Non-singular Ekpyrotic/Cyclic model in Loop Quantum Cosmology
Thomas Cailleteau, Parampreet Singh, Kevin Vandersloot
备注：
24 pages, 11 figures. Additional numerical results discussed to show robustness of non-singular bounce of the scale factor and turn-around of the moduli field. References added. To appear in Physical Review D
We study the role of non-perturbative quantum gravity effects in the Ekpyrotic/Cyclic model using the effective framework of loop quantum cosmology in the presence of anisotropies. We show that quantum geometric modifications to the dynamical equations near the Planck scale as understood in the quantization of Bianchi-I spacetime in loop quantum cosmology lead to the resolution of classical singularity and result in a non-singular transition of the universe from the contracting to the expanding branch. In the Planck regime, the universe undergoes multiple small bounces and the anisotropic shear remains bounded throughout the evolution. A novel feature, which is absent for isotropic models, is a natural turn around of the moduli field from the negative region of the potential leading to a cyclic phenomena as envisioned in the original paradigm. Our work suggests that incorporation of quantum gravitational effects in the Ekpyrotic/Cyclic model may lead to a viable scenario without any violation of the null energy condition.
The no-boundary proposal provides a compelling theory for the initial conditions of our universe. We study the implications of such initial conditions for ekpyrotic and cyclic cosmologies. These cosmologies allow for the existence of a new type of "ekpyrotic instanton", which describes the creation of a universe in the ekpyrotic contraction phase. Remarkably, we find that the ekpyrotic attractor can explain how the universe became classical. In a cyclic context, in addition to the ekpyrotic instantons there exist de Sitter-like instantons describing the emergence of the universe in the dark en…
We consider the ekpyrotic paradigm in the context of loop quantum cosmology. In loop quantum cosmology the classical big-bang singularity is resolved due to quantum gravity effects, and so the contracting ekpyrotic branch of the universe and its later expanding phase are connected by a smooth bounce. Thus, it is possible to explicitly determine the evolution of scalar perturbations, from the contracting ekpyrotic phase through the bounce and to the post-bounce expanding epoch. The possibilities of having either one or two scalar fields have been suggested for the ekpyrotic universe, and both c…
We propose the reconstruction of $F(R)$ gravity in such a way that corresponding theory admits cyclic and ekpyrotic universe solutions. The number of explicit examples of such $F(R)$ model is found. The comparison with the reconstructed scalar-tensor theory is made. We also present $F(R)$ gravity which provides the little rip evolution and gives the realistic gravitational alternative for $Λ$CDM cosmology. The time for little rip dissolution of bound structures in such theory is estimated. We demonstrate that transformed little rip $F(R)$ solution becomes qualitatively different cosmological s…
Ekpyrotic instantons describe the emergence of classical contracting universes out of the no-boundary quantum state. However, up to now these instantons ended in a big crunch singularity. We remedy this by adding a higher-derivative term, allowing a ghost condensate to form. This causes a smooth, non-singular bounce from the contracting phase into an expanding, kinetic-dominated phase. Remarkably, and although there is a non-trivial evolution during the bounce, the wavefunction of the universe is "classical" in a WKB sense just as much after the bounce as before. These new non-singular instant…
Cosmological perturbation theory fails in the new ekpyrotic and cyclic ekpyrotic scenarios, before the scale factor of the Universe reaches zero. As a result, a recently-proposed recipe for evolving the curvature perturbation through the bounce in these scenarios cannot be justified.
We propose a mechanism borrowed from string theory which yields a non-singular transition from a phase of Ekpyrotic contraction to the expanding phase of Standard Big Bang cosmology. The same mechanism converts the initial vacuum spectrum of cosmological fluctuations before the bounce into a scale-invariant one, and also changes the spectrum of gravitational waves into an almost scale-invariant one. The scalar and tensor tilts are predicted to be the same, in contrast to the predictions from the "String Gas Cosmology" scenario. The amplitude of the gravitational wave spectrum depends on the ra…
Within the context of the Fermi-bounce curvaton mechanism, we analyze the one-loop radiative corrections to the four fermion interaction, generated by the non-dynamical torsion field in the Einstein-Cartan-Holst-Sciama-Kibble theory. We show that contributions that arise from the one-loop radiative corrections modify the energy-momentum tensor, {\it mimicking} an effective Ekpyrotic fluid contribution. For these reasons, we call this effect {\it quantum Ekpyrotic} mechanism. This leads to the dynamical washing out of anisotropic contributions to the energy-momentum tensor, without introducing …
Ekpyrotic and cyclic cosmologies provide theories of the very early and of the very late universe. In these models, the big bang is described as a collision of branes - and thus the big bang is not the beginning of time. Before the big bang, there is an ekpyrotic phase with equation of state w=P/rho >> 1 (where P is the average pressure and rho the average energy density) during which the universe slowly contracts. This phase resolves the standard cosmological puzzles and generates a nearly scale-invariant spectrum of cosmological perturbations containing a significant non-gaussian component. …
Quantum decoherence and the transition to semiclassical behavior during inflation has been extensively considered in the literature. In this paper, we use a simple model to analyze the same process in ekpyrosis. Our result is that the quantum to classical transition would not happen during an ekpyrotic phase even for superhorizon modes, and therefore the fluctuations cannot be interpreted as classical. This implies the prediction of scale-free power spectrum in ekpyrotic/cyclic universe model requires more inspection.
The alternative scalar field dark sector of the Universe: Cosmological inflation, quintessence and ekpyrotic model in the framework of scalar-tensor cosmology
In a recent paper we proposed a mechanism for a continuous transition between a contracting Ekpyrotic phase and the Standard Big Bang phase of expansion: the bounce is generated by an S-brane which represents the effects of higher mass string states in the low energy effective field theory. We showed that gravitational waves on cosmological scales obtain a nearly scale-invariant spectrum. Here, we study the cosmological fluctuations in this setup, assuming that the S-brane has zero shear. We find a nearly scale-invariant spectrum of cosmological perturbations with a slight red tilt. The scenar…
A union of matter bounce and Ekpyrotic scenarios is often studied in an attempt to combine the most promising features of these two models. Since non-perturbative quantum geometric effects in loop quantum cosmology (LQC) result in natural bouncing scenarios without any violation of energy conditions or fine tuning, an investigation of matter-Ekpyrotic bounce scenario is interesting to explore in this quantum gravitational setting. In this work, we explore this unified phenomenological model for a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe in LQC filled with dust and a s…
We show that the inclusion of simple anisotropic pressures stops the isotropic Friedmann universe being a stable attractor as an initial or final singularity is approached when pressures can exceed the energy density. This shows that the situation with isotropic pressures, studied earlier in the context of cyclic and ekpyrotic cosmologies, is not generic, and Kasner-like behaviour occurs when simple pressure anisotropies are present. We find all the asymptotic behaviours and determine the dynamics when the anisotropic principal pressures are proportional to the density. We expect distortions a…
I will discuss the development of inflationary theory and its present status, as well as some recent attempts to suggest an alternative to inflation. In particular, I will argue that the ekpyrotic scenario in its original form does not solve any of the major cosmological problems. Meanwhile, the cyclic scenario is not an alternative to inflation but rather a complicated version of inflationary theory. This scenario does not solve the flatness and entropy problems, and it suffers from the singularity problem. We describe many other problems that need to be resolved in order to realize a cyclic …
We will perform a detailed study of the matter-ekpyrotic bouncing scenario in Loop Quantum Cosmology using the methods of the dynamical systems theory. We will show that when the background is driven by a single scalar field, at very late times, in the contracting phase, all orbits depict a matter dominated Universe, which evolves to an ekpyrotic phase. After the bounce the Universe enters in the expanding phase, where the orbits leave the ekpyrotic regime going to a kination (also named deflationary) regime. Moreover, this scenario supports the production of heavy massive particles conformall…
We consider models of accelerating Universe elaborated for Finsler like gravity theories constructed on tangent bundles to Lorentz manifolds. In the osculating approximation, certain locally anisotropic configurations are similar to those for f(R) gravity. This allows us to generalize a proposal (by Nojiri, Odintsov and Saez-Gomez, arXiv: 1108.0767) in order to reconstruct and compare two classes of Einstein-Finsler gravity, EFG, and f(R) gravity theories using modern cosmological data and realistic physical scenarios. We conclude that EFG provides inflation, acceleration and little rip evolut…
In the recent past there have been many attempts to associate the generation of primordial magnetic seed fields with the inflationary era, but with limited success. We thus take a different approach by using a model for nonsingular bouncing cosmology. A coupling of the electromagnetic Lagrangian $F_{μν}F^{μν}$ with a non background scalar field has been considered for the breaking of conformal invariance. We have shown that non singular bouncing cosmology supports magnetogenesis evading the long standing back reaction and strong coupling problems which have plagued inflationary magnetogenesis.…
We investigate the bounce realization in the framework of DHOST cosmology, focusing on the relation with observables. We perform a detailed analysis of the scalar and tensor perturbations during the Ekpyrotic contraction phase, the bounce phase, and the fast-roll expansion phase, calculating the power spectra, the spectral indices, and the tensor to-scalar ratio. Furthermore, we study the initial conditions, incorporating perturbations generated by Ekpyrotic vacuum fluctuations, by matter vacuum fluctuations, and by thermal fluctuations. The scale invariance of the scalar power spectrum can be…
We investigate whether successful Gravitational Leptogenesis can take place during an Ekpyrotic contraction phase. Two possible paths by which this can occur are coupling the Ekpyrotic scalar to a gravitational Chern-Simons term, or to a $ U(1) $ gauge field Chern-Simons term. These couplings lead to the production of chiral gravitational waves, which generate a lepton number asymmetry through the gravitational-lepton number anomaly. This lepton asymmetry is subsequently reprocessed by equilibrium sphaleron processes to produce a baryon asymmetry. We find successful Gravitational Leptogenesis …
We present a nonsingular bouncing cosmology using single scalar field matter with non-trivial potential and non-standard kinetic term. The potential sources a dynamical attractor solution with Ekpyrotic contraction which washes out small amplitude anisotropies. At high energy densities the field evolves into a ghost condensate, leading to a nonsingular bounce. Following the bounce there is a smooth transition to standard expanding radiation and matter dominated phases. Using linear cosmological perturbation theory we track each Fourier mode of the curvature fluctuation throughout the entire co…
In this paper, we use a known duality between expanding and contracting cosmologies to construct a dual of the inflationary flow hierarchy applicable to contracting cosmologies such as Ekpyrotic and Cyclic models. We show that the inflationary flow equations are invariant under the duality and therefore apply equally well to inflation or to cyclic cosmology. We construct a self-consistent small-parameter approximation dual to the slow-roll approximation in inflation, and calculate the power spectrum of perturbations in this limit. We also recover the matter-dominated contracting solution of Wa…
Although inflation is a natural candidate to generate the lengths of coherence of magnetic fields needed to explain current observations, it needs to break conformal invariance of electromagnetism to obtain significant magnetic amplitudes. Of the simplest realizations are the kinetically-coupled theories $f^2(ϕ)F_{μν}F^{μν}$ (or $IFF$ theories). However, these are known to suffer from electric fields backreaction or the strong coupling problem. In this work we shall confirm that such class of theories are problematic to support magnetogenesis during inflationary cosmology. On the contrary, we …
Combining intervals of ekpyrotic (ultra-slow) contraction with a (non-singular) classical bounce naturally leads to a novel cyclic theory of the universe in which the Hubble parameter, energy density and temperature oscillate periodically, but the scale factor grows by an exponential factor from one cycle to the next. The resulting cosmology not only resolves the homogeneity, isotropy, flatness and monopole problems and generates a nearly scale invariant spectrum of density perturbations, but it also addresses a number of age-old cosmological issues that big bang inflationary cosmology does no…
The possibility to study the M/string theory cosmology via 5d bulk & brane action is investigated. The role of the 4-form field in the theory of BPS branes in 5d is clarified. We describe arguments suggesting that the effective 4d description of the universe in the ekpyrotic scenario (hep-th/0103239) should lead to contraction rather than expansion of the universe. To verify these arguments, we study the full 5d action prior to its integration over the 5th dimension. We show that if one adds the potential V(Y) to the action of the bulk brane, then the metric ansatz used in the ekpyrotic scenar…
In this article, we explore the homogeneous and isotropic flat Friedmann-Robertson-Walker (FRW) model in Chameleon cosmology. By considering a non-minimal coupling between the scalar field and matter, we present a non-singular bouncing cosmological scenario of the universe. The universe initially exhibits the ekpyrotic phase during the contracting era, undergoes a non-singular bounce, and then in expanding era, it smoothly transits to the decelerating era having matter and radiation dominated phases. Further, this decelerating era is smoothly connected to the late-time dark energy-dominated er…
It is shown how quantum fluctuations of the radiation during the contraction era of a CBE (Comes Back Empty) cyclic cosmology can provide density fluctuations which re-enter the horizon during the subsequent expansion era and at lowest order are scale invariant, in a Harrison-Zel'dovich-Peebles sense, as necessary to be consistent with observations of large scale structure.
We consider the cosmology obtained using scalar fields with a negative potential energy, such as employed to obtain an Ekpyrotic phase of contraction. Applying the covariant entropy bound to the tower of states dictated by the distance conjecture, we find that the relative slope of the potential $|V^{\prime}| / |V|$ is bounded from below by a constant of the order one in Planck units. This is consistent with the requirement to obtain slow Ekpyrotic contraction. We also derive a refined condition on the potential which holds near local minima of a negative potential.
We discuss a cyclic cosmology in which the visible universe, or introverse, is all that is accessible to an observer while the extroverse represents the total spacetime originating from the time when the dark energy began to dominate. It is argued that entanglement entropy of the introverse is the more appropriate quantity to render infinitely cyclic, rather than the entropy of the total universe. Since vanishing entanglement entropy implies disconnected spacetimes, at the turnaround when the introverse entropy is zero the disconnected extroverse can be jettisoned with impunity.
In Pre-Big-Bang and in Ekpyrotic Cosmology, perturbations on cosmological scales today are generated from quantum vacuum fluctuations during a phase when the Universe is contracting (viewed in the Einstein frame). The backgrounds studied to date do not yield a scale invariant spectrum of adiabatic fluctuations. Here, we present a new contracting background model (neither of Pre-Big-Bang nor of the Ekpyrotic form) involving a single scalar field coupled to gravity in which a scale-invariant spectrum of curvature fluctuations and gravitational waves results. The equation of state of this scalar …
In this article we review recent developments of cyclic cosmology. A typical non-singular cyclic model within General Relativity requires a non-conventional fluid with negative effective energy density, in order to cancel the matter component and lead to a non-singular bounce. However, the existence of such a non-conventional fluid usually leads to quantum instabilities and makes the theory ill-defined. In the present work we follow the alternative way, obtaining two scenarios of non-singular cyclic cosmological evolutions in the context of gravitational theories beyond General Relativity. The…
The holographic principle provides a deep insight into quantum gravity and resolves the fine-tuning crisis concerning the cosmological constant. Holographic dark energy introduces new ultra-violet (UV) and infra-red (IR) cutoffs into quantum gravity which are necessarily strongly related. The equation of state for dark energy $ω= p/ρ$ is discussed from the holographic point of view. The phantom option of $ω< -1$ is resurrected, as in an earlier cyclic cosmology. Such a cyclic model can, however, equally use the cosmological constant with $ω= -1$.
As is known, in modified cosmological theories of gravity many of the cosmologies which could not be generated by standard Einstein gravity, can be consistently described by $F(R)$ theories. Using known reconstruction techniques, we investigate which $F(R)$ theories can lead to a Hubble parameter describing two types of cosmological bounces, the superbounce model, related to supergravity and non-supersymmetric models of contracting ekpyrosis and also the Loop Quantum Cosmology modified ekpyrotic model. Since our method is an approximate method, we investigate the problem at large and small cur…
A non-singular bouncing cosmology is generically obtained in loop quantum cosmology due to non-perturbative quantum gravity effects. A similar picture can be achieved in standard general relativity in the presence of a scalar field with a non-standard kinetic term such that at high energy densities the field evolves into a ghost condensate and causes a non-singular bounce. During the bouncing phase, the perturbations can be stabilized by introducing a Horndeski operator. Taking the matter content to be a dust field and an ekpyrotic scalar field, we compare the dynamics in loop quantum cosmolog…
We investigate non-singular bounce and cyclic cosmological evolutions in a universe governed by the extended nonlinear massive gravity, in which the graviton mass is promoted to a scalar-field potential. The extra freedom of the theory can lead to certain energy conditions violations and drive cyclicity with two different mechanisms: either with a suitably chosen scalar-field potential under a given Stuckelberg-scalar function, or with a suitably chosen Stuckelberg-scalar function under a given scalar-field potential. Our analysis shows that extended nonlinear massive gravity can alter signifi…
We address how to construct an infinitely cyclic universe model. A major consideration is to make the entropy cyclic which requires the entropy to be reset to zero in each cycle expansion to turnaround, to contraction, to bounce, etc. Here we reset entropy at the turnaround by selecting the introverse (visible universe) from the extroverse which is generated by the accelerated expansion. In the model, the observed homogeneity is explained by the low entropy at the bounce, The observed flatness arises from the contraction together with the reduction in size between the expanding and contracting…
We investigate cyclic and singularity-free evolutions in a universe governed by Lagrange-multiplier modified gravity, either in scalar-field cosmology, as well as in $f(R)$ one. In the scalar case, cyclicity can be induced by a suitably reconstructed simple potential, and the matter content of the universe can be successfully incorporated. In the case of $f(R)$-gravity, cyclicity can be induced by a suitable reconstructed second function $f_2(R)$ of a very simple form, however the matter evolution cannot be analytically handled. Furthermore, we study the evolution of cosmological perturbations…
We investigate non-singular bounce realizations in the framework of ghost-free generalized Galileon cosmology, which furthermore can be free of the anisotropy problem. Considering an Ekpyrotic-like potential we can obtain a total Equation-of-State (EoS) larger than one in the contracting phase, which is necessary for the evolution to be stable against small anisotropic fluctuations. Since such a large EoS forbids the Galileon field to generate the desired form of perturbations, we additionally introduce the curvaton field which can in general produce the observed nearly scale-invariant spectru…
We study the bounce and cyclicity realization in the framework of new gravitational scalar-tensor theories. In these theories the Lagrangian contains the Ricci scalar and its first and second derivatives, in a specific combination that makes them free of ghosts, and transformed into the Einstein frame they are proved to be a subclass of bi-scalar extensions of general relativity. We present analytical expressions for the bounce requirements, and we examine the necessary qualitative behavior of the involved functions that can give rise to a given scale factor. Having in mind these qualitative f…
We investigate the bounce and cyclicity realization in the framework of weakly broken galileon theories. We study bouncing and cyclic solutions at the background level, reconstructing the potential and the galileon functions that can give rise to a given scale factor, and presenting analytical expressions for the bounce requirements. We proceed to a detailed investigation of the perturbations, which after crossing the bouncing point give rise to various observables, such as the scalar and tensor spectral indices and the tensor-to-scalar ratio. Although the scenario at hand shares the disadvant…
We use the phase plane analysis technique of Madsen and Ellis to consider a universe with a true cosmological constant as well as a cosmological "constant" that is decaying. Time symmetric dynamics for the inflationary era allows eternally bouncing models to occur. Allowing for scalar field dynamic evolution, we find that if dark energy decays in the future, chaotic cyclic universes exist provided the spatial curvature is positive. This is particularly interesting in light of current observations which do not yet rule out either closed universes or possible evolution of the cosmological consta…
We analytically and numerically show that through the cycles with nonsingular bounce the amplitude of curvature perturbation on large scale will be amplified and the power spectrum will be redden. In some sense, this amplification will eventually destroy the homogeneity of background, which will lead to the ultimate end of cycles of global universe. We argue that for the model with increasing cycles, it might be possible that a fissiparous multiverse will emerge after one or several cycles, in which the cycles will continue only at corresponding local regions.
Among all cosmological quantum-gravity or quantum-gravity-inspired scenarios, only very few predict a blue-tilted primordial tensor spectrum. We explore five of them and check whether they can generate a stochastic gravitational-wave background detectable by present and future interferometers: non-local quantum gravity, string-gas cosmology, new ekpyrotic scenario, Brandenberger-Ho non-commutative inflation and multi-fractional spacetimes. We show that non-local quantum gravity is unobservable, while all the other models can reach the strain sensitivity of DECIGO but not that of LIGO-Virgo-KAG…
The dynamical systems methods are used to study evolution of the polymerised scalar field cosmologies with the cosmological constant. We have found all evolutional paths admissible for all initial conditions on the two-dimensional phase space. We have shown that the cyclic solutions are generic. The exact solution for polymerised cosmology is also obtained. Two basic cases are investigated, the polymerised scalar field and the polymerised gravitational and scalar field part. In the former the division on the cyclic and non-cyclic behaviour is established following the sign of the cosmological …
We study the effects of noncommutativity, in the form of a Lie-algebraically deformed Poisson commutation relations, on the evolution of a Bianchi type I cosmological model with a positive cosmological constant. The phase space variables turn out to correspond to the scale factors of this model in $x$, $y$ and $z$ directions. According to the conditions that the structure constants (deformation parameters) should satisfy, we argue that there are two types of noncommutative phase space with Lie-algebraic structure. The exact classical solutions in commutative and type I noncommutative cases are…
Recent measurements at the LHC suggest that the current Higgs vacuum could be metastable with a modest barrier (height 10^{10-12}{GeV})^{4}) separating it from a ground state with negative vacuum density of order the Planck scale. We note that metastability is problematic for big bang to end one cycle, bounce, and begin the next. In this paper, motivated by the approximate scaling symmetry of the standard model of particle physics and the primordial large-scale structure of the universe, we use our recent formulation of the Weyl-invariant version of the standard model coupled to gravity to tra…
In this paper, we study the possibility of model building of cyclic universe with Quintom matter in the framework of Loop Quantum Cosmology. After a general demonstration, we provide two examples, one with double-fluid and another double-scalar field, to show how such a scenario is obtained. Analytical and numerical calculations are both presented in the paper.
Inspired by the Landau two-fluid model of superfluidity, we consider a similar multifluid description for cosmology where two normal fluids occur for matter and radiation respectively. For cyclic cosmology, two dark energy superfluid components turn out to be insufficient but three superfluids can lead to a sensible five-fluid model which in a certain limit becomes indistinguishable from the brane-world cyclic model proposed earlier (Baum and Frampton). Distinguishing more general five-fluid models from brane-world models for cyclic cosmology could be feasible with more accurate observational …
Infinitely cyclic cosmology is often frustrated by the black hole problem. It has been speculated that this obstacle in cyclic cosmology can be removed by taking into account a peculiar cyclic model derived from loop quantum cosmology or the braneworld scenario, in which phantom dark energy plays a crucial role. In this peculiar cyclic model, the mechanism of solving the black hole problem is through tearing up black holes by phantom. However, using the theory of fluid accretion onto black holes, we show in this paper that there exists another possibility: that black holes cannot be torn up by…
As quotient spaces, Minkowski and de Sitter are fundamental, non-gravitational spacetimes for the construction of physical theories. When general relativity is constructed on a de Sitter spacetime, the usual Riemannian structure is replaced by a more general structure called de Sitter-Cartan geometry. In the contraction limit of an infinite cosmological term, the de Sitter-Cartan spacetime reduces to a singular, flat, conformal invariant four-dimensional cone spacetime, in which our ordinary notions of time interval and space distance are absent. It is shown that such spacetime satisfies all p…
It is generally expected that in a non-singular cosmological model a cyclic evolution is straightforward to obtain on introduction of a suitable choice of a scalar field with a negative potential or a negative cosmological constant which causes a recollapse at some time in the evolution. We present a counter example to this conventional wisdom. Working in the realm of loop cosmological models with non-perturbative quantum gravity modifications we show that a modified version of standard loop quantum cosmology based on Thiemann's regularization of the Hamiltonian constraint while generically no…
