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 ratio of the string scale to the Planck scale and may be in reach of upcoming experiments.
Following recent claims relative to the question of large anisotropy production in regular bouncing scenarios, we study the evolution of such anisotropies in a model where an Ekpyrotic phase of contraction is followed by domination of a Galileon-type Lagrangian which generates a non-singular bounce. We show that the anisotropies decrease during the phase of Ekpyrotic contraction (as expected) and that they can be constrained to remain small during the non-singular bounce phase (a non-trivial result). Specifically, we derive the e-folding number of the phase of Ekpyrotic contraction which leads…
We consider the construction of nonsingular Pre-Big-Bang and Ekpyrotic type cosmological models realized by the addition to the action of specific higher-order terms stemming from quantum corrections. We study models involving general relativity coupled to a single scalar field with a potential motivated by the Ekpyrotic scenario. We find that the inclusion of the string loop and quantum correction terms in the string frame makes it possible to obtain solutions of the variational equations which are nonsingular and bouncing in the Einstein frame, even when a negative exponential potential is p…
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…
We consider bouncing cosmologies in which an ekpyrotic contraction phase with w >> 1 is followed by a bouncing phase with w < -1 that violates the null energy condition. The bouncing phase, induced by ghost condensation, is designed to produce a classically nonsingular bounce at a finite value of the scale factor. We show that the initial curvature and anisotropy, though diluted during the ekpyrotic phase, grow back exponentially during the bouncing phase. Moreover, curvature perturbations and anisotropy are generated by quantum fluctuations during the ekpyrotic phase. In the bouncing phase, h…
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…
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…
We study density perturbations in several cosmological models motivated by string theory. The evolution and the spectra of curvature perturbations ${\cal R}$ are analyzed in the Ekpyrotic scenario and nonsingular string cosmologies. We find that these string-inspired models generally exhibit blue spectra in contrast to standard slow-roll inflationary scenarios. We also clarify the parameter range where ${\cal R}$ is enhanced on superhorizon scales.
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…
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 shea…
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 …
We examine reheating in the two-field matter bounce cosmology. In this model, the universe evolves from a matter-dominated phase of contraction to an Ekpyrotic phase of contraction before the nonsingular bounce. The Ekpyrotic phase frees the model from unwanted anisotropies, but leaves the universe cold and empty of particles after the bounce. For this reason, we explore two particle production mechanisms which take place during the course of the cosmological evolution: Parker particle production where the matter field couples only to gravity and particle creation via interactions between the …
New Ekpyrotic Cosmology is an alternative scenario of the early universe which relies on a phase of slow contraction before the big bang. We calculate the 3-point and 4-point correlation functions of primordial density perturbations and find a generically large non-Gaussian signal, just below the current sensitivity level of CMB experiments. This is in contrast with slow-roll inflation, which predicts negligible non-Gaussianity. The model is also distinguishable from alternative inflationary scenarios that yield large non-Gaussianity, such as DBI inflation and the simplest curvaton-like models…
We confront various nonsingular bouncing cosmologies with the recently released BICEP2 data and investigate the observational constraints on their parameter space. In particular, within the context of the effective field approach, we analyze the constraints on the matter bounce curvaton scenario with a light scalar field, and the new matter bounce cosmology model in which the universe successively experiences a period of matter contraction and an ekpyrotic phase. Additionally, we consider three nonsingular bouncing cosmologies obtained in the framework of modified gravity theories, namely the …
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 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 study cosmologies based on low-energy effective string theory with higher-order string corrections to a tree-level action and with a modulus scalar field (dilaton or compactification modulus). In the presence of such corrections it is possible to construct nonsingular cosmological solutions in the context of Pre-Big-Bang and Ekpyrotic universes. We review the construction of nonsingular bouncing solutions and resulting density perturbations in Pre-Big-Bang and Ekpyrotic models. We also discuss the effect of higher-order string corrections on dark energy universe and show several interesting…
The alternative scalar field dark sector of the Universe: Cosmological inflation, quintessence and ekpyrotic model in the framework of scalar-tensor cosmology
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.
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. …
The observed value of the Higgs mass indicates an instability of the Higgs scalar at large energy scales, and hence also at large field values. In the context of early universe cosmology, this is often considered to lead to problems. Here we point out that we can use the instability of the Higgs field to generate an Ekpyrotic phase of contraction. In the context of string theory it is possible that at very high energy densities extra states become massless, leading to an S-brane which leads to the transition between a contracting phase in the past and the current expanding phase. Thus, the Hig…
In recent work, two of us proposed a nonsingular Ekpyrotic cosmology making use of an S-brane which forms at the end of the phase of Ekpyrotic contraction. This S-Brane mediates a transition between contraction and expansion. Graviitational waves passing through the S-Brane acquire a roughly scale-invariant spectrum, and if the S-Brane has zero shear, then a roughly scale-invariant spectrum of cosmological perturbatiions results. Here, we study the production of gauge field fluctuations driven by the decay of the S-Brane, and we show that the reheating process via gauge field production will b…
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…
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 …
In this paper, we explore the nonsingular cosmology within the framework of the Effective Field Theory(EFT) of cosmological perturbations. Due to the recently proved no-go theorem, any nonsingular cosmological models based on the cubic Galileon suffer from pathologies. We show how the EFT could help us clarify the origin of the no-go theorem, and offer us solutions to break the no-go. Particularly, we point out that the gradient instability can be removed by using some spatial derivative operators in EFT. Based on the EFT description, we obtain a realistic healthy nonsingular cosmological mode…
We study a nonsingular bounce inflation model, which can drive the early universe from a contracting phase, bounce into an ordinary inflationary phase, followed by the reheating process. Besides the bounce that avoided the Big-Bang singularity which appears in the standard cosmological scenario, we make use of the Horndesky theory and design the kinetic and potential forms of the lagrangian, so that neither of the two big problems in bouncing cosmology, namely the ghost and the anisotropy problems, will appear. The cosmological perturbations can be generated either in the contracting phase or …
We in this paper investigate the formation and evolution of primordial black holes (PBHs) in nonsingular bouncing cosmologies. We discuss the formation of PBH in the contracting phase and calculate the PBH abundance as a function of the sound speed and Hubble parameter. Afterwards, by taking into account the subsequent PBH evolution during the bouncing phase, we derive the density of PBHs and their Hawking radiation. Our analysis shows that nonsingular bounce models can be constrained from the backreaction of PBHs.
Based on the Effective Field Theory (EFT) of cosmological perturbations, we explicitly clarify the pathology in nonsingular cubic Galileon models and show how to cure it in EFT with new insights into this issue. With the least set of EFT operators that are capable to avoid instabilities in nonsingular cosmologies, we construct a nonsingular model dubbed the Genesis-inflation model, in which a slowly expanding phase (namely, Genesis) with increasing energy density is followed by slow-roll inflation. The spectrum of the primordial perturbation may be simulated numerically, which shows itself a l…
Making use of the T-duality symmetry of superstring theory, and of the double geometry from Double Field Theory, we argue that cosmological singularities of a homogeneous and isotropic universe disappear. In fact, an apparent big bang singularity in Einstein gravity corresponds to a universe expanding to infinite size in the dual dimensions.
The thermodynamic behavior of a decaying vacuum cosmology describing the entire cosmological history evolving between two extreme (early and late time) de Sitter eras is investigated. The thermal evolution from the early de Sitter to the radiation phase is discussed in detail. The temperature evolution law and the increasing entropy function are analytically determined. The entropy of the effectively massless particles is initially zero but evolves continuously to the present day maximum value within the current Hubble radius, $S_0 \sim 10^{88}$ in natural units. By using the Gibbons-Hawking t…
We study massive spin-1/2 fermion production in nonsingular superstring cosmology, taking into account one-loop quantum corrections to a superstring effective action with dilaton and modulus fields. While no creation occurs in the massless limit, massive fermions can be produced by the existence of a time-dependent frequency. Due to the increase of the Hubble expansion rate during the modulus-driven phase, the occupation of number of fermions continues to grow until the point of the graceful exit, after which fermion creation ceases with the decrease of the Hubble rate.
We derive the equations of motion for scalar metric perturbations in a particular nonsingular bouncing cosmology, where the big bang singularity is replaced by a spacetime defect with a degenerate metric. The adiabatic perturbation solution is obtained for nonrelativistic hydrodynamic matter. We get the same result by working with conformal coordinates. This last method is also valid for vector and tensor metric perturbations, and selected results are presented. We, finally, discuss several new effects from the linear perturbations of this nonsingular bouncing cosmology, such as across-bounce …
We show that a nonsingular bounce, free of ghosts and gradient instabilities, can be realized in the framework of Horndeski or generalized Galileon cosmology. In particular, we first review that the theoretical no-go theorem, which states that the above is impossible, is based on two very strong assumptions, namely that a particular quantity cannot be discontinuous during the bounce, and that there is only one bounce. However, as we show in the present work, the first assumption not only can be violated in a general Horndeski/Galileon scenario, but also it is necessarily violated at the bounce…
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 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 investigate a particular type of classical nonsingular bouncing cosmology, which results from general relativity if we allow for degenerate metrics. The simplest model has a matter content with a constant equation-of-state parameter and we get the modified Hubble diagrams for both the luminosity distance and the angular diameter distance. Based on these results, we present a Gedankenexperiment to determine the length scale of the spacetime defect which has replaced the big bang singularity. A possibly more realistic model has an equation-of-state parameter which is different before and afte…
We study spatially homogeneous and isotropic solutions to the equations of motion derived from dilaton gravity, in the presence of a special combination of higher derivative terms in the gravitational action. All solutions are nonsingular. For initial conditions resembling those in the pre-big-bang scenario, there are solutions corresponding to a spatially flat, bouncing Universe originating in a dilaton-dominated contracting phase and emerging as an expanding Friedmann Universe.
New Planck scale physics may solve the singularity problems of classical general relativity and may lead to interesting consequences for very early Universe cosmology. Two approaches to these questions are reviewed in this article. The first is an effective action approach to including the effects of Planck scale physics in the basic framework of general relativity. It is shown that effective actions with improved singularity properties can be constructed. The second approach is based on superstring theory. A scenario which eliminates the big bang singularity and possibly explains the dimensio…
In this paper, we will study the rainbow deformation of the FRW cosmology in both Einstein gravity and Gauss-Bonnet gravity. We will demonstrate that the singularity in the FRW cosmology can be removed because of the rainbow deformation of the FRW metric. We will obtain the general constraints required for the FRW cosmology to be free from singularities. It will be observed that the inclusion of Gauss-Bonnet gravity can significantly change the constraints required to obtain a nonsingular universes. We will use a rainbow functions motivated from the hard spectra of gamma-ray bursts to deform t…
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 study the cosmology of a Lee-Wick type scalar field theory. First, we consider homogeneous and isotropic background solutions and find that they are nonsingular, leading to cosmological bounces. Next, we analyze the spectrum of cosmological perturbations which result from this model. Unless either the potential of the Lee-Wick theory or the initial conditions are finely tuned, it is impossible to obtain background solutions which have a sufficiently long period of inflation after the bounce. More interestingly, however, we find that in the generic non-inflationary bouncing cosmology, pertur…
We examine the dynamics of FLRW cosmologies in which the vacuum interacts with a perfect fluid through an energy exchange, focusing on the exploration of nonsingular configurations, including cyclic and bouncing models. We consider two specific choices for the energy transfer. In the first case, the energy transfer is proportional to a linear combination of the vacuum and fluid energy densities which makes the conservation equations exactly integrable. The resulting Friedmann equation can be interpreted as an energy constraint equation with an effective potential for the scale factor that may …
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 consider the theory obtained by adding to the usual string frame dilaton gravity action specially constructed higher derivative terms motivated by the limited curvature construction of [MukhanovET1992a] and determine the spatially homogeneous and isotropic solutions to the resulting equations of motion. All solutions of the resulting theory of gravity with these symmetries are nonsingular and all curvature invariants are bounded. For initial conditions inspired by the pre-big-bang scenario solutions exist which correspond to a spatially flat Universe starting in a dilaton-dominated superinf…
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 describe physical effects occurring in the regularized Robertson-Walker spacetime which can reveal the presence of the defect. Our analysis is based on two main physical quantities: the compressive forces acting on (human) observers and the energy possessed by massive particles and photons during their dynamical evolution. In Sec. 3, we claim that with a characteristic length scale of the order of the Planck length compressive forces become so intense near the defect that no (human) observer is able to cross it. In Sec. 4, we show that the energy exhibits an unusual character…
We present a new class of nonsingular bounce cosmology free from instabilities, using a single scalar field coupled to gravity within the framework of the Degenerate Higher-Order Scalar-Tensor (DHOST) theories. In this type of scenarios, the gradient instability that widely exists in nonsingular bounce cosmologies in the framework of scalar-tensor and Horndeski/Galileon theories is removed by the effects of new operators introduced by the DHOST, due to the modification that they later bring about to the dispersion relation of perturbations. Hence, our results demonstrate that there is indeed a…
One of the fundamental open questions in cosmology is whether we can regard the universe evolution without singularity like a Big Bang or a Big Rip. This challenging subject stimulates one to regard a nonsingular universe in the far past with an arbitrarily large vacuum energy. Considering the high energy regime in the cosmic history, it is believed that Einstein gravity should be corrected to an effective energy dependent theory which could be acquired by gravity's rainbow. On the other hand, employing massive gravity provided us with solutions to some of the long standing fundamental problem…
In the context of homogeneous and isotropic superstring cosmology, the T-duality symmetry of string theory has been used to argue that for a background space-time described by dilaton gravity with strings as matter sources, the cosmological evolution of the Universe will be nonsingular. In this Letter we discuss how T-duality extends to brane gas cosmology, an approximation in which the background space-time is again described by dilaton gravity with a gas of branes as a matter source. We conclude that the arguments for nonsingular cosmological evolution remain valid.
We consider the process of magnetogenesis in the context of nonsingular bounce cosmology. We show that large primordial magnetic fields can be generated during contraction without encountering strong coupling and backreaction issues. The fields may seed large-scale magnetic fields with observationally interesting strengths. This result leads to a theoretical constraint on the relation of the energy scale of the bounce cosmology to the number of effective e-folding of the contracting phase in the case of scale invariance for the power spectrum of primordial magnetic fields. We show that this co…
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…
We discuss an effective field theory background containing the gravitational field, the dilaton and a closed string tachyon, and couple this background to a gas of fundamental strings and D strings. Allowing for the possibility of a non-vanishing dilaton potential of Casimir type, we demonstrate the possibility of obtaining a nonsingular, static tachyon condensate phase with fixed dilaton. The time reversal of our solution provides a candidate effective field theory description of a Hagedorn phase of string gas cosmology with fixed dilaton.
Inflationary theory is already 20 years old, and it is impossible to describe all of its versions and implications in a short talk. I will concentrate on several subjects which I believe to be most important. First of all, I will give a brief review of the first versions of inflationary theory, from Starobinsky model to new inflation. Then I will describe chaotic inflation, the theory of quantum fluctuations and density perturbations, the theory of eternal inflation, and recent observational data. In the second part of the talk I will discuss the recently proposed ekpyrotic scenario and argue …
In light of the recent observational data coming from the sky we have two significant directions in the field of theoretical cosmology recently. First, we are now able to make use of present observations, such as the Planck and BICEP2 data, to examine theoretical predictions from the standard inflationary $Λ$CDM which were made decades of years ago. Second, we can search for new cosmological signatures as a way to explore physics beyond the standard cosmic paradigm. In particular, a subset of early universe models admit a nonsingular bouncing solution that attempts to address the issue of the …
