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. At the same time it produces small-amplitude gravitational waves with a blue spectrum. The dark energy dominating the present-day cosmological evolution is reinterpreted as a small attractive force between our brane and a parallel one. This force eventually induces a new ekpyrotic phase and a new brane collision, leading to the idea of a cyclic universe. This review discusses the detailed properties of these models, their embedding in M-theory and their viability, with an emphasis on open issues and observational signatures.
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.
It has recently been argued that bubble nucleation in ekpyrotic and cyclic cosmological scenarios can lead to unacceptable inhomogeneities unless certain constraints are satisfied. In this paper we show that this is not the case. We find that bubble nucleation is completely negligible in realistic models.
This is an introduction to the ekpyrotic scenario, with an emphasis on the two contexts of brane cosmology and primordial universe scenarios. A self-contained introduction to brane cosmology and a qualitative overview and comparison of the inflationary, pre-big bang and ekpyrotic scenarios are given as background. The ekpyrotic scenario is then presented in more detail, stressing various problems.
It has been pointed out by several groups that ekpyrotic and cyclic models generate significant non-gaussianity. In this paper, we present a physically intuitive, semi-analytic estimate of the bispectrum. We show that, in all such models, there is an intrinsic contribution to the non-gaussianity parameter f_{NL} that is determined by the geometric mean of the equation of state w_{ek} during the ekpyrotic phase and w_{c} during the phase that curvature perturbations are generated and whose value is O(100) or more times the intrinsic value predicted by simple slow-roll inflationary models, f_{NL…
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 …
New Ekpyrotic Cosmology is an alternative scenario of early universe cosmology in which the universe existed before the big bang. The simplest model relies on two scalar fields, whose entropy perturbation leads to a scale-invariant spectrum of density fluctuations. The ekpyrotic solution has a tachyonic instability along the entropy field direction which, a priori, appears to require fine-tuning of the initial conditions. In this paper, we show that these can be achieved naturally by adding a small positive mass term for the tachyonic field and coupling to light fermions. Then, for a wide rang…
In this paper, we present a new scenario of the early Universe that contains a pre big bang Ekpyrotic phase. By combining this with a ghost condensate, the theory explicitly violates the null energy condition without developing any ghost-like instabilities. Thus the contracting universe goes through a non-singular bounce and evolves smoothly into the expanding post big bang phase. The curvature perturbation acquires a scale-invariant spectrum well before the bounce in this scenario. It is sourced by the scale-invariant entropy perturbation engendered by two ekpyrotic scalar fields, a mechanism…
We present a simple, nearly model-independent estimate that yields the predictions of the simplest inflationary and ekpyrotic/cyclic models for the spectral tilt of the primordial density inhomogeneities. Remarkably, we find that the simplest models yield an identical result: n_s is approximately 0.95. For inflation, the same estimate predicts a ratio of tensor to scalar contributions to the low multipoles of the microwave background anisotropy of T/S=20%; the tensor contribution is negligible for ekpyrotic/cyclic models.
We analyze the non-gaussian density perturbations generated in ekpyrotic/cyclic models based on heterotic M-theory. In this picture, two scalar fields produce nearly scale-invariant entropic perturbations during an ekpyrotic phase that are converted into curvature modes {\it after the ekpyrotic phase is complete} and just before the big bang. Both intrinsic non-linearity in the entropy perturbation and the conversion process contribute to non-gaussianity. The range of the non-gaussianity parameter $f_{NL}$ depends on how gradual the conversion process is and the steepness of the scalar field p…
We analyze the evolution of cosmological perturbations in the cyclic model, paying particular attention to their behavior and interplay over multiple cycles. Our key results are: (1) galaxies and large scale structure present in one cycle are generated by the quantum fluctuations in the preceding cycle without interference from perturbations or structure generated in earlier cycles and without interfering with structure generated in later cycles; (2) the ekpyrotic phase, an epoch of gentle contraction with equation of state $w\gg 1$ preceding the hot big bang, makes the universe homogeneous, i…
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…
We analyze the general conditions on the equation of state $w$ required for quantum fluctuations of a scalar field to produce a scale-invariant spectrum of density perturbations, including models which (in the four dimensional effective description) bounce from a contracting to an expanding phase. We show that there are only two robust cases: $w\approx -1$ (inflation) and $w \gg 1$ (the ekpyrotic/cyclic scenario). All other cases, including the $w \approx 0$ case considered by some authors, require extreme fine-tuning of initial conditions and/or the effective potential. For the ekpyrotic/cycl…
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 …
We analyze a general mechanism for producing a nearly scale-invariant spectrum of cosmological curvature perturbations during a contracting phase preceding a big bang, that can be entirely described using 4d effective field theory. The mechanism, based on first producing entropic perturbations and then converting them to curvature perturbations, can be naturally incorporated in cyclic and ekpyrotic models in which the big bang is modelled as a brane collision, as well as other types of cosmological models with a pre-big bang phase. We show that the correct perturbation amplitude can be obtaine…
We respond to the criticisms by Kallosh, Kofman and Linde concerning our proposal of the ekpyrotic universe scenario. We point out a number of errors in their considerations and argue that, at this stage, the ekpyrotic model is a possible alternative to inflationary cosmology as a description of the very early universe.
We propose a cosmological scenario in which the hot big bang universe is produced by the collision of a brane in the bulk space with a bounding orbifold plane, beginning from an otherwise cold, vacuous, static universe. The model addresses the cosmological horizon, flatness and monopole problems and generates a nearly scale-invariant spectrum of density perturbations without invoking superluminal expansion (inflation). The scenario relies, instead, on physical phenomena that arise naturally in theories based on extra dimensions and branes. As an example, we present our scenario predominantly w…
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.
Inflation predicts a primordial gravitational wave spectrum that is slightly ``red,'' i.e., nearly scale-invariant with slowly increasing power at longer wavelengths. In this paper, we compute both the amplitude and spectral form of the primordial tensor spectrum predicted by cyclic/ekpyrotic models. The spectrum is blue and exponentially suppressed compared to inflation on long wavelengths. The strongest observational constraint emerges from the requirement that the energy density in gravitational waves should not exceed around 10 per cent of the energy density at the time of nucleosynthesis.
In cyclic universe models based on a single scalar field (e.g., the radion determining the distance between branes in M-theory), virtually the entire universe makes it through the ekpyrotic smoothing and flattening phase, bounces, and enters a new epoch of expansion and cooling. This stable evolution cannot occur, however, if scale-invariant curvature perturbations are produced by the entropic mechanism because it requires two scalar fields (e.g., the radion and the Calabi-Yau dilaton) evolving along an unstable classical trajectory. In fact, we show here that an overwhelming fraction of the u…
In this paper we construct an expanding phase with phantom matter, in which the scale factor expands very slowly but the Hubble parameter increases gradually, and assume that this expanding phase could be matched to our late observational cosmology by the proper mechanism. We obtain the nearly scale-invariant spectrum of adiabatic fluctuations in this scenario, different from the simplest inflation and usual ekpyrotic/cyclic scenario, the tilt of nearly scale-invariant spectrum in this scenario is blue. Although there exists an uncertainty surrounding the way in which the perturbations propaga…
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…
In this paper we establish dualities between inflationary, cyclic/ekpyrotic, and phantom cosmologies within the patch formalism approximating high-energy effects in scenarios with extra dimensions. The exact dualities relating the four-dimensional spectra are broken in favour of their braneworld counterparts; the dual solutions display new interesting features because of the modification of the effective Friedmann equation on the brane. We then address some qualitative issues about phantomlike cosmologies without phantom matter.
Non-perturbative quantum geometric effects in Loop Quantum Cosmology predict a $ρ^2$ modification to the Friedmann equation at high energies. The quadratic term is negative definite and can lead to generic bounces when the matter energy density becomes equal to a critical value of the order of the Planck density. The non-singular bounce is achieved for arbitrary matter without violation of positive energy conditions. By performing a qualitative analysis we explore the nature of the bounce for inflationary and Cyclic model potentials. For the former we show that inflationary trajectories are at…
It is suggested that dark energy in a brane world can help reconcile an infinitely cyclic cosmology with the second law of thermodynamics. A cyclic cosmology is described, in which dark energy with constant equation of state leads to a turnaround at finite future time, when entropy is decreased by a huge factor equal to the inverse of its enhancement during the initial inflation. Thermodynamic consistency of cyclicity requires the arrow of time to reverse during contraction. Entropy reduction in the contracting phase is infinitesimally smaller than entropy increase during expansion.
We study collision of two domain walls in 5-dimensional asymptotically Anti de Sitter spacetime. This may provide the reheating mechanism of an ekpyrotic (or cyclic) brane universe, in which two BPS branes collide and evolve into a hot big bang universe. We evaluate a change of scalar field making the domain wall and can investigate the effect of a negative cosmological term in the bulk to the collision process and the evolution of our universe.
In this paper we discuss the properties of the quasi-steady state cosmological model (QSSC) developed in 1993 in its role as a cyclic model of the universe driven by a negative energy scalar field. We discuss the origin of such a scalar field in the primary creation process first described by F. Hoyle and J. V. Narlikar forty years ago. It is shown that the creation processes which takes place in the nuclei of galaxies are closely linked to the high energy and explosive phenomena, which are commonly observed in galaxies at all redshifts. The cyclic nature of the universe provides a natural lin…
Based on concepts drawn from the ekpyrotic scenario and M-theory, we elaborate our recent proposal of a cyclic model of the Universe. In this model, the Universe undergoes an endless sequence of cosmic epochs which begin with the Universe expanding from a `big bang' and end with the Universe contracting to a `big crunch.' Matching from `big crunch' to `big bang' is performed according to the prescription recently proposed with Khoury, Ovrut and Seiberg. The expansion part of the cycle includes a period of radiation and matter domination followed by an extended period of cosmic acceleration at …
It is shown that any spatially flat and isotropic universe undergoing accelerated expansion driven by a self-interacting scalar field can be directly related to a contracting, decelerating cosmology. The duality is made manifest by expressing the scale factor and Hubble parameter as functions of the scalar field and simultaneously interchanging these two quantities. The decelerating universe can be twinned with a cosmology sourced by a phantom scalar field by inverting the scale factor and leaving the Hubble parameter invariant. The accelerating model can be related to the same phantom univers…
If the potential of a scalar field, Phi, which currently provides the ``dark energy'' of the universe, has a negative minimum -M_0^4, then quantum-mechanical fluctuations could nucleate a bubble of Phi at a negative value of the potential. The bubble would expand at the speed of light. Given that no such bubble enveloped us in the past, we find that any minimum in V(Phi) must be separated from the current Phi value by more than min{1.5M_0, 0.21M_Pl}, where M_Pl is the Planck mass. We also show that vacuum decay renders a cyclic or ekpyrotic universe with M_0^4 > 10^{-10}M_Pl^4, untenable.
We study the transfer of cosmological perturbations through a nonsingular cosmological bounce in a special model in which the parameters of the bounce and the equation of state of matter are chosen such as to allow for an exact calculation of the evolution of the fluctuations. We find that the growing mode of the metric fluctuations in the contracting phase goes over into the growing mode in the expanding phase, a result which is different from what is obtained in analyses in which fluctuations are matched at a singular hypersurface. Consequences for Ekpyrotic cosmology are discussed in a limi…
We consider quantum field theory on a spacetime representing the Big Crunch/Big Bang transition postulated in the ekpyrotic or cyclic cosmologies. We show via several independent methods that an essentially unique matching rule holds connecting the incoming state, in which a single extra dimension shrinks to zero, to the outgoing state in which it re-expands at the same rate. For free fields in our construction there is no particle production from the incoming adiabatic vacuum. When interactions are included the total particle production for fixed external momentum is finite at tree level. We …
In this work we develop the patch formalism, an approach providing a very simple and compact description of braneworld-motivated cosmologies with nonstandard effective Friedmann equations. In particular, the Hubble parameter is assumed to depend on some power of the brane energy density, H^2 \propto ρ^q. The high-energy limit of Randall-Sundrum (q=2) and Gauss-Bonnet (q=2/3) braneworlds are considered, during an accelerating era triggered by a single ordinary or tachyonic scalar field. The inflationary dynamics, solutions, and spectra are provided. Using the latest results from WMAP and other …
We address two questions about the past for infinitely cyclic cosmology. The first is whether it can contain an infinite length null geodesic into the past in view of the Borde-Guth-Vilenkin (BGV) "no-go" theorem, The second is whether, given that a small fraction of spawned universes fail to cycle, there is an adequate probability for a successful universe after an infinite time. We give positive answers to both questions then show that in infinite cyclicity the total number of universes has been infinite for an arbitrarily long time.
A prescription is developed for matching general relativistic perturbations across singularities of the type encountered in the ekpyrotic and cyclic scenarios i.e. a collision between orbifold planes. We show that there exists a gauge in which the evolution of perturbations is locally identical to that in a model space-time (compactified Milne mod Z_2) where the matching of modes across the singularity can be treated using a prescription previously introduced by two of us. Using this approach, we show that long wavelength, scale-invariant, growing-mode perturbations in the incoming state pass …
Dark energy in a brane world reconciles an infinitely cyclic cosmology with the second law of thermodynamics. At turnaround one causal patch with no matter and vanishing entropy is retained for the contraction.
The Cyclic Model is a radical, new cosmological scenario which proposes that the Universe undergoes an endless sequence of epochs which begin with a `big bang' and end in a `big crunch.' When the Universe bounces from contraction to re-expansion, the temperature and density remain finite. The model does not include a period of rapid inflation, yet it reproduces all of the successful predictions of standard big bang and inflationary cosmology. We point out numerous novel elements that have not been used previously which may open the door to further alternative cosmologies. Although the model is…
