Bang and inflation. E T = 0 = (+E) + ( E) = ( +m + c ) + ( m c ) + ( U) = 0 = E T Plus enegy and minus enegy simultaneously epeat pai ceation and pai annihilation micoscopically at the vacuum state. A moment, when the gavity was bithed o sepaated, enegy was changed to mass. At this time, total gavitational potential enegy has the biggest positive value(u T = nu + ). So univese is stated and expanded. this time, so hee also the tem of plus potential enegy by equation (76) nu + (if pai ceations ae 10 80, U T = U 0 suvives), and this can povide the stat powe of inflation. - Inflation finish - If plus mass is conveted to adiant enegy(pai annihilation of matte and antimatte, adiation) o enegy when stong inteaction(some mass changed to the bond enegy. Theefoe, plus mass defect has come.), weak inteaction, and electomagnetic foce ae sepaated afte the stat of inflation, the numbe of plus mass falls down below citical atio which total potential enegy is 0 in (V-.), so at this time, inflation also is natually finished. - Fine tuning poblem - Fo fine tuning poblem of mass density and cosmological constant, Univese mass density is same citical mass density, that is coespond with total potential enegy=0 define, x = n, y = n +, if U + = U = U ++ = U (103) I can t seek exactly solution fo total potential enegy equation. So I conside that these thee potential can be the same U, and I will seek to the whole tendency. Maybe, conside of unifomly distibution, it is nea to stable state when thee value of potential enegy ae almost in same level. equation(91) is U T = xy x + x y + y U (104) If x=y=n, U max = nu (105) If, x, y ; n h (t) = y x = n+ n Figue : Concept of Bigbang and Inflation Existence can be stated fom nothing. Also, equation means that ou univese can be stating at zeo enegy by physically. And it s means that ou univese must not be stating at specially enegy value. - Inflation stat - If we conside that inflation stated at the point of time that thee wee lage-scale pai ceations of minus mass and plus mass afte Big Bang, not at the point of time that the gavity was sepaated, the numbe of plus mass and minus mass might be bon togethe at U T = x [{1 + ( y x ) { y x + 1 x + y }]U (106) x U T x [{1 + ( y x ) { y x }]U (107) U T = x (1 y x ) U (108) U T = n (1 n h(t)) U (109) y n, at most the section, Total potential enegy is popotion squae tem of minus mass numbe(simila plus mass numbe) divide U max by equation(104), 17

18 Ratio of potential size U max U T = n = n (1 n h(t)) n (1 n h (t)) (110) n is total numbe of minus mass. If n is 10 80, we can know how the pesent potential values ae smalle than the maximum potential values of univese, how this pesent potential value is close to zeo. It is means that pesent dak enegy(cosmological constant) has a small plus value. Because that dak enegy is potential enegy of univese(in case of Expession by ΛCDM model, dak enegy is that plus potential tem in total potential enegy) and then total potential enegy has plus value at now. Othe pocess, total potential enegy tem by n geneal paticles, has a (n-1)! U. The othe side, Umax(Plus maximum potential enegy by minus mass and plus mass) has a nu. So, U lim max nu n U GP = lim n (n 1)!U = lim n n (n 1)! 0 U max is that the uppe limit of total potential enegy. Figue 3: Changes in univese s potential enegy ove time About the fine tuning of citical mass density in the ealy univese, even though the mass density of pesent univese is equally same with the value of citical mass density, when minus mass and plus mass coexist, it doesn t mean that the density of ealy univese must be vey close with the value of citical density. And also because minus and plus mass s ate is going close to 1, that pesent univese is almost at the same with citical density values. The mass density of univese close to citical mass density was fom basic mechanism of pai ceation, namely 1:1 coespondence of minus mass to plus mass, and fom of potential enegy. In fig., minus and plus mass ceated n pais, and in this peiod that potential enegy values in U max = nu. That cause acceleates expansion of univese(bigbang o Inflation). Stong inteaction, weak inteaction and electomagnetic foce ae sepaate(some mass change to the bond enegy) and also antimatte and matte geneate pai annihilation in duing inflation. So most of plus matte became adiation. Then total potential enegy become minus value(esult of V-, fig.17). Theefoe we call this time t if (inflation finish time) As the univese is getting coole, the adiation is getting lowe and that adiation changed the matte with plus mass. And afte values of plus mass became the citical atio of minus mass, that potential enegy becomes zeo. We call this time by t h. At this time, plus mass numbe is n + = n n (111) Accoding to hypothesis with minus mass, The last state of univese is when plus mass and minus mass almost the same and potential enegy has the value of U T = n(t)u(t) at this time. - Inflation Enegy and Cosmological Constant - This value is stong powe that can geneate inflation in ealy univese. But oll of this value is vey smalle than inflation peiod in the gowth univese(mean distance is vey bigge than initial mean distance 0 ) and because of ou univese have positive potential enegy, so its doing expansion now. It is vey impotant. Because that U T explain dak enegy that vey big plus value in ealy univese(inflation Enegy) and vey small plus value at now(cosmological Constant). Consideing of pai annihilation, potential enegy of univese can unde the zeo again. 7.Calculate to the dak enegy fom minus mass hypothesis In minus mass hypothesis, Dak enegy is coesponding to that plus potential tem in total potential enegy. In equation (91) E de = U de = (n n + )( Gm m + + ) (11) Fom analysis of V-, V-6, If U T > 0, n n +, Thus Define, n = n + = n = ( is about total poton numbe of ou univese), Obseved geneal matte density is about hydogen atom 1ea/5m 3, So, m + = m p, m = 5m +, m p =poton mass(1.67x10 7 kg), 18

19 + = (13.7Gy/)=6.85Gy= x10 5 m U de = (5n )( Gm p ) = 5n ( )( ) (113) 1J = 1kg(m/s) = ev U de = (5n ) ev = (5n ) GeV U de of paticle 1ea = U de /n U de total paticle = U de n = (5n) GeV ρ de = (U de/n) 5m 3 = (n) GeV m 3 (114) paticles (geneal matte and dak matte) contained in 5m 3, so multiply. Unit tansfomation by( 1GeV 1 = cm ) ρ de = (n) GeV cm 3 1cm = GeV 1 (115) = (n) GeV (10 14 GeV 1 ) 3 ρ de = GeV 4 (116) Obsevation value is ρ obs GeV 4 ρ de ρ obs (117) In QFT(Quantum Field Theoy), the enegy density of the vacuum is estimated as GeV 4, which is about odes of magnitude lage than the obsevation value GeV 4. Theefoe, You can see that minus mass hypothesis how to close to the fact and the univese. 8.Result of obseving WAMP Fom the esults of obseving WAMP at the beginning of univese, the existence of tempeatue deviation [8] has an influence on cosmic backgound adiation owing to non-unifomity of matte caused by the existence of minus mass, o the gavity that minus mass woks on time and space. Accodingly, if we ty to intepet the esult of obseving WMAP with minus mass, we can find the basis of minus mass. 9.Simulation of the aspect of colliding with Bullet Cluste 1)Plus mass, plus mass : attactive )Minus mass(dak matte), minus mass(dak matte) : epulsive 3)Massive plus mass, minus mass : attactive 4)Result : At least, fom 3 chaacteistics above, we can pedict that plus mass and plus mass ae aanged on the close side, and minus mass(dak matte) and minus mass(dak matte) ae aanged on the fa side. Figue 4: Collision of bullet cluste. We can see that geneal mattes(ed colo) ae close to each othe, and dak mattes(blue colo) ae on the fa side. Can we explain the phenomenon [5] that dak matte is aanged on the fa side and visible positive matte is aanged on the close side in Fig.4 with othe dak mattes? Minus mass shows the esult matched with the phenomena, and it means that it is necessay to pefom moe stict simulation with minus mass. 10.We must obseve the exteio of galaxy, not its inteio to obseve dak matte(minus mass) Most of obsevation equipments focus on the inteio including galaxy coe in exploing dak matte, but accoding to the hypothesis of minus mass, dak matte made up with minus mass exists out of galaxy, so we must obseve the exteio of galaxy to find the evidence of dak matte. 11. Investigation of minus mass in acceleato Thee is the possibility that minus mass is bon in acceleato, so it is necessay to conside minus mass with opening the possibility of minus mass while pefoming an expeiment with acceleato. VI. Conculsion If minus enegy and plus enegy wee bon togethe at the time of Big Bang, then minus enegy may ceate minus mass, and plus enegy may exist in the univese at the state of plus enegy such as plus mass, electomagnetic wave, etc. Newton s law of motion can explain that plus mass fomed massive plus mass stuctue such as planet o galaxy, minus mass was disappeaed when meeting plus mass nea massive plus mass stuctue at the peiod of galaxy fomation, but minus mass bon at the beginning of univese still exists out of galaxy, this minus mass can pefom a ole of centipetal foce that binding galaxy in galaxy cluste, o stas in individual 19