In this letter we point out the existence of solutions to General Relativity with a negative cosmological constant in four dimensions, which contain solitons as well as traversable wormholes. The latter connect two asymptotically locally AdS$_{4}$ spacetimes. At every constant value of the radial coordinate the spacetime is a spacelike warped AdS$_{3}$. We compute the dual energy momentum tensor at each boundary showing that it yields different results. We also show that these vacuum wormholes can have more than one throat and that they are indeed traversable by computing the time it takes for a light signal to go from one boundary to the other, as seen by a geodesic observer. We generalize the wormholes to include rotation and charge. When the cosmological constant is positive we find a cosmology that is everywhere regular, has either one or two bounces and that for late and early times matches the Friedmann-Lema\^ıtre-Robertson-Walker metric with spherical topology.
We show that bouncing open or flat Friedmann-Robertson-Walker cosmologies are inconsistent with worldsheet string theory to first approximation. Specifically, the Virasoro constraint translates to the null energy condition in spacetime at leading order in the alpha-prime expansion. Thus one must go beyond minimally-coupled Einstein gravity in order to find bounce solutions.
We review the status of bouncing cosmologies as alternatives to cosmological inflation for providing a description of the very early universe, and a source for the cosmological perturbations which are observed today. We focus on the motivation for considering bouncing cosmologies, the origin of fluctuations in these models, and the challenges which various implementations face.
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 …
The observed temperature fluctuations in the cosmic microwave background can be traced back to primordial curvature modes that are sourced by adiabatic and/or entropic matter perturbations. In this paper, we explore the entropic mechanism in the context of non-singular bouncing cosmologies. We show that curvature modes are naturally generated during `graceful exit,' i.e., when the smoothing slow contraction phase ends and the universe enters the bounce stage. Here, the key role is played by the kinetic energy components that come to dominate the energy density and drive the evolution towards t…
Cyclic universes with bouncing solutions are candidates for solving the big bang initial singularity problem. Here we seek bouncing solutions in a modified Gauss-Bonnet gravity theory, of the type $R+f(G)$, where $R$ is the Ricci scalar, $G$ is the Gauss-Bonnet term, and $f$ some function of it. In finding such a bouncing solution we resort to a technique that reduces the order of the differential equations of the $R+f(G)$ theory to second order equations. As general relativity is a theory whose equations are of second order, this order reduction technique enables one to find solutions which a…
We review matter bounce scenarios where the matter content is dark matter and dark energy. These cosmologies predict a nearly scale-invariant power spectrum with a slightly red tilt for scalar perturbations and a small tensor-to-scalar ratio. Importantly, these models predict a positive running of the scalar index, contrary to the predictions of the simplest inflationary and ekpyrotic models, and hence could potentially be falsified by future observations. We also review how bouncing cosmological space-times can arise in theories where either the Einstein equations are modified or where matter…
We calculate the running of the scalar index in the ekpyrotic and matter bounce cosmological scenarios, and find that it is typically negative for ekpyrotic models, while it is typically positive for realizations of the matter bounce where multiple fields are present. This can be compared to inflation, where the observationally preferred models typically predict a negative running. The magnitude of the running is expected to be between $10^{-4}$ and up to $10^{-2},$ leading in some cases to interesting expectations for near-future observations.
In the framework of massive gravity with a de Sitter reference metric, we study homogeneous and isotropic solutions with positive spatial curvature. Remarkably, we find that bounces can occur when cosmological matter satisfies the strong energy condition, in contrast to what happens in classical general relativity. This is due to the presence in the Friedmann equations of additional terms, which depend on the scale factor and its derivatives and can be interpreted as an effective fluid. We present a detailed study of the system using a phase space analysis. After having identified the fixed po…
We consider the question of deriving initial conditions for scalar fields in driving both an early and late quintessence phase. The dark energy field presents an unresolved uniformity problem. Further difficulties with initial conditions for assisted, kinetic and phantom inflation are presented. We review the use of the canonical measure and find the negative conclusions of Gibbons and Hawking can be allayed by means of a reasonable quantum cosmological input. We remark upon some attempts at incorporating inflationary schemes into cyclic and bouncing models.
We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini $f(R)$ and $f(R,R_{μν}R^{μν})$ theories of gravity and consider the existence of non-singular bouncing solutions in the early universe. We find that all $f(R)$ models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model $R+a R^2/R_P+R_{μν}R^{μν}/R_P$ exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for $a<0$) and radiation (for arbitrary $a$). It thus represents a p…
Given the proliferation of bouncing models in recent years, we gather and critically assess these proposals in a comprehensive review. The Planck data shows an unmistakably red, quasi scale-invariant, purely adiabatic primordial power spectrum and no primary non-Gaussianities. While these observations are consistent with inflationary predictions, bouncing cosmologies aspire to provide an alternative framework to explain them. Such models face many problems, both of the purely theoretical kind, such as the necessity of violating the NEC and instabilities, and at the cosmological application lev…
The Pre-Big Bang cosmology inspired generations of cosmologists in attempts to cure the initial Big Bang singularity using a fundamental length scale as proposed by String Theory. The existence of a phase of collapse/inflation with increasing curvature followed by a cosmic bounce has been proposed as an alternative to standard inflation in the solution of the horizon and curvature problems. However the generation of a nearly scale-invariant spectrum of perturbations is not an automatic prediction of such scenarios. In this paper I review some general statements about the evolution of perturbat…
Bouncing cosmologies are often proposed as alternatives to standard inflation for the explanation of the homogeneity and flatness of the universe. In such scenarios, the present cosmological expansion is preceded by a contraction phase. However, during the contraction, in general the anisotropy of the universe grows and eventually leads to a chaotic mixmaster behavior. This would either be hard to reconcile with observations or even lead to a singularity instead of the bounce. In order to preserve a smooth and isotropic bounce, the source for the contraction must have a super-stiff equation of…
We consider a two-component regular cosmology bouncing from contraction to expansion, where, in order to include both scalar fields and perfect fluids as particular cases, the dominant component is allowed to have an intrinsic isocurvature mode. We show that the spectrum of the growing mode of the Bardeen potential in the pre-bounce is never transferred to the dominant mode of the post-bounce. The latter acquires at most a dominant isocurvature component, depending on the relative properties of the two fluids. Our results imply that several claims in the literature need substantial revision.
We show how the large-scale cosmological dynamics can be obtained from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the semi-classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.
We consider non-singular bouncing cosmologies, such as the new ekpyrotic model, in which the universe undergoes a slow contraction phase with equation of state $w \gg 1$, followed by a bounce that occurs at a finite scale factor when quantum gravity corrections are still negligible. Such a non-singular bounce requires a violation of the null energy condition in which $w$ falls below -1 at some time before the bounce. In this paper, we show that a component of the adiabatic curvature perturbations, though decaying and negligible during the ekpyrotic phase, is exponentially amplified just before…
We calculate the gravitational waves (GW) spectrum produced in various Early Universe scenarios from gauge field sources, thus generalizing earlier inflationary calculations to bouncing cosmologies. We consider generic couplings between the gauge fields and the scalar field dominating the energy density of the Universe. We analyze the requirements needed to avoid a backreaction that will spoil the background evolution. When the scalar is coupled only to $F \tilde F$ term, the sourced GW spectrum is exponentially enhanced and parametrically the square of the vacuum fluctuations spectrum, ${\cal…
We study the dynamics of a homogeneous and isotropic Friedmann-Robertson-Walker universe in the context of the Eddington-inspired Born-Infeld theory of gravity. We generalize earlier results, obtained in the context of a radiation dominated universe, to account for the evolution of a universe permeated by a perfect fluid with an arbitrary equation of state parameter $w$. We show that a bounce may occur for $κ>0$, if $w$ is time-dependent, and we demonstrate that it is free from tensor singularities. We argue that Eddington-inspired Born-Infeld cosmologies may be a viable alternative to the inf…
Bouncing cosmologies, suggested by String/M-theory, may provide an alternative to standard inflation to account for the origin of inhomogeneities in our universe. The fundamental question regards the correct way to evolve the scalar perturbations through the bounce. In this work, we determine the evolution of perturbations and the final spectrum for an arbitrary (spatially flat) bouncing cosmology, with the only assumption that the bounce is governed by a single physical scale. In particular, we find that the spectrum of the pre-bounce growing mode of the Bardeen potential (which is scale-inva…
The simplest possible classical model leading to a cosmological bounce is examined in the light of the non-Gaussianities it can generate. Concentrating solely on the transition between contraction and expansion, and assuming initially purely Gaussian perturbations at the end of the contracting phase, we find that the bounce acts as a source such that the resulting value for the post-bounce $f_{\mathrm{NL}}$ may largely exceed all current limits, to the point of potentially casting doubts on the validity of the perturbative expansion. We conjecture that if one can assume that the non-Gaussianit…
The results from Planck2015, when combined with earlier observations from WMAP, ACT, SPT and other experiments, were the first observations to disfavor the "classic" inflationary paradigm. To satisfy the observational constraints, inflationary theorists have been forced to consider plateau-like inflaton potentials that introduce more parameters and more fine-tuning, problematic initial conditions, multiverse-unpredictability issues, and a new 'unlikeliness problem.' Some propose turning instead to a "postmodern" inflationary paradigm in which the cosmological properties in our observable unive…
The Asymptotically Safe Gravity provides a framework for the description of gravity from the trans-Planckian regime to cosmological scales. According to this scenario, the cosmological constant and Newton's coupling are functions of the energy scale whose evolution is dictated by the renormalization group equations. The formulation of the renormalization group equations on foliated spacetimes, based on the Arnowitt-Deser-Misner (ADM) formalism, furnishes a natural way to construct the RG energy scale from the spectrum of the laplacian operator on the spatial slices. Combining this idea with a …
We study the conditions under which thermal fluctuations generated in the contracting phase of a non-singular bouncing cosmology can lead to a scale-invariant spectrum of cosmological fluctuations at late times in the expanding phase. We consider point particle gases, holographic gases and string gases. In the models thus identified, we also study the thermal non-Gaussianities of the resulting distribution of inhomogeneities. For regular point particle radiation, we find that the background must have an equation of state $w = 7/3$ in order to obtain a scale-invariant spectrum, and that the non…
We review the general features of nonsingular universes ({\em i.e.} those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes. We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms. Observational consequences of such regular cosmologies are also considered, with emphasis in the behavior of the perturbations.
We investigate the post-bounce background dynamics in a certain class of single bounce scenarios studied in the literature, in which the cosmic bounce is driven by a scalar field with negative exponential potential such as the ekpyrotic potential. We show that those models can actually lead to cyclic evolutions with repeated bounces. These cyclic evolutions, however, do not account for the currently observed late-time accelerated expansion and hence are not cosmologically viable. In this respect we consider a new kind of cyclic model proposed recently and derive some cosmological constraints o…
Non-gaussianity in the microwave background radiation is bound to play a key role in giving us clues about the physics of the very early universe. However, the associated calculations, at second and even third order in perturbation theory, tend to be complicated to the point of obscuring simple underlying physical processes. In this note, we present a simple analytic procedure for approximating the non-linearity parameters f_{NL} and g_{NL} for cyclic models in which the cosmological perturbations are generated via the entropic mechanism. Our approach is quick, physically transparent and agree…
In this note, we construct a family of non-singular time-dependent solutions of a six-dimensional gravitational theory that are warped products of a four dimensional bouncing cosmological solution and a two dimensional internal manifold. The warp factor is time-dependent and breaks translation invariance along one of the internal directions. When the warp factor is periodic in time, the non-compact part of the geometry bounces periodically. The six dimensional geometry is supported by matter that does not violate the null energy condition. We show that this 6D geometry does not admit a closed …
We elaborate further on the evolution properties of cosmological fluctuations through a bounce. We show this evolution to be describable either by ``transmission'' and ``reflection'' coefficients or by an effective unitary S-matrix. We also show that they behave in a time reversal invariant way. Therefore, earlier results are now interpreted in a different perspective and put on a firmer basis.
For bouncing cosmologies such as the ekpyrotic/cyclic scenarios we show that it is possible to make predictions for density perturbations which are independent of the details of the bouncing phase. This can be achieved, as in inflationary cosmology, thanks to the existence of a dynamical attractor, which makes local observables equal to the unperturbed solution up to exponentially small terms. Assuming that the physics of the bounce is not extremely sensitive to these corrections, perturbations can be evolved even at non-linear level. The resulting spectrum is not scale invariant and thus inco…
We present nonsingular, homogeneous and isotropic bouncing solutions of the conformal Galileon model. We show that such solutions necessarily begin with a radiation-dominated contracting phase. This is followed by a quintom scenario in which the background equation of state crosses the cosmological constant boundary allowing for a nonsingular bounce which in turn is followed by Galilean Genesis. We analyze the spectrum of cosmological perturbations in this background. Our results show that the fluctuations evolve smoothly and without any pathology, but the adiabatic modes form a blue tilted sp…
We present a full investigation of scalar perturbations in a rather generic model for a regular bouncing universe, where the bounce is triggered by an effective perfect fluid with negative energy density. Long before and after the bounce the universe is dominated by a source with positive energy density, which may be a perfect fluid, a scalar field, or any other source with an intrinsic isocurvature perturbation. Within this framework, we present an analytical method to accurately estimate the spectrum of large-scale scalar perturbations until their reentry, long after the bounce. We also prop…
We investigate the realization of two bouncing paradigms, namely of the superbounce and the loop quantum cosmological ekpyrosis, in the framework of various modified gravities. In particular, we focus on the $F(R)$, $F(G)$ and $F(T)$ gravities, and we reconstruct their specific subclasses which lead to such universe evolutions. These subclasses constitute from power laws, polynomials, or hypergeometric ansatzes, which can be approximated by power laws. The qualitative similarity of different effective gravities which realize the above two bouncing cosmologies, indicates to some universality ly…
We exhibit a situation in which cosmological perturbations of astrophysical relevance propagating through a bounce are affected in a scale-dependent way. Involving only the evolution of a scalar field in a closed universe described by general relativity, the model is consistent with causality. Such a specific counter-example leads to the conclusion that imposing causality is not sufficient to determine the spectrum of perturbations after a bounce provided it is known before. We discuss consequences of this result for string motivated scenarios.
We study spatially flat bouncing cosmologies and models with the early-time Genesis epoch in a popular class of generalized Galileon theories. We ask whether there exist solutions of these types which are free of gradient and ghost instabilities. We find that irrespectively of the forms of the Lagrangian functions, the bouncing models either are plagued with these instabilities or have singularities. The same result holds for the original Genesis model and its variants in which the scale factor tends to a constant as $t\to -\infty$. The result remains valid in theories with additional matter t…
We show that, in the presence of a string gas, simple higher-derivative modifications to the effective action for gravity can lead to bouncing and cyclic cosmological models. The modifications bound the expansion rate and avoid singularities at finite times. In these models the scale factors can have long loitering phases that solve the horizon problem. Adding a potential for the dilaton gives a simple realization of the pre-big bang scenario. Entropy production in the cyclic phase drives an eventual transition to a radiation-dominated universe. As a test of the Brandenberger-Vafa scenario, we…
The string effective action at tree level contains, in its bosonic sector, the Einstein-Hilbert term, the dilaton, and the axion, besides scalar and gauge fields coming from the Ramond-Ramond sector. The reduction to four dimensions brings to scene moduli fields. We generalize this effective action by introducing two arbitrary parameters, $ω$ and $m$, connected with the dilaton and axion couplings. In this way, more general frameworks can be analyzed. Regular solutions with a bounce can be obtained for a range of (negative) values of the parameter $ω$ which, however, exclude the pure string co…
We consider linear perturbation equations for long-wavelength scalar metric perturbations in generalised gravity, applicable to non-singular cosmological models including a bounce from collapse to expansion in the very early universe. We present the general form for the perturbation equations which follows from requiring that the inhomogeneous universe on large scales obeys the same local equations as the homogeneous Friedmann-Robertson-Walker background cosmology (the separate universes approach). In a pseudo-longitudinal gauge this becomes a homogeneous second-order differential equation for…
We study the cosmology induced on a brane probing a warped throat region in a Calabi-Yau compactification of type IIB string theory. For the case of a BPS D3-brane probing the Klebanov-Strassler warped deformed conifold, the cosmology described by a suitable brane observer is a bouncing, spatially flat Friedmann-Robertson-Walker universe with time-varying Newton's constant, which passes smoothly from a contracting to an expanding phase. In the Klebanov-Tseytlin approximation to the Klebanov-Strassler solution the cosmology would end with a big crunch singularity. In this sense, the warped defo…
A four-dimensional timelike brane is considered as the boundary of the $SAdS_{5}$ bulk background. Exploiting the CFT/FRW-cosmology relation, we derive the self-gravitational corrections to the first Friedmann-like equation which is the equation of the brane motion. The additional term that arises due to the semiclassical analysis, can be viewed as stiff matter where the self-gravitational corrections act as the source for it. This result is contrary to standard analysis that regards the charge of $SAdS_{5}$ bulk black hole as the source for stiff matter. A very interesting feature of the solu…
We investigate scalar particle creation in a set of bouncing models where the bounce occurs due to quantum cosmological effects described by the Wheeler-DeWitt equation. The scalar field can be either conformally or minimally coupled to gravity, and it can be massive or massless, without self interaction. The analysis is made for models containing a single radiation fluid, and for the more realistic case of models containing the usual observed radiation and dust fluids, which can fit most of the observed features of our Universe, including an almost scale invariant power spectrum of scalar cos…
In a quantum theory of gravity spacetime behaves classically when quantum probabilities are high for histories of geometry and field that are correlated in time by the Einstein equation. Probabilities follow from the quantum state. This quantum perspective on classicality has important implications: (a) Classical histories are generally available only in limited patches of the configuration space on which the state lives. (b) In a given patch states generally predict relative probabilities for an ensemble of possible classical histories. (c) In between patches classical predictability breaks d…
We consider f(Q) extended symmetric teleparallel cosmologies, where Q is the non-metricity scalar, and constrain its functional form through the order reduction method. By using this technique, we are able to reduce and integrate the field equations and thus to select the corresponding models giving rise to bouncing cosmology. The selected Lagrangian is then used to develop the Hamiltonian formalism and to obtain the Wave Function of the Universe which suggests that classical observable universes can be recovered according to the Hartle Criterion.
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 …
We develop a Gauss-Bonnet extension of Loop Quantum Cosmology, by introducing holonomy corrections in modified $F(\mathcal{G})$ theories of gravity. Within the context of our formalism, we provide a perturbative expansion in the critical density, a parameter characteristic of Loop Quantum Gravity theories, and we result in having leading order corrections to the classical $F(\mathcal{G})$ theories of gravity. After extensively discussing the formalism, we present a reconstruction method that makes possible to find the Loop Quantum Cosmology corrected $F(\mathcal{G})$ theory that can realize va…
We study a cosmological scenario in which inflation is preceded by a bounce. In this scenario, the primordial singularity, one of the major shortcomings of inflation, is replaced by a non-singular bounce, prior to which the universe undergoes a phase of contraction. Our starting point is the bouncing cosmology investigated in Falciano et al. (2008), which we complete by a detailed study of the transfer of cosmological perturbations through the bounce and a discussion of possible observational effects of bouncing cosmologies. We focus on a symmetric bounce and compute the evolution of cosmologi…
Recently, interesting braneworld cosmologies in the Randall-Sundrum scenario have been constructed using a bulk spacetime which corresponds to a charged AdS black hole. In particular, these solutions appear to `bounce', making a smooth transition from a contracting to an expanding phase. By considering the spacetime geometry more carefully, we demonstrate that generically in these solutions the brane will encounter a singularity in the transition region.
The so called $f(X)$ hybrid metric-Palatini gravity presents a unique viable generalisation of the $f(R)$ theories within the metric-affine formalism. Here the cosmology of the $f(X)$ theories is studied using the dynamical system approach. The method consists of formulating the propagation equation in terms of suitable (expansion-normalised) variables as an autonomous system. The fixed points of the system then represent exact cosmological solutions described by power-law or de Sitter expansion. The formalism is applied to two classes of $f(X)$ models, revealing both standard cosmological fix…
A complete qualitative study of the dynamics of string cosmologies is presented for the class of isotopic curvature universes. These models are of Bianchi types I, V and IX and reduce to the general class of Friedmann-Robertson-Walker universes in the limit of vanishing shear isotropy. A non-trivial two-form potential and cosmological constant terms are included in the system. In general, the two-form potential and spatial curvature terms are only dynamically important at intermediate stages of the evolution. In many of the models, the cosmological constant is important asymptotically and anis…
Using the dynamical system approach, properties of cosmological models based on the Horava-Lifshitz gravity are systematically studied. In particular, the cosmological phase space of the Horava-Lifshitz model is characterized. The analysis allows to compare some key physical consequences of the imposition (or not) of detailed balance. A result of the investigation is that in the detailed balance case one of the attractors in the theory corresponds to an oscillatory behavior. Such oscillations can be associated to a bouncing universe, as previously described by Brandenberger, and will prevent a…
Exact cosmological solutions for effective actions in D dimensions inspired by the tree-level superstring action are studied. For a certain range of free parameters existing in the model, nonsingular bouncing solutions are found. Among them, of particular interest can be open hyperbolic models, in which, without any fine tuning, the internal scale factor and the dilaton field (connected with string coupling in string theories) tend to constant values at late times. A cosmological singularity is avoided due to nonminimal dilaton-gravity coupling and, for D > 11, due to pure imaginary nature of …
We provide an $F(R)$ gravity description of a $Λ$CDM bouncing model, without the need for matter fluids or for cosmological constant. As we explicitly demonstrate, the two cosmological eras that constitute the $Λ$CDM bouncing model, can be generated by $F(R)$ gravity which can lead to accelerating cosmologies. The resulting F(R) gravity has Einstein frame inflationary properties that have concordance to the latest Planck observational data. Both the $F(R)$ gravity stability properties are thoroughly investigated and also, the gravitational particle production, a feature necessary for the viabi…
Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of c…
We study thermodynamics of dynamical traversable wormholes. These wormholes are investigated in the background of different cosmological models, with and without the cosmological constant, and which include the power-law and exponential cosmologies also. We work out the generalized surface gravity for wormholes of different shapes. The surface gravity is evaluated at the trapping horizon and the unified first law of thermodynamics is set up. The thermodynamic stability of these wormholes has also been investigated. Some cases of asymptotically flat, de Sitter and anti-de Sitter wormholes have …
We study mimetic $F(R)$ gravity with potential and Lagrange multiplier constraint. In the context of these theories, we introduce a reconstruction technique which enables us to realize arbitrary cosmologies, given the Hubble rate and an arbitrarily chosen $F(R)$ gravity. We exemplify our method by realizing cosmologies that are in concordance with current observations (Planck data) and also well known bouncing cosmologies. The attribute of our method is that the $F(R)$ gravity can be arbitrarily chosen, so we can have the appealing features of the mimetic approach combined with the known featu…
