ENERGY CONTENT OF GRAVITATION AS A WAY TO QUANTIFY BOTH ENTROPY AND INFORMATION GENERATION IN THE EARLY UNIVERSE

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1 ENERGY CONTENT OF GRAVITATION AS A WAY TO QUANTIFY BOTH ENTROPY AND INFORMATION GENERATION IN THE EARLY UNIVERSE ANDREW WALCOTT BECKWITH beckwih@iibep,og,abeckwih@uh.edu Chongquing Univesiy depaen o physics; Insiue o Theoeical Physics o Chongquing Univesiy, Aeican Insiue o Beaed Enegy Populsion ( aibep.og) Based upon Alcubiee s oalis abou enegy lux o gaviaional waves, as well as Saunde s eaen o epeaue dependence o he Hubble paaee in he ealy univese, we iniiae a paicle coun eaen o gavions, and subsequen enopy geneaion which gives, via he sandad odel eaen o he FRW eic a way o explain/ jusiy a value o enopy o he ode 6 7 o a he vey onse o inlaion. S ~ 0 0 Inoducion The supposiion advanced in his aicle is ha elic enegy lux iniially is cenal o aking pedicions as o S enopy ~ n, whee n is a paicle coun pe phase space volue in he beginning o inlaion. The auho is awae o how any eseaches have linked elic GW as o iniial phase ansiions as o he eleco weak phase 6 7 ansiion, in cosology. The supposiion is ha S ~ 0 0 is deonsable as an iniial enopy / inoaion coun in he onse o inlaion i he Weyl scala is iniially ie independen.. Wha can be said abou gaviaional wave densiy value deecion? We begin wih a use o paicle coun n o a way o pesen iniial GW elic inlaion densiy using he deiniion given by Maggioe as a way o sae ha a paicle coun algoih is de igo expeienally. And ha he is place o sa would be in obaining a way o quaniy n geneaion in elic condiions, as a way o showing a linkage beween elic GW geneaion, enopy, and enegy lux values o he onse o inlaion. We begin wih Ω gw ρ gw ρ c n = khz = d(log ) Ω gw ( ) h0 Ω gw ( ) ()

2 whee n is he equency-based nueical coun o gavions pe uni phase space. While Maggioe s explanaion, and his eaen o gaviaional wave densiy is vey good, he poble we have is ha any elic condiions o GW involve sochasic back gound, and also ha any heoiss have ixaed upon eihe ubulence/ and o ohe os o plasa induced geneaion o shock waves, as saed by Duee and ohes looking a he eleco weak ansiion as a GW geneao. The enegy lux oalis o Alcubiee is a naual way o obain a cieia which we hink explains how ula low values o enopy, as given by Soo, and ohes in he Ecole Chalonge Pais colloquia 007, would aise in iniial inlaionay cosology. In doing so, we will expand upon a couning algoih o enopy as given by boh he auho and Y. J. Ng 5, which will, when cobined wih an expession o enegy caied pe gavion coplee ou analysis o he elaive ipoance o paicle couning, GW enegy, enegy pe gavion and he linkage o all hese acos o iniially low enopy. The auho suggess ha n ay also depend upon he ineacion o gavions wih neuinos in plasa duing ealy-univese nucleaion, as odeled by M. Maklund e al 6. Bu he ain dau o conside would be in analyzing an expession given by Alcubiee s oalis abou enegy lux, assuing ha hee is a solid angle o enegy disibuion Ω o he enegy lux o avel hough. de d 6π ' = [ li ] Ψd dω () The expession Ψ is a Weyl scala which we will wie in he o o Ψ i x x x [ h h h ] [ h h h ] = () Ou assupions ae siple, ha i he enegy lux expession is o be evaluaed popely, beoe he eleco weak phase ansiion, ha ie dependence o boh h and x x h is iniscule and ha iniially h h, so as o iniiae a e wie o Eq. () above as [ h ] ( i) Ψ (5) The upsho, is ha he iniial enegy lux abou he inlaionay egie would lead o looking a

3 Ψ d ' [ ] h ( n~ Planck ) (6) This will lead o an iniial enegy lux a he onse o inlaion which will be pesened as de d = 6π [ n~ ] Ω h Planck (7) I we ae alking abou an iniial enegy lux, we hen can appoxiae he above as Einiial lux h 6π Inpus ino boh he expession h docuen, plus ou conclusions. The deived value o [ n~ Planck ] Ωeecive (8), as well as Ω eecive will copise he es o his Ω eecive as well as Einiial lux will be ied ino a way o pesen enegy pe gavion, as a way o obaining n. The n value so obained, will be used o ake a elaionship, using Y. J. Ng s enopy 5 couning algoih o oughly S ~ n. We asse ha in ode o obain enopy S enopy ~ n o iniial gavion poducion, as a way o quaniy ass o he gavion can be assued. n, ha a sall. Does he gavion have sall ass iniially? Seeing violaion o he coespondence pinciple. And a aco eec o sall gavion ass. We begin ou inquiy by iniially looking a a odiicaion o wha was pesened by R. Maaens 7,8 65 n ( Gavion) 0 gas (9 ) = L n Noe ha Rubakov 9 wies KK gavion epesenaion as, ae using he ollowing dz noalizaion [ h ( z) h ( z) ] ( ~ ~ ) a( z) δ whee J, J, N, N ae dieen os o Bessel uncions, o obain he KK gavion/ DM candidae epesenaion along RS ds bane wold ( / k) N ([ / k] exp( k z) ) N ( / k) J ([ / k] exp( k z) ) [ J ( / k) ] [ N ( / k) ] J = (0) h ( z) / k

4 This Eq. (0) is o KK gavions having a TeV agniude ass M Z ~ k (i.e. o ass values a.5 TeV o above a TeV in value) on a negaive ension RS bane. Wha would be useul would be anaging o elae his KK gavion, which is oving wih a speed popoional o H wih egads o he negaive ension bane wih h h ( z 0 ) = cons as an iniial saing value o he KK gavion ass, k beoe he KK gavion, as a assive gavion oves wih velociy H along he RS ds bane. I so, and i h h ( z 0) = cons epesens an iniial sae, hen one k ay elae he ass o he KK gavion, oving a high speed, wih he iniial es ass o he gavion, which in ou space in a es ass coniguaion would have a ass 8 lowe in value, i.e. o gavion ( Di GR) ~ 0 ev, as opposed o M X ~ 9 M KK Gavion ~.5 0 ev. Whaeve he ange o he gavion ass, i ay be a way o ake sense o wha was pesened by Dubovsky e.al. 0 who ague o gavion ass 0 using CMBR easueens, o M KK Gavion ~ 0 ev Dubosky e. al. 0 esuls can be conlaed wih Alves e. al. 9 aguing ha non zeo gavion ass ay lead o an acceleaion o ou pesen univese, in a anne usually conlaed wih DE, i.e. hei gavion ass would be abou gavion ( Di GR) ~ 0 0 ev ~ 0 gas. Also Eq. () will be he saing poin used o a KK owe vesion o Eq. () below. So o Maaen s pape, ~ Λ κ ρ a a& = ρ a K () λ a Maaens 8 also gives a nd Fiedan equaion, as ~ Λ [ ] a K H& κ ρ = p ρ () λ a a Also, i we ae in he egie o which ρ P, o ed shi values z beween zeo o.0-.5 wih exac equaliy, ρ = P, o z beween zeo o.5. The ne eec will be o obain, due o Eq. (), and Eq. (), and use a [ a = ] ( z) Beckwih 7 0. As given by aa && q = a& ~ κ [ ρ / ] ( z) ( ρ λ) ()

5 5 Eq. () assues Λ = 0 = K, and he ne eec is o obain, a subsiue o DE, by pesening how gavions wih a sall ass done wih Λ 0, even i cuvaue K =0. The densiy uncion, ρ, assued is siila o wha was done by Alves, e al.. Consequences o sall gavion ass o eacceleaion o he univese Using Eq. () lead o he pedicion given in Fig () below 0.5 qz ( ) Fig. : Reacceleaion o he univese based on Beckwih 7 (noe ha q < 0 i z <.) Now ha his is pesened, we should conside wha he eecs o a sall gavion ass would be o iniial enopy/ inoaion couning a he onse o inlaion.. Exainaion o Weyl scala in he onse o inlaion, o obain enopy couning iniially?. Noe, o Valev, z gavion RELATIVISTIC λ gavion gavion <. 0 h h <.8 0 c ev / c 8 ees () This could be an aguen wih non zeo gavion ass wha o expec as a way o oulae ou n which would pei, i given a equency ange oe pecise ways o obain n, so as o ind a bee way o use Eq. () oe eecively. To sa his, look a seing, wih â a adiaion consan, and using a value given by Sande s wih an obsevaionally based Fiedan Equaion based value o 5

6 6 H iedan [( T ) c] πg ˆ N( T ) a ep ep (5) So, hen ha, i one uses N ( T ep ) ~ 0, as opposed o an uppe lii speciied by Kolb, e al o, a o ae eleco weak, N ( T ep ) ~ 0, ha hen h ( T ) H c x iedan ep ~ h ~ N( T ) ep π Planck Planck G aˆ (5) Fo he sake o inlaionay applicaions, we will assue ha πg aˆ N( T ep ) has no spaial dependence woh speaking o, which leads o, ( ) Tep c i consan o ode uniy. Also N ( T ep ) 0 0. Then one has Planck N( Tep ) Einiial lux ~ [ n~ Planck ] Ω 6 eecive (6) 6π Fo he sake o aguen, Beckwih used Ω eecive < π, and expeiened wih values o < 0 6, and also, o ~ n Planck sec, Einiial lux ~ 0 ev. I one uses he gavion ~ 0 gas, hen Beckwih obained n 0 o 0. This is assuing a vey high iniial equency o he elic paicles. We will in he nex secion coen upon. Conclusion. Exaining inoaion exchange beween dieen univeses? Beckwih 7 has concluded ha he only way o give an advanage o highe diensions as a as cosology would be o look a i a ih diension ay pesen a way o acual inoaion exchange o give he ollowing paaee inpu o a pio o a pesen univese, i.e. he ine sucue consan, as given by 7 ~ e λ α e h c (7) d hc 6

7 The wave lengh as ay be chosen o do such an inoaion exchange would be pa o a gavion as being pa o an inoaion couning algoih as can be pu below, naely: Ague ha when aking he log, ha he /N e dops ou. As used by Ng 5 Z N ( N! ) ( V ) N ~ λ (8) This, accoding o Ng, 5 leads o enopy o he liiing value o, i S ( log[ ]) = will be odiied by having he ollowing done, naely ae his use o quanu ininie saisics, as coened upon by Beckwih 7 ( log[ V ] 5/ ) N S N λ (9) Evenually, he auho hopes o pu on a sound oundaion wha Hoo is doing wih espec o Hoo deeinisic quanu echanics and equivalence classes ebedding quanu paicle sucues.. Fuheoe, aking a coun o gavions wih 7 S N ~ 0 gavions 7,, wih Seh Lloyd s 5 [# opeaions] / ~ I = Soal / k B ln = 0 7 (0) as iplying a leas one opeaion pe uni gavion, wih gavions being one uni o inoaion, pe poduced gavion 7. Noe,Soo gave iniial values o he opeaions as 0 [ ] ~ 0 # opeaions iniially () The aguen so pesened, gives a is ode appoxiaion as o how o obain Eq. () Reeences. M. Maggioe, Gaviaional Waves, Volue : Theoy and Expeien, Oxod Univ. Pess(008). R. Due, Massiiliano Rinaldi, Phys.Rev.D79:06507,009, hp://axiv.og/abs/ M. Alcubiee, Inoducion o Nueical elaiviy, Oxod Univesiy Pess, 008. G. Soo, hp://chalonge.obsp./pais07_soo.pd 5. Y. Ng, Enopy 008, 0(), -6; DOI: 0.90/e M. Maklund, G. Bodin, and P. Shukla, Phys. Sc. T8 0- (999). 7. A. Beckwih, hp://vixa.og/abs/09.00, v 6 (newes vesion). 8. R. Maaens, Bane-Wold Gaviy, hp:// (00).; R, Maaens Bane wold cosology, pp -7 o he coneence The physics o he Ealy Univese, edio Papanonopoulos, ( Lec. noes in phys., Vol 65, Spinge Velag, 005). 9. V. Rubakov,Classical Theoy o Gauge Fields, Pinceon Univesiy pess, S. Dubovsky, R. Flauge, A. Saobinsky, I. Tkachev,,epo UTTG-06-09, TCC-- 09, hp://axiv.og/abs/ E. Alves, O. Mianda. and J. de Aaujo, axiv: (July 009).. D. Valev, Aeospace Res. Bulg. :68-8, 008; ; hp://axiv.og/abs/hep-ph/ ; 7 Z N 7

8 8 hp://axiv.og/abs/ R. Sandes, Obsevaional Cosology, pp 05-7, in The Physics o he Ealy Univese, Lecue Noes in physics, 65, E. Papanonopoulou, Edio, Spinge Velag, 005. G. ' Hoo, hp://axiv.og/ps_cache/quan-ph/pd/0/0095v.pd (00); G. ' Hoo., in Beyond he Quanu, edied by Th. M. Nieuwenhuizen e al. (Wold Pess Scieniic 006), hp://axiv.og/ps_cache/quan-ph/pd/060/060008v.pd, (006). 5. S. Lloyd, Phys. Rev. Le. 88, 790 (00) 8

Fig. 1S. The antenna construction: (a) main geometrical parameters, (b) the wire support pillar and (c) the console link between wire and coaxial

Fig. 1S. The antenna construction: (a) main geometrical parameters, (b) the wire support pillar and (c) the console link between wire and coaxial a b c Fig. S. The anenna consucion: (a) ain geoeical paaees, (b) he wie suppo pilla and (c) he console link beween wie and coaial pobe. Fig. S. The anenna coss-secion in he y-z plane. Accoding o [], he