New solution to the cosmological constant problem and cosmological model with superconductivity

Transcription

1 Alksandr V Bukalo DC 53:547:539:5454:530 w soluton to th osmologal onstant probl and osmologal modl wth suprondutty Th Cntr of hysal and Spa Rsarhs, IIS, Mlnkoa str,, K-050, 04050, kran -mal: bukalophyss@soonnfo Applaton of a quantum thory of suprondutty to th formaton of th prmary dark nrgy at th lank sal allows us to sol th osmologal onstant probl and to obtan th obsrd alu of th dark nrgy dnsty, orrspondng to LAK rsults It s offrd th nw modl of xponntal xpanson and th hot stag of th nrs It s followd that th modrn oluton of th unrs an b wd as a pross of phas transton, and th physal tm s an ndator of ths transton Kywords: dark nrgy thory, physs of th arly unrs, osmologal phas transtons, osmologal onstant, auum nrgy dnsty, osmology ACS numbrs: 90 k; x; 30Rd; 440- Introduton As t s known, th standard stmatons wthn th lmts of th quantum fld thory g alus of auum nrgy dnsty at ω k k + m, kmax m []: whr 5 / 3 4 kmax 4 4 πk kmax E GV 3 dk k m π π π 0 4 +, ( ) 6 6 E ( / πg ) s th lank nrgy Ths alu s n 0 0 tms mor than th obsrd on ( obs) ( 0 V) Ths s on of th most srous probls n physs, baus t s also rlatd to th natur of dark nrgy By ths tm th st of arants of th soluton of th probl of th osmologal onstant and nrgy of auum s offrd [ 4] Howr th maorty of suh solutons rqur th us of spf paramtrs, xot arants of th fld thory or modfaton of th grataton thory Thrfor thos drtons of th soluton of ths probl ha adantag, whh ar haratrzd by maxmum physal naturalnss and smplty It s possbl to rfr to suh drtons th attpts to sol th osmologal onstant probl by analogy to th suprondutty thory But wthn th lmts of suh approah usually th spal assumptons on gratatonal ntraton btwn prmary frmons, whh dfns alu of dark nrgy, ar mad n [3, 4] An approah offrd n ths artl dos not us suh addtonal hypothss, and th law of ntraton btwn prmary frmons follows from th thory and xprmntal data It n turn gs th alu of th osmologal onstant los to th obsrd on and xplans th natur of dark nrgy Thus t boms lar not only th mhansm of formaton of modrn alu of dark nrgy dnsty, but also arty of th probls rlatd to th thory of a Bg Bang and to th osmologal oluton of th nrs [5] ossbl strutur of spa-tm on lank sals and suprondutty sually t s supposd that th spa-tm on lank sals has a foamy strutur Howr, thr ar alulatons of ntratons on lank dstans whh show that domans, wth th masss los to lank mass, an form rgular struturs [6] Suh struturs an form a rgular rystal-lk 3 / latt wth th lls los to lank sals L ( G / ) As th domans ar th quas slfontand obts, thr fft mass s los to zro Thy also an ntrat among thsls by quadrupol gratatonal fors At suh dsrpton t s possbl to onsdr th spa-tm on lank sals as analogu of a sold body [6, 7] Collt xtatons n suh strutur play a rol of phonons, arsng n a rystal-lk latt wth th prod los to th lank ntral

2 Th alulaton of th ntropy of blak hols, n whh a mnmum possbl sz s th lank lngth, also ponts on th dsrtnss of spa at th lank sal In thory loop quantum graty spa s also onsdrd as a ntwork wth th lls of lank sz [] Lt s onsdr ntraton of suh strutur wth th prmary frmons (b-frmons), whh may b prmary xtatons of th latt Ths frmons an ntrrat wth th spatal latt and, undr rtan ondtons, an oupl by mans of phonon ntraton, t s smlar to Bardn-Coopr- Shrffr modl (BCS) [9] for ltrons wth th bos-ondnsat formaton Thus th maxmum osllaton frquny of latts, as an analogu of Dby frquny, s los to lank frquny ωd ω A numbr of authors alrady onsdrd BCS-modls for frmons, usng lank frquny as an analog Dby frquny [3, 4] Th marosopal quaton, whh dsrbs ntraton of frmons [0], looks lk: ζ( ψψ) ψ 0 () t m At th us of pulsng rprsntaton of ths quaton w fnd for Frm nrgy: E F pf / ( m) + ζ ψψ, whr p F s an mpuls of subfrmons by Frm surfa, p pf E EF + ζ( ψψ ψψ ) () m Rasng both sds of th squar, aragng and usng ( ) Ψ ψψ ψψ, w an mak th substtuton nar th Frm surfa ( p pf) / ( m) ( p pf), whr pf / m s a loty of subfrmons at ths surfa, and obtan [0] E E ± ( p p ) +ζ Ψ F F ψ s an nrgy gap, rlatd to fft of ouplng of frmons, whh sparats th bas and xtd stat [0] As t appars from thory BCS, thus 4 ωd 4 ωd 35kT B, (3) snh V M(0) whr V M(0) s a onstant of frmon-phonon ntratons, V s a potntal, M (0) s a dnsty of frmon stats on Frm s surfa, T s a rtal tpratur [] Thn, at whr M 4 Λ, 4M, (4) π / ( / G ) s lank mass 3 Dark nrgy and suprflud Frm gas W an gt th sam rsult as (4), onsdrng th ondnsaton of frmon gas wth a wak attraton btwn frmons, prodd that th mass of th frmons s los to lank, wthout th onpt of quas-rystalln latt Th ntal dnsty of th nrs s qual to lank on: 4 3M 3( ω) 0 (5) ( πl ) ( π) In that as th dark nrgy dnsty s dfnd by dnsty of nrgy gaps as bndng nrgs of frmon pars, whh form a ondnsat as th dffrn btwn th nrgy dnsts of th suprflud and normal omponnts aordng to th thory of suprflud frmon gas [5]: mpf mpfc ω ( s n ) 3 3 / / Λ, (6) 4π 4π C πg whr s onstant ntraton of frmons Th mnus sgn mans th nstablty of th normal stat of th frmon gas wth wak attraton btwn frmons [5] And th of dffrn ntrops s ngat [5]:

3 4mpFT T Ss Sn V 3 7 (3) T, (7) ζ whr V s a olum, at whn T T At, C π, C : π T T T 3, 063T 7 (3) T, () ζ T Λ 0 /4 and C πg / ( πt ) assumng that (370599) w obtan: / / Λ M / C, m M, p M π / and kg/m / 3 4 G ( ) t 56 G (0) π π π n xllnt agrnt wth th LAK data [6] Thus, th agrnt wth xprmntal data rqurs alu of offnt of ntratons : () Lt s not that s dfnd also by a rato of alu of a harg of a Dra magnt monopol to an ltral harg: g / But qualty and dos not man dntty an b a onstant for th othr, unobsrd forms of mattr, suh as mrror or n othr dmnsons * / Ths rsult naturally onfrms our pont of w on haratr of ntraton of frmons Thus, th mhansm of ondnsaton of prmary frmons has not th gratatonal natur, but s dfnd by spal ntraton Thrfor, th xstn of dark nrgy of th nrs s dfnd by phas hang pross ondnsaton of prmary frmons and formaton of a Bos ondnsat of ths pars 4 Dynams of th modrn auum dnsty Lt s onsdr th pross of formaton of th up-to-dat dark nrgy n th hot arly nrs As t s known from quantum ltrodynams, a alu of ltromagnt fn-strutur onstant s funton of four-mpuls Q : 3 m β Q ln, () π whr m s th mass of ltron, / s th fn-strutur onstant [] Thn th fft dark nrgy dnsty as dnsty of nrgy gaps wll mak: 4β 5 3 Q 3π 3 G m ond Ω, (3) ( π) whr Q s a 4-mpuls of quanta of radaton and substan n th arly nrs Th nrgy dnsty of a auum ondnsat s drn by th nrgy dnsty of radaton and substans Thus rahs a mnmum and boms a statonary alu at Q m 0 MV 5 For nrgs 0 ( µ ) ( µ ) b ln µ / µ / π, µ V, ( ) ( ) 4 ( p ) b ω µ π V 3 ( 0 ) µ π µ F (9)

4 Lt's onsdr now a quston on quantty of hang At th lank nrgs th alu for auum s and Q 0 0 For dfnton of th law of formaton If th nrs startd from lank dnsty th momnt of phas transton undr th law Thus th alu of an ltral harg qually prmary on: hang w wll onsdr som aspts of th nrs ~ M 4, t xtndd n a auum-lk stat tll Λ, (4) πg πgτ and th radus of th nrs at th momnt of transton from auum-lk stat n a hot stat was R R RT H CMBR / T t π, whr RH H s th up-to-dat Hubbl radus, T CMBR s th tpratur of rlt radaton (tpratur of osm mrowa bakground radaton) Thus τ plays a rol of paramtr of tm for phas transton Thus th alu ould hang from to 0 At th momnt of phas transton w an stmat th radus of th nrs R and, aordngly, alu at 3( 3 G t ) π (0 5 GV) 4 dpndng on alu of nrgy of a dark nrgy / / So, at E ( MΛ ) GV and kt B 0 6 GV th nrs radus s R sm at /65 * At E m GV and kt B GV th nrs radus s R H 9 sm at 73 At * 9 GV and Z 0 B E m 67 sm at 75 At * W ± kt GV th nrs radus s R E m 04 GV and kt B GV th nrs radus s R 49 sm at 77 Lt s not that th alu of ntal xponntal xpanson of th nrs orrsponds to that whh arss also n th nflaton thory Thrfor th suprondutng mhansm of th nrs's xpanson prods ausalty and homognty of th nrs Moror, whl n th nflatonary thory mantnan of th nrs homognty s a on-tm nt, n th suprondutng snaro xstn of a quantum auum ondnsat ontnuously prods homognty of th nrs It rsols th nros s paradox: R nros rpatdly undrlnd th lak of mhansm of syn of ltrowak phas transton n arous ponts of spa, whh ours muh mor aftr nflatonary dlatng [3] It mans that th brth of substan durng a Bg Bang s dfnd by prsn of spal dark nrgy tor bosons and, possbly, th Hggs fld Th nrgs of prospt usual X, Y- bosons wth E G orrspond to ths bosons Thrfor th hghr nrgs E 0 GV and 6 E r > 0 GV, sngly, ar not ralzd baus th nrs warmng up at transton from a auum stat to radaton-domnatng stat bgns wth E G At th sam tm thr s a possblty of nrs xpanson not from lank, but from bggr olum, for xampl from olum wth radus r πl / sm Suh olum orrsponds to th gratst possbl pakagng of th lank domans whh numbr s As far as th quantty of fundamntal partls n th nrs s los to ths numbr, t s obous that phonon osllatons of th latts, formd by domans of spatal quas-rystal, at phas transton ha srd as th aus of formaton of ths partls Lt s not that th prsn of a auum ondnsat wth (3 0 3 GV) 4 prods homognty of suh olum and thr s no nssty to ar of xstn of 0 9 ausally unrlatd lank olums: all of th pro to b

5 rlatd to a auum ohrnt frmons ondnsat It follows that th nrs brth ould our n stags: th frst was th formaton of quas-stabl auum-lk stat wth / r π l and th 37 sond was th xpanson of ths olum for t 0 n tms At xtror nrgy aton th auum-lk nrs ould bgn transton nto radaton-domnatd stat wth an nrgy lbraton E E It ausd th phas transton and th bgnnng of th hot nrs Thus, aordng to (3), a rorgansaton of strutur of auum happnd baus of hang At 0 a radus of auum uratur Λ boms los to R : H Z 0 Λ ~ R H at Q m At th sond snaro phas transton wth ondnsat formaton looks natural, baus th rtan alu of paramtr of ntraton alrady xst 5 hysal tm as phas hang funton thn If th dnsty of th ondnsat of nrgy gaps s los to th up-to-dat rtal dnsty 3 3 / πg t π πg 5 / / / H ( / ) H t π G πt с, From hr w an alulat a alu of ntraton onstant H 0, (5) As H t H yars th ln 37 πt (6) Thus th dynam paramtr, th Hubbl paramtr, s ry los to a alu of th onstant or s qual to t Suh xat ondn, apparntly, s rlatd to affnty of alus of dnsty of substan and auum n prsnt prod Wthn th lmts of suprondutng osmology th radus / Λ and th Hubbl radus ar / narly qual Th osmologal tm t s t th H πt (3 ΩΛ ) π t ow, at z 0, Thn t s possbl to prsnt th oluton of th rtal dnsty of th nrs nrgy also n th form of oluton: 3 3 Q πg t m ( πth ) H πg β 3π, (7) whr Q s a 4-mpuls of quanta of radaton and substan, whh ar so far unknown and, probably, rlatd to othr dmnsons Thus, urrnt osmologal tm t H and obsrabl oluton of th nrs an b dsrbd as pross of phas transton wth hang of paramtr of ntraton btwn frmons and phonons lnt, smlar to So a hrarhy of paramtrs of oluton or tms appars, t rlats to th hrarhy of th nrgs of th frmons ondnsats, ah of th plays a rol of auum for orlyng ll 6 Vauum nrgy dnsty Ourrn and dstruton of ondnsats n th hot nrs orrspond to th law (7) Thrfor usually alulatd auum of ltrowak ntratons and a QCD auum, whh aros durng phas transtons n th arly nrs [], ar dstnt from ral auum Thy, possbly, rprsnt fals auums n rlaton to th auum ondnsat, onsdrd abo Durng oolng of th hot nrs thy dsappar It s asy to undrstand f to tak nto onsdraton that th hypothtal auum should stop oluton at ll of nrgy dnsty of gluon ondnsat ~ (0 GV) 4 or π- msons (04 GV) 4 [] Ths alu s gratr than th modrn auum nrgy dnsty ( 0-3 эв) 4 to 44 ordrs, but thr ar no obsrabl phas transtons to th modrn auum dnsty

6 Howr th nrs oolng to th up-to-dat tpratur gs th han to dsplay th tru auum ondnsat It s thus obous that th arag dnsty of ral auum nrgy of othr flds of th obsrabl nrs dos not xd th nrgy of ths dark nrgy ondnsat Apparntly, th tru auum of flds both n hot and n th up-to-dat nrs onds f wth a dark nrgy olng ondnsat as th nfror nrgy ll 7 Th onluson Wthn th lmts of th thory of suprondutty th ral alu of dnsty of dark nrgy as dnsty of nrgy ntratons of a prmary frmons ondnsat s rd Ths frmons wth lank mass, apparntly, do not g a ontrbuton to obsrabl nrgy dnsty Th ontrbuton to obsrabl forms of nrgy s gn only by th ntraton nrgy of th prmary frmons Intal xponntal xpanson of th auum-lk nrs wthn th lmts of suprondutng osmology allows to prod th brth of th hot nrs and sols th sam probls whh ar sold by an nflatonary osmology Thus n th ntal nrs at last two omponnts xst: th frst omponnt s, probably, th suprondnsat, t braks up and gnrats th hot nrs wth tpratur T GV; th sond omponnt wth muh lowr nrgy plays a rol of dark nrgy for th hot nrs 3 Orgn of osmologal tm t th boms lar: n th obsrabl nrs tm s a onsqun of prodng phas transton of II knd, whh s smlar to th phas transton, whh has ratd th up-to-dat auum nrgy dnsty wth hang and fxng of a fn-strutur ln t / π t onstant ( H ( ) 4 Th losnss of th dnsts, M and (ondn probl) s du to th smlarty or dntty of th ntraton onstants: 5 Transton nto a suprondutng stat at T < T s aompand by ntropy rduton, baus ntropy of a suprondutng stat S S s lss than ntropy of a normal stat S : SS S < 0 It mans that durng th nrs xpanson pross both ntropy of a auum ondnsat S / t < 0 and ntropy of th nrs ( S / t < 0) at ts oolng dras It xplans th ( ) µ 0t formng of omplx struturs, nludng lng bngs, togthr wth obsrrs, durng th nrs oluton, ontrary to th thrmal dath onpt Ths dos not xlud that mor globally outsd of our nrs as an analogu of th suprondutor, whh s oold, th total ntropy nrass n aordan wth th II law of thrmodynams 6 If ourrn of th obsrr of trrstral typ s th ndator of th trmnaton of phas transton and th bgnnng of a nw stag of th nrs oluton, t xplans th aus of applablty of Anthrop prnpl: th dtrmnd phas transton of th nrs n a rtan stat gnrats th obsrabl nrs wth obsrrs [4] 7 Exstn of a ohrnt ondnsat of prmary frmons wth on wa funton ψ lmnats a probl of homognty of th nrs at all stags of ts oluton Thus, th ondnsats of prmary frmons formng dffrnt phass, dfnng th prmary nrs xpanson, dfn also modrn dynams of ts oluton Rfrns: Wnbrg S // Modhys 6 (99) Burdyuzha V arx: Alxandr S, Bswas T arx:hp-th/ Alxandr S hysltt B69, 53 (005) [arx:hp-th/050346] 5 Bukalo AV On th soluton of th osmologal onstant probl // ro Gamo onfrn, (Odssa), 0 6 Fomn I Zro osmologal onstant and lank sals phnomnology // ro of th Fourth Snar on Quantum Graty, May 5 9, Moskow / Ed by MAMarko Sngapor: World Sntf, Fomn I On th rystal-lk strutur of physal auum on lank dstans // robl phys knts and physs of sold body K: aukoa dumka, Smoln L An ntaton to loop quantum graty hp-th/04004 f

7 9 Bardn J, Coopr L, Shrffr J R hysr, 0, 75 (957) 0 Krzhnts A // Sohyssp, (97) Fynman R Statstal mhans A st of lturs Massahustts: W A Bnamn, In, 97 Klapdor-Klngrothaus HV und Zubr K Tlhnastrophysk Tubnr-Studnbühr: hysk Tubnr, Stuttgart, nros R Th Road to Ralty London: Jonathan CA, Bukalo AV // rogamo onfrn 00 5 task L, Lfshtz EM Statstal hyss, art : Thory of th Condnsd Stat Vol 9 (st d) Buttrworth-Hnann, 90 6 lank Collaboraton lank 03 rsults I Orw of produts and sntf rsults arx: [astro-phco] Bblography 6 rfrns