The Phantom Bounce: a New Oscillating Cosmology

JCAP03(2008)002 hysics $30.00 grows 8 ρ P − p< whkinney@buffalo.edu and 1 and stroparticle stroparticle A [email protected] , , Katherine Freese 1 2 astro-ph/0405353 An oscillating universe cycles through a series of expansions and trans-Planckian physics, cosmology of theories beyond the SM osmology and and osmology stacks.iop.org/JCAP/2008/i=03/a=002 [email protected] C Michigan Center for Theoretical Physics, Department of Physics, University of Department of Physics, University at Buffalo, SUNY, Buffalo, NY 14260, USA William H Kinney contractions. We propose a model in which ‘phantom’ energy with ArXiv ePrint: Abstract. Keywords: 1 2 doi:10.1088/1475-7516/2008/03/002 Matthew G Brown E-mail: Received 29 September 2007 Accepted 11 February 2008 Published 3 March 2008 Online at Michigan, Ann Arbor, MI 48109, USA rapidly and dominatesdensity the is late-time so expandingthe large phase. beginning that and The thebe the universe’s caused end effects by energy of of high eachthe energy quantum cosmology expansion modifications gravity non-singular. to (or the are contraction).universes The Friedmann is important equation, classic The resolved which black at bounce make due hole both to can overproduction their of destruction oscillating by the phantom energy. ournal of ournal

An IOP and SISSA journal 2008 IOP Publishing Ltd and SISSA 1475-7516/08/03002+ c 

cosmology The phantom bounce: a new oscillating J JCAP03(2008)002 2 2 3 5 7 7 7 (1) with Q ) calculations break stacks.iop.org/JCAP/2008/i=03/a=002 ] plays a crucial role. In addition, our The phantom bounce: a new oscillating cosmology 3 )[ ntracting phase so that the expanding phase might be explained we will call ‘turnaround’, and then begins the success of oscillating models. First, the ρ porate via Hawking radiation.) The second ished from other proposed cyclic universe − es its current expanding phase, the universe ]. The black holes, which cannot disappear due 4 p< 03 (2008) 002 ( . 1 − < Q /ρ Q p = Q w ] in that cosmological acceleration due to ‘phantom’ energy (i.e., dark energy 2 , 1 The idea of an oscillating universe was first proposed in the 1930’s by Tolman. Over Our scenario resolves these problems. Our resolution to the black hole overproduction Acknowledgments References Journal of Cosmology and Astroparticle Physics In this paper, weexpansions consider and a contractions. scenarioreaches After in a it which state finish the ofto universe maximum oscillates recollapse. expansion through which begin a Once series to it of expand. reaches its This smallest scenario extent is at distingu the ‘bounce’, it will once again 1. Introduction 2. The bouncing cosmology 3. Destruction of black holes 4. Discussion scenarios [ 1. Introduction Contents equation of state with a supernegative equation of state, formation of large scaleproblems structure during and the of contracting blackto phase holes Hawking [ during area the theorems,occupy expanding the phase grow entire leads ever horizon to larger volume during during the subsequent co cycles. Eventually, they the subsequent decades, two problems stymied problem is providedstructures towards the by end of aexplanation the universe’s for ‘phantom’ expanding the stage. component acceleration Phantom of energy, to a the proposed the universe, is universe, characterized by which a destroys component all work differs fromtime recent dimension proposals (though thescenarios). in proposed that mechanism for our the model bounce takes arises from place braneworld in 3 space and one down. (Only the smallest black holes can eva by invoking aremoves that closed possibility. universe, Forclosed the but universe observationally favored will the densityobservations. expand of recent forever. ‘dark evidence energy’, Thus, even for cyclic a cosmologies cosmological appeared acceleration to conflict with unsolved problem of oscillatingturnaround. models was The the lack turnaround of at a the mechanism for end the of bounce and JCAP03(2008)002 3 (2) ) ]. As an 9 , 8 as ]. In ‘big rip’ a 5 ]. The energy density ] scenario proposed by nding, it turns around 7 , 11 6 ]. This is currently a very 12 stacks.iop.org/JCAP/2008/i=03/a=002 The phantom bounce: a new oscillating cosmology nsible for the alternating expansion and oint has its smallest extent (smallest scale edmann equations to provide a mechanism depends on the scale factor e. The idea is economical in that it is the avity governs the behavior of the universe to be ‘The Big Bang’ really is the universe ism for a bounce and turnaround, and we Q urface situated in extra dimensions. Several on. Another example is the quantum bounce ities may cause the universe to bounce when ion: if it has been expa energy density becomes infinite. We therefore r that produces a bounce at the end of the w round at the end of the expanding phase. In 03 (2008) 002 ( ], which is complicated by a number of physical 2 . ]. Once the energy density of the universe reaches a critical ) Q 10 grows as the universe expands. Of course, we expect that an w Q ρ 3(1+ − ], which involves a negative brane tension and a timelike extra dimen- 1, a 8 − ∼ < Q ρ which operates at both bounce and turnaround. Q ], the rapidly accelerating expansion due to this growing phantom component w 6 In this paper we use modifications to the Fri The phantom energy density becomes infinite in finite time [ We emphasize that the two components we propose here work together: we use Journal of Cosmology and Astroparticle Physics Since the sum of thegeneral pressure and relativity energy is density violated; is yet negative,energy the recent dominant work can energy explores bound dominate such of becomes models the nevertheless. ever universe more Phantom of dominant today state, as and the the drive Hawking universe area the expands. theorems current fail, With acceleration. and such black an holes Then unusual can equation it disappear [ Hence, for epoch of quantum gravity setsarrive in at before the the peculiar notion that quantum gr same physics both at the beginninglargest and values at of the endenergy the of density scale the physics factor). expanding maywe universe play consider (i.e., Here on the at we both idea theit consider that smallest ends is and large an of small, energy the example and dens lifetime to of of turn the around an role when expanding that it universe: high is larg tears apart allthese bound black objects holes below.) including black holes. (We speculate about remnants of scenarios [ of any field described by equation of state scenarios for implementing a bounce have been proposed in the literature [ contraction of the universe.observable In universe particular, we is focus a on three-dimensional ‘braneworld’ scenarios s in which our for the bounce and the turnaround that are respo in loop quantum gravity [ addition, the bounceproposed and by turnaround Steinhardt are and both Turok nonsingular, [ unlike the cyclic scenario sion leading to a modified Friedmann equati a modified Friedmann equation as a mechan example, we focus onShtanov the and modification Sahni to [ the Randall–Sundrum [ value, cosmological evolution changes direct and begins to recontract. If it has been contracting, it bouncesadd and a begins phantom to componentcomponent, expand. to the the same universecontracting high to phase destroy energy also black behavio holes. produces a Due turna to the phantom In an oscillating cosmology, what we observe 2. The bouncing cosmology controversial topic. emerging from a bounce. The universe at this p singularities related to brane collisions near the bounce [ JCAP03(2008)002 . 4 Q (5) (3) (4) ) ), ). ρ 3 ( f = O(1), the universe z ), and starts to contract. As p )inequation( M , ρ 4 ( ) can be motivated in the context C a . 3 f 0 + 2 stacks.iop.org/JCAP/2008/i=03/a=002 corresponds to the metric signature of The phantom bounce: a new oscillating cosmology ρ ρ>  eaches a characteristic maximum density 2 ) 1. The energy density of this component s through the classic radiation dominated  w nditions on our brane, can give rise to an le universe is a three-dimensional surface 3 − 5 ] showed that Einstein’s equations in higher torn apart by the extremely rapid expansion ion become important at high densities, and π ure. A period of inflation may or may not M 4 < 13 3 Q (1 + 3  must be negative for the expansion to reverse. A w 03 (2008) 002 (  − a ) + 0, which results in a condition on ρ , ). Different values of energy/momentum in the extra ( ρ 3 )] f  ρ 2 a> ( 2 p f π − M 8 ) 3 − ρ ( ρ  [ is an integration constant) appears as a form of ‘dark radiation’ ) is positive. For a contracting universe to reverse and begin 2 p + ρf ρ ]. We will also assume that the bulk cosmological constant is set π ) ( 4 8 C M 8 3 f w 3 Λ = = ]is 2 2 14 , 3(1+ H H . In the context of extra dimensions, however, one can have a bounce at finite 13 a , 8 ) and largest energy density, somewhere near the Planck density. The universe a (which might be anywhere in the range from TeV to In particular, we focus on ‘braneworld’ motivated modifications to the Friedmann In the standard cosmology, there is no way to avoid a singularity for small radius or , the universe stops contracting, bounces, and once again expands. | | so that singularities are avoided. A nonsingular bounce is obtained if the Friedmann σ σ | | Journal of Cosmology and Astroparticle Physics be necessary to establish flatness and homogeneity. At a redshift and matter dominatedbackground, phases, and formation with of the large usual struct starts primordial to accelerate nucleosynthesis, dueWe microwave to take the a existence ‘phantom’ of component a with vacuum component or quintessence field factor then expands, its density decreases, and it goe provided by the phantom component.‘Big Bang’ Any again physics becomes relevantphase. at important the Modifications at high to the densities the highcause near Friedmann the densities equat the universe near to the turn around. end of The universe the r expanding grows rapidly asphase, the including universe galaxies expands. and black holes, Any are structures produced during the expanding 2 the extra dimension [ where the last term(that ( is constrained like ordinary radiation), and expanding again, we must have ¨ where the function it contracts, atin first importance), its energy butEventually density then it decreases it reaches (as the againbecome high the increases important. values phantom as at component Once matter which2 the decreases the and modifications energy radiation to density become Friedmann again dominant. equations reaches the same characteristic scale equation, whereobserver the [ modification to the Friedmann equation for the brane bound dimensions, together withequation Israel of boundary the co formdimensions of (the equation bulk) ( can be responsible for different of braneworld scenarios, where our observab embedded in extra dimensions. Reference [ Similarly, for an expandingmodified universe, Friedmann ¨ equation of the form of equation ( a equation is modified by the addition of a new negative term on the right hand side: scale factor JCAP03(2008)002 5 ]; 0, (6) (7) 10 , but p < ) M = .For | σ σ | 2 / ]hasshownthat 2 5 0) and turnaround ρ . Hence the relevant 3 riedmann equation [ )= ρ w> ( ρ, ;itisatthisscalethatthe | f ) σ w | dimension: models with more . In models motivated by the 1, Davies [ ), nd turnaround remain sensible. 1 ρ − =2 ( is negligible f )breaksdownindetail.However, 4 < ] described the dissolution of bound 6 TeV. 6 [ =3(1+ Q stacks.iop.org/JCAP/2008/i=03/a=002 The phantom bounce: a new oscillating cosmology timelike bounce w ρ ρ ) σ> apply here; e.g., the same modifications w et al verse are torn apart before they can create e source for a gravitational potential is the he standard classical F uld need to address these other issues to form o the Friedmann equation might work as well, =0at ] to motivate the choice of sign in the Friedmann (1 + 3 8 H 03 (2008) 002 ( − ) . ρ  ( is satisfied at both bounce ( | f 2 σ 2 | a ρ 2 − he most natural value of the brane tension is ) − ρ ρ , the validity of equation ( (  2 0 corresponds to an extra p ρf π ) M 8 ρ>σ w 3 < = 0 and thus the existence of a bounce a = 2 H 3(1+ H 1). On one end of the cycle it goes from contracting to expanding (this bounce − When are the black holes destroyed? We want to be certain that they are torn apart Alternatively, in loop quantum gravity, there is a quantum bounce that takes place at The expansion rate of the universe At scales above This fine-tuning is the usual cosmological constant problem, which is not addressed in this paper. w< before turnaround. In general relativity, th structures in the ‘bigholes rip’ formed towards in the anproblems end expanding during of phase contraction. a of the phantom uni dominated universe. Any black 3 so that the three-dimensional cosmological constant Λ Journal of Cosmology and Astroparticle Physics the theorem does not hold. Recently, Caldwell equation, but a more detailed treatment wo Planck densities in lieu of the singularity in t One way to obtain than one time coordinateand typically non-unitarity. suffer We use from the pathologies model such in [ as closeda timelike fully curves consistent picture. if one couples this quantumagain bounce with obtain a the phantom same component as oscillating in cosmology this as paper, one discussed would in this paper. correction to the Friedmann equation is the quadratic term, universe bounces and turns around. For this choice of we treat the problem generally for any value of the Friedmann equation becomes to gravity thatsingularities give in a the bounce black rather holes. than a Indeed, singularity when in the cosmology may avoid Black holes poseHawking a area theorems serious thatconstructed problem guarantee in the in continued special a existence settings standard of and black oscillating holes may universe. have not been However, the 3. Destruction of black holes as long as there is the requisite minus sign in the equation. In any case, weFriedmann equation. use Other this modifications braneworld t model merely as an example of a correction to the the approach to ( looks to us like the Bigto Bang), contracting. and then This at the behavior other end is of illustrated the cycle in it goes the from figure expanding and the required condition on ¨ Randall–Sundrum scenario, t JCAP03(2008)002 6 ∼ (9) (8) 6 p for the /M ,which ) 3 4 p M M GM 90 )8 − Q w =2 . However, for 10 solar mass black 4 3 to illustrate the p / R ∼ 6 4 M ρ − (1 + 3 = ρ = ) these will be shredded | 3) 9 σ w is pulled apart when | π/ (4 M , i.e. earlier. It is the smallest 3. Then 10 − ρ − = Q stacks.iop.org/JCAP/2008/i=03/a=002 The phantom bounce: a new oscillating cosmology w and mass ) and is large at turnaround due to phantom 4 . R | − e relics of larger black holes that Hawking Q a w ∝ 1 . We note that the energy density is large at the σ 03 (2008) 002 ( radn 1+3 ρ | = π 3 . The plots are presented for ρ | 32 M. Q 2 w ∼  1+ | p 3 ) during phantom domination and taking 3 Q R M a M ) Scale factor (left) and energy density (right) at the bounce and w . An object of radius p  ∝ p 4 p Q +3 ρ M +3 ρ , before turnaround if the brane tension (1 + 3 .Asanexample,wecantake ( ρ p ∼ | ρ π σ 3 M | 4 = 2 BH − Figure 1. turnaround, plotted asenergy functions density of show time. The dotted lines in the plot of the energy bounce due to radiation ( basic behavior of the model (detailed numbers are irrelevant). − ρ p =2 10 +3 ∼ ρ turn ρ <ρ We must ensure that the black holes are destroyed before turnaround, so that which happens when the energy density of the universe has climbed to a value BH black hole, we find that black holes are pulled apart when ρ More massive black holesblack are holes destroyed that at get lower shredded values of last. Writing Journal of Cosmology and Astroparticle Physics volume integral of holes, such as those at the centers of galaxies, get pulled apart when M, when easily satisfies theholes, above which condition. either Theradiated. formed primordially most Even these or tricky should ar case still would be be disrupted. Planck From mass equation ( black JCAP03(2008)002 . 7 ]. is p 15 M 5 M ). In 4 a ) =10 ∝ )where M Q 4 are disrupted. p ρ p /M M 3 5 ] ] 10 πM ≥ (25 SPIRES M SPIRES [ 1 without any pathologies. ∼ [ − τ ] 023509 031302 w< (Oxford: Oxford University Press) 68 92 stacks.iop.org/JCAP/2008/i=03/a=002 D SPIRES The phantom bounce: a new oscillating cosmology sec for a black hole with [ ) and phantom energy ( ] have investigated a cosmological model 4 turnaround, a symmetry which might be 27 − 18 a − evolution by redshifting entropy out of the nce dangerous structures may form during of fluctuations in the collapsing phase [ 10 ly periodic) cosmology within the context of ts exchange identity under a transformation tracting phase, there is no phantom energy to ∝ 126003 ing the phantom energy dominated epoch near ∼ Phys. Rev. 65 rad D 03 (2008) 002 ( ρ Phys. Rev. Lett. , only black holes with 3, although disfavored by observation, possesses an / 4 GUT 7 m − Phys. Rev. = = | Q σ | w Relativity, Thermodynamics and Cosmology ].) However, Parker and Raval [ 17 ], effectively exchanging bounce for 16 [ /a 1 Khoury J, Steinhardt P and Turok N, 2004 → [3] Carroll S M, Hoffman M and Trodden M, 2003 [2] Steinhardt P and Turok N, 2002 [1] Tolman R, 1934 Journal of Cosmology and Astroparticle Physics GUT scale brane tension intriguing duality between radiation ( wipe out whatever structureformation is in this formed. picture Inturnaround are this set or either sense, by dur the the initial quantum conditions for generation structure the contracting phase. At the end of the con Several additional areas also remainthose to modes be addressed. ofexpanding the First, as universe) density the are fluctuations universe instead is that contracting, growing. we usually He throw away as decaying (in an References We thank Backnowledge support Burrington, from J DOE(MCTP) Liu, as via well the R as Univ.of McNees, the this of Michigan work and Michigan. Center was WHK completed. M for thanks Theoretical Trodden the Physics for MCTP for conversations. hospitality while part We Acknowledgments exploited to achieve truly cyclic evolution. the black hole mass. This occurs in only Fortunately these black holes Hawking evaporate in a time Our proposal contains theby novel feature the that sameprice both of bounce modification including and to morerequires turnaround than are the a one produced Friedmann speculative braneworldphantom element: equation. energy. model the to modified Ina However, Friedmann fundamental many achieve, equation standpoint cases it andfor without a does example, the severe [ phantom pathologies so cosmology component such at is must as difficult an the be unstable to dominated vacuum implement (see, by from 4. Discussion We also speculatecontaining that the Planck singularity) may mass be remnant dark matter black candidates. holes that cannot disappear (still with zero cosmological constant,free but containing scalar the field vacuum energy of of low a simple mass, quantized and found that it has Black hole formationpossible could to create still athe kill ‘Phantom truly Bounce’ the cyclic scenario. (i.e. model.that The perfect it reason may for Second, be this possible is it to entropy is create production. quasi-cyclic not We speculate obvious that it is horizon during thethat period the of special accelerating case expansion. of Even more speculatively, we note this case, thea behaviors of these componen JCAP03(2008)002 8 ) ] ] ] ] ] ] SPIRES [ ed S Hawking and SPIRES ] SPIRES [ SPIRES [ [ gr-qc/0607039 ] ][ ] hep-ph/0311312 043509 ] ][ SPIRES [ 123513 68 071301 103519 ] SPIRES D SPIRES [ 65 91 [ 68 34 SPIRES [ D ] D SPIRES SPIRES [ [ 462 ] ] 269 SPIRES ] [ B ] 024011 ] 084003 hep-th/0401010 4245 565 SPIRES ] gr-qc/0402089 62 Phys. Rev. stacks.iop.org/JCAP/2008/i=03/a=002 [ 74 The phantom bounce: a new oscillating cosmology 043543 83 B SPIRES SPIRES D [ Phys. Rev. [ D Phys. Rev. SPIRES [ SPIRES 211301 70 [ ] SPIRES [ 3370 Phys. Rev. Lett. Preprint D 91 SPIRES Phys. Lett. [ Preprint 83 749 024014 1 ] 061301 ] 123508 297 023511 SPIRES ] 86 Phys. Rev. 68 Nucl. Phys. [ 92 Phys. Rev. 557 astro-ph/040551 03 (2008) 002 ( 67 49 61 D B D Phys. Rev. D Phys.Rev.Lett. SPIRES astro-ph/0404441 [ SPIRES 1583 [ SPIRES [ 16 23 Phys.Rev.Lett. Preprint A General Relativity: An Einstein Centenary Survey Phys.Rev.Lett. 173 545 Phys. Rev. Preprint 043511 Phys. Lett. Phys. Rev. Phys. Rev. B Phys. Rev. Lett. Phys. Rev. Lett. 526 68 gr-qc/0405055 B D um R, 1999 Phys. Lett. Preprint Mod. Phys. Lett. Ann. Poincare Phys. Theor. Phys. Lett. Phys. Rev. ll L and Sundr W Israel (Cambridge: Cambridge University Press) Csaki C, Graesser M,Cline Kolda J, C Grojean and C Terning and J, Servant 1999 G, 1999 Mersini L, 2001 Chimento L P and Lazkoz R, 2003 Lidsey J E, 2004 Chimento L P and Lazkoz R, 2004 Gordon C and Turok N, 2003 Flanagan E E, Tye S and Wasserman I, 2000 Martin J, Peter P, Pinto Neto N and Schwarz D J, 2002 Martin J and Peter P, 2004 Battefeld T J, Patil S P and Brandenberger R, 2004 Melchiorri A, Mersini L, Odman C J and Trodden M, 2003 Foffa S, 2003 Babichev E, Dokuchaev V and Eroshenko Y, 2004 [5] Davies P, 1988 [4] Dicke R and Peebles P J E, 1979 [7] Caldwell R, 2002 [9] Kanti P and Tamvakis K, 2003 [6] Caldwell R, Kamionkowski M and Weinberg N, 2003 [8] Shtanov Y and Sahni V, 2003 Journal of Cosmology and Astroparticle Physics [18] Parker L and Raval A, 2001 [17] Cline J M, Jeon S and Moore G D, 2004 [16] Dabrowski M P, Stachowiak T and Szydlowski M, 2003 [15] Allen L E and Wands D, 2004 [14] Binetruy P, Deffayet C and Langlois D, 2000 [11] Randa [12] Lyth D, 2002 [13] Chung D and Freese K, 2000 [10] Ashtekar A, Pawlowski T and Singh P, 2006