ompeing osmology Models. n enropy producion help flsify cyclic models of cosmology, or vrins long he lines discussed by Roger Penrose he IG conference in Penn Se, 7? A. Beckwih, F.Y. Li, N. Yng, J. Dicku, G. Sephenson 5, L. Glink 6, R. Bker 7 ) beckwih@uh.edu, hongquing Universiy deprmen of physics; Insiue of heoreicl Physics; Beckwih@iibep.org, Americn Insiue of Bemed Energy Propulsion ( ibep.org); Seculine onsuling, USA ) cqufngyuli@homil.com, hongquing Universiy deprmen of Physics, Insiue of heoreicl Physics ) cqunnyng@homil.com, hongquing Universiy deprmen of Physics, Universiy of exs Brownsville ) gry.sephenson@gmil.com, Seculine onsuling, USA 5) jondu@oponline.ne, Independen Science resercher, dvisory bord of Prespceime Journl 6) lglink@gmil.com, Seculine onsuling, USA 7) drroberbker@grvwve.com,grvwve LL nd rnsporion Science orporion, 8 uscny Avenue, Ply d Rey, A 99, USA Absrc: In he inugurl IG meeing, on Augus, 7 Penn Se, Roger Penrose[] gve presenion bou n lernive o cyclic cosmologicl models, which needs experimenl ess for flsifibiy. As discussed by Beckwih, in EJP [], Penrose brough up how De Alberin wve equion, s simplified in fl spce could led o rising vcuum nucleion field which would engender he pop up behvior s sough in mos emergen field models of grviy. he sclr field pop up wih cerin qulificions is no so srling in iself. Now for he rdicl exension Penrose brough o ber. Penrose ssered in his IG lecure h here ws good chnce h here ws no collpse in fuure evens, bu h mer would be evenully sucked up by millions of blck holes, creing clen up of mos inersellr mer. he issue o be brough up is how o come up wih mpping for re combinion of he blck hole colleced meril, for big bng. A opic which ws no solved by Penrose. We lso discuss crieri for firs order phse rnsiion which would be feed ino new universe, which wis experimenl confirmion. Inroducion Penrose ssered h he millions of blck holes would evenully undergo Hwking s evporion [], i.e. h in some fshion h here would be relese of he mer- energy For hose who wish o look i up, Hwking s evporion of blck holes, involves suble qunum rgumens nd ries o reconcile blck hole physics wih known hermodynmics.,eg. As n exmple he nd lw of Blck hole dynmics. rschen[] ses he bsic ssumpions involved, while Hwkings [] sed evporion s o wys which my ie in wih ypicl enropy / re clculions s given by Bernsein nd oher wriers. he esies concepul sring poin is o use he equivlence beween number of operions which Lloyd [5] used in his model, nd ol unis of enropy s he uhor referenced from rroll [6], nd oher heoriss. he key equion Seh Lloyd [5] wroe is s follows, ssuming low enropy vlue in he beginning 5 6 [# operions] / ~ Sol ~ k B ln () Seh Lloyd[5] is mking direc reference o linkge beween he number of operions qunum compuer model of how he Universe evolves is responsible for, in he onse of big bng picure, nd enropy. Needless o se hough, Eq () bove, nd he issue of if or no here is well defined hreshold bulk elecric nd mgneic chrge conribuion o energy. If here is, indeed n evporion effec of blck
hole physics, wh juncure does one hve collpse of hreshold effec for clculions bou he minimum enropy bsed upon blck hole models involving elecric nd mgneic chrges? Assuming hen, h he relevn Blck holes evpore, Penrose [] nex presened he quesion of n undeermined mpping of he evpored Hwking rdiion bck o he nexus poin for new big bng. he uhor, Beckwih, sked Penrose repeedly he IG bou he nure of he mpping of relesed Hwking rdiion bck o new big bng. Penrose hrew he quesion bck o Beckwih, s Beckwih s reserch problem, no his..assume, if one will h here re N number of universes under going Penrose syle expnsion nd hen blck hole clen up of mer- energy s hese N universes expnd. Ech universe conins roughly 88 enropy unis of compuionl informion s embedded in sy spirl 9 glxies. If ech spirl glxy hs n enropy reding of bou enropy unis, his leds o n over 88 hng of bou enropy unis, s opposed o n observble enropy unis for he universe s cn be ccessed by insrumenion. Which leds sking wh is he significnce of h enropy gp? Secondly, nd mos imporn o his discussion, here is srnge rcor suck up of bis of informion from ech of he N expnding universes, nd he Hwking rdiion is, wihin meg srucure mpped bck o he locus poin of noher sen of N big bngs vi ypicl phse spce srnge rcor dynmics. How o verify his wild supposiion experimenlly? See he conclusion of his ricle for Beckwih s guess s o wh o ry o do experimenlly o indirecly infer he exisence of his meg srucure nd of srnge rcor collpse of Hwkings rdiion bck o N locus poins for N number of big bngs. Wh is needed o be experimenlly flsified: relic grvion producion involves HFGWs, indiced by rpid drop off of grvion creion fer he onse of he big bng We should firs look he key ssumpion of he Ng [7],[8] pproch o enropy : he wvelengh of he pricles conribuing o enropy re ulr-long, i.e., here is n order of mgniude difference beween he cube of he wvelenghs of he pricles nd of he conining volume of spce, V, which is nlyzed o obin he enropy figure Ng [7],[8] uses o ge his infinie qunum sisics.he sme mehodology of compring he cube of wvelenghs wih he expeced spceime volume is used o ge Ng s [7,[8]infinie qunum sisics, ssuming h relic grvion producion involves HFGWs. hen one nlyzes enropy producion wh Ng did wih DM nd wvelenghs, nd he volume of spce V,. Bu insed of DM, his involves grvions, wih n ulr-shor wvelengh, necessiing smll volume of spce in he beginning of grvion producion. So he sme infinie qunum sisics procedure Ng used for DM cn be used for grvions, excep h he grvions re produced in he very beginning of he inflionry er. So he creion of grvions is enhnced in he beginning of cosmologicl nucleion by he requiremen of oneo-one relionship beween shorwve lenghs of HFGW nd smll spce ime volume for relic grvion creion.hen i s likely h he d ses observed in he Li-Bker deecor could indice rpid drop off of grvion creion fer he onse of he big bng. his should be invesiged by flsifible experimenl procedures. Predicion: relively nrrow rnge of GW frequencies for relic grvion producion Appendix exmines his ssumpion nd compres i direcly wih noher ssumpion mde by Giovnnini[9], which is reformuled o sser h if ll frequency rnges for GW rdiion were 9 permissible, one would see ol vlue of enropy of nerly. his is done while no ssuming s we did HFGW condiions. herefore, Giovnnini s (99) predicion s wrien up in 8 [9] is ssumed o be indefensible, nd h
relively nrrow rnge of GW frequencies for relic grvion producion is wh should be looked for vi eiher he Li-Bker HFGW deecor or by he sellie mission. Implicion: How n inflon could rise nd fll from herml inpus from prior universe Here re some ddiionl possible spinoffs of hese sors of ides, if hey re experimenlly verified. Appendix D bsed upon Beckwih s work, [9] shows o-he-poin presenion of how n inflon could rise nd fll from herml inpus from prior universe. hese re noes dped from presenion by Dr. Penrose regrding his lernives o ypicl cyclic-universe cosmologies []. We elbore upon Penrose s srling conclusions, bu his firs pr of his presenion is useful, since i fis very closely wih he uhor s mehodologies for herml inpus from prior universe. Are irregulriies in he MBR specr reled o enropy producion? If his cn be verified experimenlly, he bigges pyoff would be o ddress n issue h he uhor discussed wih Srkr of Oxford[]. Appendix A gives he bsic ide: re he irregulriies in he MBR specr, due o non-sndrd physics, which re n exension of he sndrd inflon model, used o jusify enropy producion? We hink h here is meri o his ide nd h i should be invesiged. A he minimum, undersnding enropy producion would llow us o nlyze if he srucure formion mehodology experimenlly presened by Ruu, e l. [] ies in wih models of enropy producion, nd if no, wh bou verifying he sndrd model for MBR producion, s G. Hingsw [] nd ohers promoe? Or wh if Srkr [] is righ? A summry of wh A.W. Beckwih [] hinks of hese issues my be found in presenion mde IDM 8 Srucure formion from enropy generion Sring wih wh Beckwih used in 8 [], nd lso in Renconres De Blois [] /' 5 [ ] / N S ~ k ln # operions N log logv log E ~ inf B ol Iniil cond () Aiding in he developmen of confirming/flsifying Eqn. () bove re srucure formion quesions h we leve s open quesions o be ddressed by he MBR/srophysics communiy: his would be ligned wih he quesion of how srucure formion could rise s resul of enropy generion. Srkr [] nd ohers, wih heir rce rck models of inflion, hve done useful pioneering work in defining coupled fields undergoing symmery breking h re coupled o he inflon. he uhor, A.W. Beckwih, hinks h such supposiions need experimenl verificion, nd h he boos of ol enropy by he relic grvion vlue given in ΔS grvion producion 5 in ime inervl could led o ddiionl insighs ino wheher or no Srkr [] (8) or Hingsw [] is righ bou he origins of irregulriies in he MBR specr. Srkr {} ses h he irregulriies mens physics beyond he sndrd cosmologicl model ssumed for WMAP, while Hingsw[] ses h he irregulriies re merely sisicl nomlies. How iniilly huge vcuum energy nd is rpid collpse in spce-ime o much smller cosmologicl consn vlue ids in he brekup nd reformulion of enropy producion???? he uhor, A.W. Beckwih, wishes o close wih wh will be fuure projecs o ddress some of he bove issues. As discussed wih chrkin,[5]bremen, Augus 9 h, 8, he uhor wishes o deermine if or no he dichoomy beween n iniilly huge vcuum energy, s specified bove in his mnuscrip, nd is rpid collpse in spce-ime o much smller cosmologicl consn vlue, ids in he brekup nd reformulion of enropy producion. he uhor s supposiion is h i is relevn o wo res. Firs, he
uhor ssume h here is brekup of he iniil insnon srucure from prior universe. Since he uhor lso views grvions s kink-nikink srucure, he supposiion is h iniilly, from prior o presen universe, here would be similr phenomenon: iniil lck of numericl densiy of grvions jus before second-order phse rnsiion, which is discussed in pr in Appendix. Secondly if, fer second-order phse rnsiion we see evidence of srophysicl d supporing he rebirh of boh enropy nd grvion producion, we should ke his hypohesis seriously. Should he cosmologicl consn/vcuum energy linkge be proved o be consisen wih he brekup nd hen reformulion of grvion producion in phse rnsiion, hen he uhor, A.W. Beckwih, hinks h reserchers could be on rck for new experimenlly flsifible crieri, o be developed for MBR physics. Finlly, Relic grvion produced enropy he onse of he big bng. Why sring enropy would be so smll while MBR enropy would be so lrge As closing remrk, Beckwih wishes o sugges soluion o Penrose s implied quesion bou enropy s rised in Edingborough, Scolnd [6] conference proceedings. Penrose lks bou he nd lw, nd is implied requiremens s o he smll iniil vlue of erly universe enropy, nd hen ses h grviionl enropy would no be so mjor, wheres MBR mer conribued enropy would be much lrger. Beckwih is convinced h relic grvion producion he onse of he big bng, i.e. before he 5 conribuion of enropy from mer iself would be necessry o boos enropy from is smll vlue he onse of he big bng, o much higher level, nd h enropy would be iniilly drmiclly boosed by h process. I.e. he uniformiy requiremen Penrose lks bou in srucure would be cully s of up o he Elecro wek rnsiion, nd fr fer he iniil onse of inflion iself. A new ide exending Penrose s suggesion of cyclic universes, blck hole evporion, nd he embedding srucure our universe is conined wihin Beckwih srongly suspecs h here re no fewer hn N ( lrge number) of universes under going Penrose infinie expnsion nd ll hese re conined wihin meg universe srucure. Furhermore, h ech of he N universes hs blck hole evporion commencing, wih he Hwking rdiion from decying blck holes. Ξ i i i N If ech of he N universes is definble by priion funcion, we cn cll { }, hen here exis n 7 informion minimum ensemble of mixed minimum informion roughly correled s bou i bis of informion per ech priion funcion in he se { } conserved beween se of priion funcions per ech universe i i N before Ξ, so minimum informion is 8 i i { } { Ξ } i i N i i N before fer Ξ () Ξ i i. i N However, h here is non uniqueness of informion pu ino ech priion funcion { } Furhermore h wihin he meg srucure, h Hwking rdiion from he blck holes is colled vi srnge rcor collecion in he meg universe srucure o form new big bng for ech of he N
Ξ i i i N universes s represened by { }. Verificion of his meg srucure compression nd expnsion of informion wih non unique venue of informion plced in ech of he N universes would srongly fvor Ergodic mixing remens of iniil vlues for ech of he N universes expnding from qusi singulriy beginning.if his ide is in ny wy confirmble, i would lend credence s o he formion of he drk flow hypohesis, nd of how nhrmonic perurbive conribuions o iniil inflionry expnsion my occur, wihin prilly rndom ergoic bckground. Beckwih clims h such process would inherenly fvor 7 he smll bis of informion per ech priion funcion represening he sr of expnsion of new universe. Hopefully, in doing so, one cn explin, evenully, he problems wih enropy modeling presened in Appendix below. his hs similriy wih consrucion done by Beckwih [8], nmely looking he following expression of energy flux being re formuled for ech universe. I.e. sr wih he Alcubierre s formlism bou energy flux, ssuming h here is solid ngle for energy disribuion Ω for he energy flux o rvel hrough. [8] de d r 6π ' = [ lim r ] Ψd dω () he expression Ψ is Weyl sclr which we will wrie in he form of Ψ i x x x [ h h h ] [ h h h ] = r r r r () Our ssumpions re simple, h if he energy flux expression is o be evlued properly, before he elecro x x wek phse rnsiion, h ime dependence of boh h nd h is miniscule nd h iniilly h h, so s o iniie re wrie of Eq. () bove s Ψ [ h ] ( i) r (5) he upsho, is h he iniil energy flux bou he inflionry regime would led o looking Ψ d ' [ r ] h ( n~ ) (6) his will led o n iniil energy flux he onse of inflion which will be presened s de d r = 6π [ n~ ] Ω r h (7) If we re lking bou n iniil energy flux, we hen cn pproxime he bove s E iniil flux Inpus ino boh he expression r h our conclusions. he derived vlue of r 6π r h [ n~ ] Ωeffecive, s well s Ω effecive will comprise he res of his documen, plus Ω effecive s well s Einiil flux will be ied ino wy o presen (8)
energy per grvion, s wy of obining n f. he n f vlue so obined, will be used o mke S ~ n. We sser h relionship, using Y. J. Ng s enropy [7,8] couning lgorihm of roughly enropy f in order o obin S enropy ~ n f from iniil grvion producion, s wy o qunify n f, h smll mss of he grvion cn be ssumed. How o ie in his energy expression, s given in Eq. (8) will be o look he formion of non rivil grviionl mesure which we cn se s new big bng for ech of he N universes s represened by [9] nd n( Ei ) he densiy of ses given energy E i for priion funcion defined by i N N Ei i de i i n Ei e ( ). (9) i i { Ξ } Ech of he erms N universes E i would be idenified wih Eq.(8) bove, wih he following ierion given, nmely for N N Ξ j= j jbeforenucleionregime Ξ vcuumnucleionrnfer i i fixed fernucleionregime () For N number of universes, wih ech Ξ for j = o N being he priion funcion j jbeforenucleionregime of ech universe jus before he blend ino he RHS of Eq. () bove for our presen universe. Also, ech of he independen universes given by Ξ would be consruced by he bsorion of j jbeforenucleionregime sy one million blck holes sucking in energy. I.e. in he end Ξ j jbeforenucleionregime Mx k = ~ Ξ k blck holes jhuniverse () One cn re Eq. () s de fco Ergoic mixing of prior universes o presen universe, wih he priion funcion of ech of he universes defined by Eq (9) bove. Filling in he impus ino Eq. (9) o Eq. () is wh will be done in he monhs ghed. r h will be he one o fill in, vi considering [] plus oher models. Doing so will begin o llow us o form more precise evluions of Eq. (9) o Eq. () For he ske of convenience, one cn wrie [, ] So, hen r h ~ k h () For our purposes, we shll cll E r ~ l iniil flux [ h ] [ n~ ] Ω effecive r ~ k () 6π cm, ~ sec, Ω effecive n effecive cross secionl re s o he emission of grvions, nd k defined s physicl wve vecor. L. rowell
sed h GW would undergo mssive red shifing []. Needless o se, he vlue of k o consider would be for he GHz bnd of GW [,] d ( k kgw ) >> () dη 9 Also, for he frequences of [,] Hz, hen h ~ h rms ~ (5) hen he numericl coun fcor cn eiher be of wo imes, eiher s bi coun, or jus s srigh For primordil blck hole. Nmely, if ne ccelerion is such h ccel = π B h s menioned by Verlinde [], [] s n Unruh resul, nd h he number of bis is * ΔS c (.66) g c nbi = (6) Δx π k B [ Δx l p ] π k B his Eq. (6) hs emperure dependence for informion bis, s opposed o [5] Should he Δx l p k [ g ~.66 ] n f c S ~ ~ (7) order of mgniude minimum grid size hold, hen conceivbly when ~ 9 GeV[] n Bi (.66) g [ Δx l ] p * c π k B / / l ~ [.66 g~ ] he siuion for which one hs [], [5] Δ x l wih l wheres n Bi if Δx l / l / >> l Here, we mke hs ssumpion h eiher ~n ~. n Bi or ~n ~ l ~ corresponds o n Bi (8) n Bi per uni volume of phse spce wih he emperure vrying from low vlue o up o Kelvin ( emperure scle). All hese scling prmeers would be plced in Eq. () bove, wih Eq. () hen pu in discreized version of Eq. (9), Eq. (), nd Eq. (). We shll nex lk bou if his nlysis of bis nd he like cn be reled o Sephn-Bolzmnn nd simir remens of qunum flucuions. Looking generl relion beween herml nd qunum flucuions in relivisic field heories From considering sclr field remen of energy densiy nd pressure for non inercing gses, nd hen rele he nlysis o how domin wll brek down would led o GW generion, we shll consider how GW my be inroduced in he presen universe. o begin wih, go o he [6, 7, 8] consrucion given in ble below which compres he vlues s given by ble Sefn Bolzmnn smir ε = π 5 π P = [ ] 5 L
p = π π [ ] 5 ε = 5 L he concep of qunum phse rnsiion involving he geomery of spil box of lengh L wih criicl emperure is sed s [6, 7, 8] by prmeers for qunum phse rdiion [9] Depending upon he geomery of L = (9) Qunum phse rnsiion, se by wih differen vlues of L Δx l / / l If one picks he vlue of corresponds o L Δx l / / l, where if / / Δ x l l wih l ~ l n Bi nd he vlue of n Bi corresponding o Δx l / l / >> l will hen ell us how he bsolue mgniude of energy densiy in smir ple remen of n iniil energy densiy would scle s n Bi. o ge o he ide, we would mke he nex ble, nmely L Δx ~ l n Bi [ Δx l ] when l ~ l ble L Δx >> l n Bi [ Δx >> l ] he number of bis goes highes when number of bis when L Δx >> l L Δx ~ l n Bi n Bi low. high, nd he lower he min poin is h hving high criicl emperure [ Δx l ] is no he sring heory picure, nd corresponds o more rdiionl picure of dimensionl universe. Hivng [ Δx >> l ] is nmore consisen wih regrds o sring heory nd is congruen wih [,,] L Δx >> l When he bis drop is when, i.e. he sring heory version minimum unceriny mens h one hs less number of pek bis, wheres L Δx ~ l mens much higher pek vlue of bis my be possible. his cn,be ied ino model of he universe where we ge mximum chnge in he flux of bis from so clled cold universe model. I.e. wh if here ws nerly zero degrees Kelvin sring poin for he increse in ermperure? Assessing wh would hppen in he brne heory cse would be, for GW equivlen o,
Figure, he mpliude nd frequency of he HFGWs expeced by he brne oscillion models in he submillimere-size exr dimensions. he figure is ken from [], where l is he curvure sclr of he bulk, d is he disnce beween he "visible" brne nd he "shdow" brne If one hs high frequency Grviionl wves, wih regrds o brne heory, hen his figure bove would hve o be reconciled o he vlue of Eq. (8) bove, wih, up o poin he iniil energy defined vi looking Fig. () bove, wih Eq. (8) se s proporionl o. Einiil Energy flux ~ hω () GrviyWve he iner relionship beween Eq. () nd n bsolue vlue of energy densiy for, sy relic pricles i.e. grvions s informion crriers ε π = 5 π [ L ] 5 () 5 π E [ ] his would hve o be esblished, i.e. how iniilenergyflux L = ε () he ide which we hve is h he deils of filling in he seps of Eq. () bove, nd reconciling i o Eq. () nd Eq. (8) will llow us o sr o esime he number of bis rnsferred from prior o he presen universe, in erms of when he precise vlue of L is obined, h we re looking poin where he qunum effecs, nd firs order phse rnsiion hve occurred.. hen, s n exmple, he precise vlue of ~ Δx being reched, vi build up of emperure, is defined by. phse rnsiion delineed L wih he rise of emperure going from low vlue up o reching [ Δx >> l ] We cn close wih his consrucion by sying h reching up o criicl emperure is phse rnsiion, wih subsequen decy of domin wll occurring ferwrds, in order o void he well
known dum h if domin wlls did no decy rpidly, h he MBR specrum would be drmiclly differen from wh is observed ody. [] onclusion, orgnizing inpus ino finding he mpping for Eq. (), from blck Holes Job one will be in deermining if ~n ~ n Bi or ~n ~ n Bi per uni volume of phse spce wih he emperure vrying from low vlue o up o Kelvin ( emperure scle). Once his would be esblished, hen coming up wih deils of Eq. () mpping would be fesible. he uhor views his s wy o esblish if here is n ergoic mixing proocol, of millions of blck holes from differen universes. he deils of his mpping, s specified s n invesigive proocol, where discreizion of Eq.(9) would be necessrily pr of he physics reserch work. Also, i would necessie mking linkge o wh Beckwih e l pu up s fr s numericl coun for mssive grvion couns in per uni phse spce volume of GW deecor which cn be wrien s [,5] J effecive ncoun mdgrvion () ~ 65 m grms As sed by Beckwih, in [5], DGrvion n, while coun is he number of grvions which my be in he deecor smple. Geing Eq. () srigh for deecor while undersnding he iner n relionship of coun o ~n ~ n Bi or ~n ~ n Bi per uni volume of phse spce iniilly is wh we should be doing.[6]. In ddiion, our ble resuls should be reconciled o Eq. ()., i.e. wh o do wih he mximum energy densiy. h will require lo of work. Noe h he iniil GW emerging from inflion would be defined by some equivlen srucure s defined in [7] wih regrds o n iner relionship beween enropy, bis of informion, nd inflon physics, deils which we expec would be seled if nd when GW sronomy becomes n iompericl science. Wh we would like o see, would be o ge he mppings described by Eq. () rigorously defined. Doing so would enble use o mke connecion wih wh ws done by Beckwih i.e. mking connecion beween Eq. () nd hen he increse in he degrees of freedom problem Beckwih wroe bou s follows. he formul E herml k B emperure ~ β is feed ino ω g provided h we pick ime ime, nd lso by seing up he E ~ herml k Bemperure β. In oher words, for relic GW/ grvion producion, opologicl rnsformion nd inerrelionship beween he componens ~ α nd Eherml k Bemperure ~ β in he iniil increse in he degrees of freedom problem denoed by [] ~ ~ x i = exp α x [ ] β i () Appendix A: Vriions in he MBR specr nd wh hey imply for enropy producion Our guess is s follows: he mer-energy flux implied by he exisence of wormhole ccouns for 7 perhps bis of informion. hese could be rnsferred vi wormhole soluion from prior universe
o our presen, nd here could be perhps 7 minus bis of informion emporrily suppressed during he iniil bozonificion phse of mer righ he onse of he big bng iself. hen we predic h here is drmic drop in he degrees of freedom during he beginning of he descen of emperure from bou Kelvin o les hree orders of mgniude less. he drop in degrees 5 of freedom hppens s we move ou in ime from n iniil red shif, z, o somehing lower, which is when he emperure drops from bou Kelvin o significnly lower vlue of [7] h H εv 8 Kelvin ~ Hwkings π k iniil B Which model we cn come up wih h does his is he one we need o follow, experimenlly. And i gives us hope of confirming wheher or no we cn evenully nlyze he growh of srucure in he iniil phses of qunum nucleion of emergen spce-ime. We lso need o consider he dum so referenced for he irregulriies of he cooling-down phse of inflion, s menioned by Skr [8] in n e mil o he uhor, Beckwih,. Qusi-DeSier spce-ime during inflion hs no "lumpiness" -- i is necessrily very smooh. Neverheless one cn genere srucure in he specrum of qunum flucuions origining from inflion by disurbing he slow-roll of he inflon -- in our model his hppens becuse oher fields o which he inflon couples hrough grviy undergo symmery breking phse rnsiions s he universe cools during inflion. he rce rck models, fer he inflon begins o decline, would be idel in obining he necessry couplings beween he inflon, nd fields which undergo symmery breking rnsformion. We will refer o his opic in fuure publicion. We cn mke few observions hough bou he ssumed coupling. Firs, here is quesion of wheher here is finie or infinie fifh dimension. Sring heoriss hve rgued for brne world wih wrped, infinie exr dimension, llowing for he inflon o decy ino he bulk so h fer inflion, he effecive drk energy disppers from our brne. his is chieved by shifing wy he decy producs ino he infiniy of he 5h dimension. Nice hypohesis, bu i presumes MB densiy perurbions could hve heir origin in he decy of MSSM fl direcion. I would reduce he dynmics of he inflon if here were seprion beween Dp brne nd Dp nibrne vi moduli rgumen. h if we do no hve n infinie fifh dimension? Wh if i is compced only? We hen hve o chnge our nlysis. Anoher hing. We plce limis on inflionry models; for exmple, minimlly coupled λ is disfvored more hn σ. Resul? Forge quric inflionry fields, s hs been shown by. Peiris, Hingshw e l. [9] We cn relisiclly hope h WMAP will be ble o prse hrough he rce rck models o disinguish beween he differen cndides. So fr, Firs-Yer Wilkinson Microwve Anisoropy Probe (WMAP) Observions: Implicions For Inflion is giving choic inflion run for is money. (A)
Figure by Srkr shows he gliches h need o be ddressed in order o mke MBR d se congruen wih n exension of he sndrd model of cosmology. Pssed o he uhor, Februry 8 [8, ], nd brough up in IDM 8 [] Appendix B: Formulion of crieri for second-order phse rnsiion he onse of nucleion of new universe Le us firs review orrieri s nd Mushunin s [] conribuion o sbiliy nlysis of wve funcionl remen of QD bulk viscosiy-over-enropy consn-rio se equion. he ide is h we hve iniilly super ho plsm reching pek vlue of viscosiy for given emperure, which is less hn or equl o criicl emperure, reflecing he QD plsm hving pek vlue for viscosiy. For hose who wish o undersnd how his my work ou, we cn refer o pper by Askw e l [6] which specified sheer bulk viscosiy pproximed by viscosiy vlue wih d f O(), which wekly depends upon he number of qurk flvors n f in he qurk-gluon plsm [ g ln ] η = g (B) d f Here, g is fixed by he number of degrees of freedom of he sysem. Askw e l.[] lso specify h in qurk-gluon plsm, frequenly here is n ddiionl nomlous conribuion o viscosiy, η A cused by urbulen fields wihin he qurk-gluon plsm. Askw e l. [] concluded in heir documen h frequenly we hve η (B) = ol = η η A
Frequenly we lso hve for exremely high emperures o good firs pproximion, s Densiy π g 5 = Where For high emperures, if g is he ne degrees of freedom of he plsm gs h we cn model s n ulr-relivisic fluid. g is on he order of, i.e., reflecing mny iniil degrees of freedom, [ ] η cons ~ π s Densiy ol (B) Wih clssicl fluid models, even for qurk-gluon plsms, his ssumes we re working wih η A s no very srong conribuing fcor o Eq (B), leding o lmos infinie viscosiy if we hve viscosiy lmos enirely dependen upon emperure, s he emperure climbs.. Wih he model of enropy so offered bove, we hve if he emperure is no eleved nd he wo erms in Eq. (B) conribue, rouble in obining sble vlue for Eq. (B) bove s consn. I so hppens h orrieri s nd Mushunin s [] ide is o incorpore modificion of he Bjorken equion for cosmology pplicions, τ [ τ s] d s = dτ Rτ where τ is conforml ime, nd R is he Reynolds number, nd s is enropy densiy. his Eq. (B5) is well bove he complexiy level of wh one expecs from he simple linerized models, where we look, sy, if y represens spce ime lengh, ec., wih s ( τ ) s ( τ ) δ s( y) exp[ iky] = (B6) τ, And velociy sbiliy nlysis we hve is v x / so h evenully we look x = δ s s nd x y y spce ime (B) (B5). So he x τ x A A A x x τ (B7) A his is when we hve high emperures mjor simplificion of he Aij erms in he mrix in he righ hnd side of Eq. (B7).his simplificion of he righ hnd side of Eq. (7) hppens when we wrie η nd s. We obin wih his simplificion of enropy nd viscosiy relively consn Reynolds number R, nd relively consn speed of sound in he viscous medi c s. he resuling simplificion nd drop ou of erms in he evoluion equion llows us o wrie [,] A = cs R (B8) nd A = k ( R ) (B9) nd A = kcs R /( R (B) ( ) )
nd A ( c ) c R c R ( R ) k R ]/( ) = [ s s s R (B) In his limi we hve sbiliy nlysis performed for he eigenvlues of A A (B) Where we re using (B) re such h, if A A A A, nd wih he summrized resuls h for { min,λ mx } A λ of Eq λ we lwys hve insbiliy (B) λ we lwys hve sbiliy (B) > min mx < λ <, λ, we some imes hve sbiliy, (B5) min mx > nd someimes we do no hve sbiliy. he forms of Eq (B) o Eq (B5) remin he sme, bu we sser h if we devie from sric dherence o η nd s due o mrked iniil condiions, i.e., unusul conribuions due o he nhrmonic conribuion o viscosiy η A we will hve incresingly involved crieri for forming he mrix for Eqn. (B) nd Eq. (B7) o Eqn. (). We re looking ino wh hese crieri should be for very unsble iniil GU crieri, wih he proviso h we re no ble o use simple linerizion in GU iniil condiions, bu h he rio of ηol s Densiy ~ [ π ] holds.[,]. Appendix : ompring implemenion of Jck Ng s Δ S ΔN for wvelenghs cubed, of he order of mgniude of n enropy genering volume of spce, wih Giovnnini s clculion of enropy for ll permissible rnges of frequencies. As sed bove, our implemenion of he Δ S ΔN rule for HFGW [7,8] ssumes we re ble o mke direc comprison beween he wvelengh of HFGWs nd he region of spce in which hey re evlued. his comprison yields n inerpreion of growh of enropy due o n infusion of vcuum energy he onse of inflion, which we hink needs o be flsified experimenlly. I.e., h in he 7 beginning of qunum nucleion, here were perhps bis of informion presen. h he producion of relic grvions in HFGW erly universe nucleion environmen perhps dded up o bis of informion in 5 seconds -- perhps closer o n order of mgniude of seconds in he boos effecs of enropy from informion rnsferred from prior universe o our presen universe. he nlysis for how his could hppen depends upon he verificion of supposiion h HFGWs hve wvelengh whose vlue cubed would be wihin n order of mgniude of he iniil volume of spce-ime in which he HFGW re nucleed in relic inflionry condiions. Sying his hough leds us o consider: do ll frequencies conribue o he generion of grviionl wves eqully? (his hs implicions for he generion of enropy, for resons we will ge o nex.) On he fce of i, his quesion is nonsense. LISA nd LIGO, wo very well engineered deecors, re superb deecors of low frequency grviionl wves, s ws given by he Amldi 5 meeing. In ddiion, he being is h llegedly h signl/noise issues will mke deecion of HFGWs, especilly from relic condiions, excepionlly difficul. he Li-Bker design effor, wih is emphsis on sic mgneic field h cn be impinged upon by HFGWs hs redy nswer o his lleged difficuly. However, he sheer number of conribuions o enropy if ll rnges of frequencies conribue o GW producion in he universe should be considered.[]
Forunely, here is clculion uhored by Giovnnini [9] nd ohers h does coun o enropy generion in ol from he enire specrum of GW genered, wih srling conclusion: h he presen high level of enropy ody cn be effecively genered by GW producion! his clculion reds s 8 follows. If we se V s he spce-ime volume, hen look v ~ Hz, nd v ( ) / ~ H M P ~ Hz s n upper bound, ssuming no relionship like he GW wvelengh cubed, s proporionl o erly universe volume, which leds o r( ν ) ln ngrvions, where n grvions refers o he number of produced grvions over very wide specrl rnge of frequencies. his ssumes h we re working wih S H M v gw = V r P ν P 9 87 88 ( ) v dv ( ) ( H M ) / ν () ΔN ~ his should be compred wih HFGW producion in relic condiions righ relichfgw fer he onse of nucleion of new universe. I.e. here is hve relic grviionl producion, s occurring fer he nd order iniil phse rnsiion referenced in Appendix B, for GU, wih informion/enropy 7 5 for universe which Dr. Smoo pegs s less hn or equl o informion / enropy 88 informion / enropy in our presen universe, which will be nd order phsernsiion explined more fully in fuure publicions. his should be compred wih he resul h Sen rroll [6] cme up wih: h for he universe s whole 88 S ol ~ () his Eq.() should be compred wih he even odder resul h he uhor discussed in quesion nd nswer period in he Bd Honnef perspecives in qunum grviy [] meeing, April 8 o reconcile Eq. () wih he odd predicion given in Eq. () nmely, s presened by rroll, [6] ΔS BlckHole 9 M ~ 6 M SolrMss S () I.e. he blck hole in he cener of our glxy my hve purporedly more enropy hn he enropy of he enire KNOWN universe. Our hierrchy of how o genere enropy from iniil condiions presen in he iniil cosmologicl evoluion is n emp o mke sense of he inheren weirdness presen in Eq. (), Eq. (), nd Eq. (). he hree equions ogeher do no fi s consisen whole. We sser h here is no wy h we cn meningfully jusify he conclusions of Eq. (). And while we view grvion producion s crucilly imporn for he rise in enropy, s oulined by Dr. Smoo [5], grvion producion is mos likely o be concenred s nrrow relic grvion producion s n onse o enropy generion. We hope h he ricles following his mnuscrip will enble us o hndle he frnkly physiclly bsurd implicions inheren in ll hree of he bsic equions wrien in his documen nd permi us o develop n experimenlly flsifible se of experimenl procedures o resonbly invesige enropy creion from firs principles.
Appendix D: Emergen inflon field due o herml inpu from prior universe (he D Albemberin operion in n equion of moion for emergen sclr fields) his ws presened he IUAA meeing in Indi by he uhor, Beckwih, in December 7[6] nd Beckwih [ ] We begin wih he D Alberin operor s pr of n equion of moion for n emergen sclr field. We refer o he Penrose poenil ( wih n iniil ssumpion of Euclidin fl spce for compuionl simpliciy) o ccoun for, in high emperure regime, n emergen non-zero vlue for he sclr field due o zero effecive mss high emperures. When he mss pproches fr lower vlues is when non-zero sclr field reppers. Le us now begin o model he Penrose quinessence sclr field evoluion equion. Look he fl spce version of he evoluion equion = V & & (D) In he Friedmn-Wlker meric, his uses he following s poenil sysem o work wih, nmely: ( ) ( ) ( ) () R ~ 6 ~ 6 ~ κ M M V (D) his ssumes ±, κ, nd curvure signure compible wih n open universe. h mens, = κ s possibiliies. So we will look he, = κ vlues, beginning wih () ( ) ( ) c e M c V r exp 6 ~ = = α κ α & & (D) We find he following bsic phenomen, nmely () ( ) ( ) 6 ~ ) ~ ( = ε κ α high M M c (D) () ( ) ( ) 6 ~ ) ~ ( = ε κ α Low M M c (D5)
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