Solution of the Horizon and Flatness Problem in Cosmology without Inflation


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1 Solution of the Hoizon and Flatness Poblem in Cosmology without Inflation F. Wintebeg Deatment of Physis College of Siene 66 N. Viginia Steet Univesity of Nevada, Reno Reno, Nevada Offie: (77) Fax: (77)
2 Abstat: It is shown that the hyothesis of an inflationay univese to solve the hoizon and flatness oblem an be avoided by Loentzian elativity assuming the existene of a efeed efeene system at est with the zeo oint vauum enegy ut off at the Plank enegy. Unde this assumtion thee will be a fiewall at the event hoizon of an exanding univese whee all matte disintegates into adiation having eveywhee the Unuh blak body adiation temeatue. The elaement of the Einsteinian elativity by the Loentzian elativity to solve the oblem of quantum gavity was suggested to the autho by Heisenbeg.. Intodution The obseved unifomity of the osmi miowave bakgound adiation showing an almost efet dislay of Plank s adiation law has been a geat mystey, as was the obseved flatness of the univese obtained by the ounting of galaxies. Of muh less imotane is the absene of magneti monooles deending on unoven elementay atile hysis theoies. It was shown by Guth [] that all thee unsolved oblems ould be exlained by the extemely aid 0 78 fold (inflationay) exansion of the univese fom a small ausally onneted univese. Aat fom solving the hoizon oblem osed by the unifomity of the osmi bakgound adiation, the aid exansion would ion out small iegulaities exlaining the obseved flatness of the univese, whih is not a dimensional sae of onstant uvatue. And it would also exlain the absene of magneti monooles odued duing the big bang, simly by thei dilution to unobsevable levels. It is shown that with Loentzian elativity of the eeinstein theoy of elativity by Loentz and Poinaé the obseved mateial an be exlained without inflation as well. What has been alled Loentzian elativity efes to the eeinstein theoy of elativity by Loentz and Poinaé. It still assumed the existene of an ethe, found by Einstein suefluous with his ostulates. Howeve, though quantum mehanis and its zeo oint vauum enegy, a tansmogified ethe had to be eintodued into hysis. It is Loentzinvaiant fo enegies small omaed to the Plank enegy.. Einsteinian vesus Loentzian elativity While Loentzian elativity exlains the exeimental mateial as well as Einsteinian elativity, diffeenes between them show u at extemely high enegies. The inial diffeene between Einsteinian and Loentzian elativity is that the latte has a efeed efeene system. Though a efeed efeene system something absolute entes the theoy, absent in Einstein s seial theoy of elativity, and by imliation in his geneal theoy of elativity. This absolute element is the maximum absolute veloity against this efeed efeene system. In this That the zeo oint vauum enegy is a kind of an ethe was fist eognized by Nenst, and it an elae the ethe in the LoentzPoinaé eeinstein theoy of elativity.
3 efeed efeene system the maximum veloity is the veloity of light. In Einstein s theoy the onstany of the veloity of light in all inetial efeene systems is the esult of his lok synhonization onvention whih exludes the measuement of the oneway veloity of the light. Poinaé uses this onvention too, but beause he still assumes the existene of a efeed efeene system he must intodue an additional ostulate whih is that all objets suffe a tue ontation equal to 0 v / against the efeed efeene system. And Loentz, in his eleton theoy, finds a lausible exlanation fo this ontation effet to esult fom a flattening of the eletial otential sufaes by an eleton in an absolute motion against the ethe, whih is the same as the absolute motion against a efeed efeene system. Thee then, fo veloities lage than the veloity of light, an elliti diffeential equation fo the equiotential sufaes, esonsible fo the equilibium of matte, goes ove into a hyeboli diffeential equation whee no equilibium solutions ae ossible. A deision between the inteetation of Einstein and LoentzPoinaé ould be made at atile enegies aoahing the Plank enegy at 0 9 GeV. Comaed to the 0 GeV of the Lage Hadon Collide, this enegy is 6 odes of magnitude lage. It is theefoe out of eah fo atile aeleatos, but not fo blak holes. At the event hoizon of a blak hole, a atile would eah an infinite enegy in an infinite time. But if it only has to eah the Plank enegy, this time is finite and well within the time needed to obseve the deay of matte into adiation in aoahing an event hoizon.. The Minkowski SaeTime as a Consequene of Quantum Mehanis Aoding to quantum mehanis eah mode of the eletomagneti field with the fequeny has the zeo oint enegy 0 () Fom thee one obtains the fequeny setum f ( ) of the quantum mehanial zeo oint vauum enegy by multilying () with the volume element in fequeny sae With / k one has d : f ( )d onst d () f ( )d onst d () o in wave numbe sae k k, k, k, k, whee k i /,
4 f ( k) dk onst dk () whee dk dk, dk, dk, dk is the Loentz invaiant volume element in foudimensional momentum sae. It thus follows that () is Loentz invaiant. The imotane of this esult is that quantum theoy though its zeo oint vauum enegy geneates fom the thee dimensions of sae and one dimension of time the Minkowski saetime and by imliation the seial theoy of elativity. With the zeo oint enegy ut off at the Plank length the Plank enegy l G/ ~ 0 m, that is, at 9 E / G ~ 0 GeV, Loentz invaiane is violated, establishing a efeed efeene system in whih the zeo oint enegy is at est. The agument that the sae uvatue at the event hoizon is small and that fo this eason quantum gavity an thee be ignoed is not valid with the zeo oint vauum enegy ut off at the Plank enegy, beause at 0 9 GeV in the efeed efeene system, an elementay atile is subjet to the sae uvatue at the Plank length, whih by the quantum flutuations of the saetime an thee be lage. The saetime uvatue nea the Plank length equies a moe detailed analysis. The widely aeted assumtion that at the Plank length saetime is a kind of tubulent saetime foam [], is likely wong. As it was fist notied by Sakhaov [], this assumtion imlies a huge osmologial onstant about 0 odes of magnitude lage than what is obseved. Beause of it, Sakhaov oosed the hyothesis that the vauum of sae is ouied by an equal numbe of Plank mass atiles ( maximons ) and omensating ghost atiles, whih must be negative mass Plank mass atiles. A vauum filled with ositive Plank mass atiles only, would also be unstable []. Following Sakhaov s oosal, the autho has made the hyothesis that the vauum of sae is a kind of lasma made u of ositive and negative Plank mass atiles in equal numbes [], and it was shown by Redington [6], that suh a onfiguation leads to stable solutions of Einstein s gavitational field equations, desibing a liteal iling of saetime. This hyothesis also satisfies the aveage null enegy ondition of geneal elativity, with all atiles omosed of ositive and negative masses, with the gavitational field mass oviding thei obseved ositive mass [7,8].. Deivation of the de Sitte Sae fom Loentzian Relativity The obseved flatness of the univese an with easonable auay be desibed by setting [9], with the adial exansion veloity whee H / R is the Hubble onstant and R the wold adius. v H ( / R) ()
5 In Loentzian elativity ods suffe a tue length ontation and slowe going loks (ultimately made fom ods), a likewise tue time dilation. Theefoe, the tansfomation of the Minkowskian line element fo an obseve in an initial efeene system ds ' dt' d' (6) into a efeene system at est with the zeo oint vauum enegy whee d d' v / d' / R and dt dt' / v / dt' / / R hanges (6) into ds ( / R ) dt d / R (7) This is the line element of a de Sitte sae with an event hoizon at the wold adius R. The lage R exlains the flatness of the univese in Loentzian elativity.. Disintegation of Matte ossing the Event Hoizon in the Loentzian Inteetation Beause the zeo oint vauum enegy is ut off at the event hoizon, whee the Plank enegy fo an infalling elementay atile is eahed, Loentz invaiane is violated nea the event hoizon and matte an oss the event hoizon. Howeve, beause in the Loentzian inteetation matte is held in a stable equilibium by diffeential equations whih fo enegies below the Plank enegy ae elliti, but hyeboli fo enegies above the Plank enegy, whee no suh equilibium is ossible, matte disintegates in ossing the event hoizon. The tansition fom an elliti to a hyeboli diffeential equation in ossing the event hoizon an be exlained by a simle examle in eletostatis. In the Loentzian inteetation the eletostati otential in the efeed efeene system is given by d d d (8) Q dx dy dz whee Q is the distibution of eleti hages, but in a efeene system moving with the absolute veloity v in the xdietion against the efeed efeene system, it is given by v d d d (9) Q( ') dx dy dz Setting x' v / x, y' y, z' z, (9) beomes equal to (8). It emains an elliti diffeential equation only fo v, while fo v it beomes hyeboli.
6 6 Having eahed the event hoizon whee the Loenz invaiane is destoyed, matte is subjet to the EinsteinHof fition foe given by [0] f ( ) F onst f ( ) v (0) whee f ( ) is the setum of the adiation field ausing the fition foe and v the veloity of a atile moving though this field. One immediately sees that F 0, if f ( ) as it is given by (). But if it is ut off at the Plank fequeny f ( ) / 0 at the ut off fequeny. /, then one has F 0fo Alied to a Plank mass atile moving with the veloity v though zeo oint enegy field of the ositivenegative mass Plank mass lasma, the fition foe is then F m m () whee m and ae the Plank mass and length onneted by fo the aeleation (deeleation) at the ut off fequeny m /. Fom () one obtains a F m () Inseting this value of a into the exession fo the DaviesUnuh temeatue T u[,,] one finds that a () kt u kt u m () u to the fato / equal to the Plank temeatue at the Plank sale. This temeatue is univesal exlaining the unifomity of the osmi miowave bakgound adiation without the assumtion of inflation. The elaement of inflation with the blak body adiating event hoizon at the wold adius whee v seems to equie at least a small aeleation, whih in fat is obseved and
7 7 an be exessed by a small osmologial onstant. The obseved K blakbody miowave adiation is then simly the Doleshifted adiation emitted at the event hoizon. The oigin of a small ositive osmologial onstant an be exlained by a small exess of negative ove ositive masses in the system of all obseved galaxies inside the event hoizon of the wold adius R. The wold adius would thee be the Debye length of the onjetued ositivenegative mass Plank mass lasma [7]. Thee the eulsive negative masses would dive a gavitational exansion, as an attative ositive mass would dive a gavitational ollase. The obseved system of galaxies would just fill one Debye ell of a muh lage system of galaxies, o a metagalaxy, outside the wold adius of the obseved galaxies, with an equal numbe of them having a sulus in ositive o negative mass, with those having a ositive sulus ollasing, and those with a negative sulus exanding. 6. Disussion It is instutive to omae the osmologial event hoizon with the event hoizon of a blak hole. Fo both of them the veloity of light is eahed, and in both ases matte would disintegate. The fate of matte in aoahing the event hoizon of a blak hole has most eently attated geat inteest [], with the onlusion that these thee illas of hysis:. The geneal theoy of elativity;. Quantum mehanis; and. Quantum field theoy annot all be oet. Quantum theoy is a theoy fo all objets, with Einstein s theoy of gavitation, Maxwell s eletodynami field theoy, Boh s theoy of the atom, et al., diffeent objets, but all of them without exetion subjet to the laws of quantum mehanis. Fom this esetive quantum mehanis has eedene, and with it the quantum mehanial dotine of unitaity, violated in Hawking s blak hole theoy. It was fo this eason that the existene of a fiewall at the event hoizon was oosed by Almheii, Maolf, Polhinski, Stanfod and Sully [], exluding the fomation of a blak hole and theeby saving quantum mehanial unitaity. An exlanation how the fiewall an atually be fomed was not given. With the emission of adiation at the event hoizon it would have to involve quantum mehanis, but beause fo a lage blak hole the sae uvatue at the event hoizon is quite small, one might think that quantum gavity annot be the ause of it. Howeve, this ignoes the quantum mehanial zeo oint vauum enegy, leading to a efeed efeene system in whih this enegy is at est, and a violation of Loentz invaiane at the Plank length in the efeed efeene system. This makes it ossible fo matte to oss the event hoizon, whih in the Loentzian inteetation is a ossing fom a egion whee all matte is held in a stable equilibium by otentials deived fom an ellitial diffeential equation into a egion whee the oesonding equations ae hyeboli whee no suh equilibium solutions exist. This idea ovides a simle exlanation fo the obseved most oweful gamma ay busts [6], fo whih all othe oosed models fail. Suh an assumtion though invalidates the geneal theoy of elativity but only at extemely high enegies nea the Plank enegy. The intodution of a efeed efeene system intodues an absolute element, whih is the absolute veloity against this efeene system. It is against the siit of the geneal and seial theoy of elativity, but beoming imotant only nea an event
8 8 hoizon, be it the event hoizon of the exanding univese o of a blak hole. Aat fom these extavagant onditions, the geneal and seial theoy of elativity emain extemely good aoximations, inluding the enegies of ~0 GeV eahed at the Lage Hadon Collide, whih ae about 6 odes of magnitude smalle than the Plank enegy of 0 9 GeV. Conlusion It is shown that the unifomity of the osmi miowave bakgound adiation and with it the osmi hoizon oblem, does fo its solution not equie suh an extavagant assumtion as an inflationay exansion by 78 odes of magnitude. It athe has a muh moe simle exlanation by Loentzian elativity, unlike Einsteinian elativity still assuming a efeed efeene system, established by the zeo oint vauum enegy ut off at the Plank length. It is this ut off zeo oint vauum enegy whih elaes the ethe, disaded by Einstein. The oosal to elae the inflationay assumtion with something less extavagant is not the only one. A diffeent altenative oosed by Alfvén [7] was that the miowave bakgound adiation omes fom egions of the metagalaxy whee galaxies made of matte get in ontat with galaxies made of antimatte. The bounday between those neighboing galaxies would by the annihilation of matte with antimatte fom a eulsive Leidenfosteffettye laye, eventing the matte and antimatte galaxies fom mixing and mutually annihilating eah othe.
9 9 Refeenes. A. Guth, The Inflationay Univese: The Quest fo a New Theoy of Cosmi Oigins, Basi Books,.  (997).. J. A. Wheele, in Tois in Nonlinea Physis, Poeedings of the Physis Session Intenational Shool of Nonlinea Mathematis and Physis, Edited by N. J. Zabusky, Singe Velag, New Yok, 968,.69.. A. Sakhaov, Doklady Akademii Nauk SSSR, vol. 77, 777 (967).. I. A. Redmount and WaiMo Suen, Phys. Rev. 7, R 6 (99).. F. Wintebeg, Z. Natufosh. Physial Sienes a, (988). 6. N. Redington, axiv: gq/ F. Wintebeg, Z. Natufosh. 8a, (00). 8. F. Wintebeg, Phys. S. 8 (0) E.W. Kolb and M.S. Tune: The Ealy Univese, Addison Wesley, Redwood City, Califonia, 990,. 0. A. Einstein and L. Hof, Ann. Physik, 0 (90).. S.A. Fulling (97). Physial Review D 7 (0): 80.. P.C.W. Davies (97). Jounal of Physis A 8 (): W.G. Unuh (976). Physial Review D (): A. Almheii, D. Maolf, J. Polhinski, and J. Sully. JHEP 0 (0) 06.. A. Almheii, D. Maolf, J. Polhinski, D. Stanfod and J. Sully. JHEP 09 (0) F. Wintebeg, Z. Natufosh. 6a, 889 (00). 7. H. Alfvén, Astohysis and Sae Siene, 89, (96).
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