Non-singular Cosmological Solutions Research Articles

Healthy Horndeski cosmologies with torsion

We show that the full Horndeski theory with both curvature and torsion can support nonsingular, stable and subluminal cosmological solutions at all times. Thus, with torsion, the usual No-Go theorem that holds in a curved spacetime is avoided. In particular, it is essential to include the nonminimal derivative couplings of the ℒ5 part of the Horndeski action (Gμν ∇ μ ∇ νϕ, and (∇2 ϕ)3). Without the latter a No-Go already impedes the eternal subluminality of nonsingular, stable cosmologies.

Singularity free cosmological models in viscous symmetric teleparallel gravity

In this paper, we have investigated the possibility of deriving exact non-singular cosmological solutions in a combined scenario of bulk viscous fluid and symmetric teleparallel gravity (f(Q) gravity). Interestingly, we have found that the general solutions obtained from our models are flexible enough for demonstrating the emergent Universe scenario, inflation and late-time dark-energy-like behaviour. We have found that these phases of the Universe depend crucially on the viscosity parameters ζ0, ζ1 considered in this work and also the parameter n associated with the f(Q) model. Hence, we performed an analysis concerning the model’s relevance with the observed data to constrain the aforementioned parameters.

Stable nonsingular cosmologies in beyond Horndeski theory and disformal transformations

In this paper, we collect, systemize and generalize the existing results for relations between general Horndeski theories and beyond Horndeski theories via disformal transformations of metric. We focus on those subclasses of beyond Horndeski theories which are disformally related to Horndeski theories and derive additional transformation rules relating the Lagrangian functions of these two theories. Then we demonstrate that some of these transformation rules become singular at some moments(s) once one constructs a nonsingular cosmological solution in beyond Horndeski theory that is free from ghost, gradient instabilities and strong gravity regime during the entire evolution of the system. The key issue here is that such solutions are banned in Horndeski theory due to the existing no-go theorem. The proof of singular behavior of disformal relations in this case resolves the apparent contradiction between the fact that Horndeski and beyond Horndeski theories were initially implied to be related via healthy field redefinition and at the same time these theories describe different physics in the context of nonsingular cosmologies.

New nonsingular cosmological solution of nonlocal gravity

We present a new bouncing cosmological solution of the non-local theory known as infinite derivative gravity, which goes beyond the recursive ansatz, ${\Box R = r_1 R +r_2}$. The non-local field equations are evaluated using the spectral decomposition with respect to the eigenfunctions of the wave operator. The energy-momentum tensor computed for this geometry turns out to be much more sensitive to the choice of the non-local form-factor, since it depends on the value of the function on a continuous infinite interval. We show that this stronger dependence on the form-factor allows us to source the geometry by the perfect fluid with the non-negative energy density satisfying the strong energy condition. We show that this bouncing behaviour is not possible in the local theories of gravity such as in general relativity or $R+R^2$ gravity sourced by a fluid which meets the non-negative energy and strong energy conditions.

Bouncing cosmological isotropic solutions in scalar-tensor gravity

Bouncing non-singular isotropic cosmological solutions are investigated in a simple model of scalar-tensor gravity. New families of such solutions are found and their properties are presented and analyzedusing an effective potential as the main tool.Bouncing solutions are shown to exist for a Higgs-like self-interactionpotential which is bounded from below, in contrast to previous solutions that appeared in the literature based on potentials which were unbounded from below. In the simplest version of a scalar field with the quartic potential and conformal coupling to gravity, bouncing spatially flat solutions either have the Hubble function diverging in the past beforethe bounce, but with a well-behaved future, or are globally regular but unstable with respect to anisotropic or inhomogeneousperturbations at some finite values of the scalar field and curvature. Regular solutions can only exist in the part of the parameter space where the maximum ofthe effective potential is larger than the first zero of the potential, and gravity becomesrepulsive at the bounce.

Scenario for a singularity-free generic cosmological solution

We develop a scenario for the emergence of a non-singular generic cosmological solution based on the a WKB characterization of one of the two anisotropy degrees of freedom. We investigate the dynamics of the so-called inhomogeneous mixmaster in the "corner" configuration and inferring that one of the two anisotropic variables becomes small enough to explore the uncertainty principle. Then, we apply a standard WKB approximation to the dynamics of the Universe which has macroscopic volume, one macroscopic anisotropy and one microscopic quantum degree of freedom. Our study demonstrates the possibility that the Universe acquires a non-singular classical behavior, retaining the quantum degree of freedom as a small oscillating ripple on a stationary Universe. The role of the so-called "fragmentation process" is also taken into account in outlining the generality of such a behavior in independent local space regions.

Cuscuton gravity as a classically stable limiting curvature theory

Finding effective theories of modified gravity that can resolve cosmological singularities and avoid other physical pathologies such as ghost and gradient instabilities has turned out to be a rather difficult task. The concept of limiting curvature, where one bounds a finite number of curvature-invariant functions thanks to constraint equations, is a promising avenue in that direction, but its implementation has only led to mixed results. Cuscuton gravity, which can be defined as a special subclass of k-essence theory for instance, is a minimal modification of gravity since it does not introduce any new degrees of freedom on a cosmological background. Importantly, it naturally incorporates the idea of limiting curvature. Accordingly, models of cuscuton gravity are shown to possess non-singular cosmological solutions and those appear stable at first sight. Yet, various subtleties arise in the perturbations such as apparent divergences, e.g., when the Hubble parameter crosses zero. We revisit the cosmological perturbations in various gauges and demonstrate that the stability results are robust even at those crossing points, although certain gauges are better suited to analyze the perturbations. In particular, the spatially-flat gauge is found to be ill defined when H=0. Otherwise, the sound speed is confirmed to be generally close to unity in the ultraviolet, and curvature perturbations are shown to remain essentially constant in the infrared throughout a bounce phase. Perturbations for a model of extended cuscuton (as a subclass of Horndeski theory) are also studied and similar conclusions are recovered.

Non-singular string cosmology via \u03b1\u2032 corrections

In string theory, an important challenge is to show if the big-bang singularity could be resolved by the higher derivative α′ corrections. In this work, based on the Hohm-Zwiebach action, we construct a series of non-singular non-perturbative cosmological solutions with the complete α′ corrections, for the bosonic gravi-dilaton system. In the perturbative regime, these solutions exactly match the perturbative results given in literature. Our results show that the big-bang singularity indeed could be smoothed out by the higher derivative α′ corrections.

Cosmological Scenarios with Bounce and Genesis in Horndeski Theory and Beyond

This essay is a brief review of the recent studies of non-singular cosmological scenarios with bounce and Genesis and their stability in a subclass of scalar–tensor theories with higher derivatives—beyond Horndeski theories. We discuss the general results of stability analysis of the nonsingular cosmological solutions in beyond Horndeski theories, as well as other closely related topics: 1) the no-go theorem, which is valid in the general Horndeski theories but not in their extensions, 2) singularities in disformal transformations relating beyond Horndeski theories with general ones, 3) healthy behavior of the scalar sector in the unitary gauge despite divergencies of coefficients in the quadratic action for perturbations (“γ-crossing”). We describe several specific examples of bouncing cosmologies and models with Genesis epoch which have neither ghosts nor gradient instabilities among the linearized perturbations about the homogeneous isotropic background during entire evolution.

General theory of cosmological perturbations in open and closed universes from the Horndeski action

Our Universe is nearly spatially flat, but this does not mean that it is exactly spatially flat. In this paper we derive general quadratic actions for cosmological perturbations in nonflat models from the Horndeski theory. This allows us to study how the spatial curvature influences the behavior of cosmological perturbations in the early Universe described by some general scalar-tensor theory. We show that a tiny spatial curvature at the onset of inflation is unlikely to yield large [or $\mathcal{O}(1)$] effects on the primordial spectra even if one modifies gravity. We also argue that nonsingular cosmological solutions in the Horndeski theory are unstable in spatially open cases as well as in flat cases.

Singularities and Phenomenological aspects of Asymptotic Safe Gravity

Asymptotic Safety (AS) Program for quantum gravity keeps the same fields and symmetries with General Relativity and studies the associated gravitational action as a fundamental part of the complete theory at the nonperturbative level with the help of functional renormalization group (RG) techniques. An important phenomenological task that can test the new point of view of AS approach is the discovery of RG improved cosmologies and black holes. In this work, we analyze the properties of recently found non-singular spherically symmetric and non-singular cosmological solutions. Furthermore, we derive a novel consistent set of modified Einstein field equations, in the spirit of AS, which respects the Bianchi identities. This new set of equations completes previously published modified Einstein equations which arise by adding appropriate covariant kinetic terms to the action.

Space-time slicing in Horndeski theories and its implications for non-singular bouncing solutions

In this paper, we show how the proper choice of gauge is critical in analyzing the stability of non-singular cosmological bounce solutions based on Horndeski theories. We show that it is possible to construct non-singular cosmological bounce solutions with classically stable behavior for all modes with wavelengths above the Planck scale where: (a) the solution involves a stage of null-energy condition violation during which gravity is described by a modification of Einstein's general relativity; and (b) the solution reduces to Einstein gravity both before and after the null-energy condition violating stage. Similar considerations apply to galilean genesis scenarios.

Cosmological bounce in Horndeski theory and beyond

We discuss the stability of the classical bouncing solutions in the general Horndeski theory and beyond Horndeski theory. We restate the no-go theorem, showing that in the general Horndeski theory there are no spatially flat non-singular cosmological solutions which are stable during entire evolution. We show the way to evade the no-go in beyond Horndeski theory and give two specific examples of bouncing solutions, whose asymptotic past and future or both are described by General Relativity (GR) with a conventional massless scalar field. Both solutions are free of any pathologies at all times.

Do massive compact objects without event horizon exist in infinite derivative gravity?

Einstein's General theory of relativity is plagued by cosmological and blackhole type singularities Recently, it has been shown that infinite derivative, ghost free, gravity can yield non-singular cosmological and mini-blackhole solutions. In particular, the theory possesses a {\it mass-gap} determined by the scale of new physics. We will use this property to argue that it is possible to form a non-singular super-massive compact objects without having any event horizon in this class of theories.

On gravitational waves in Born-Infeld inspired non-singular cosmologies

We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. We also investigate the role of the adiabatic sound speed of the matter sector in the regularisation of the gravitational waves evolution. We extend our analysis to more general Born-Infeld inspired theories where analogous solutions are found. As a general conclusion, we obtain that the bouncing solutions are generally more prone to instabilities, while the asymptotically Minkowski solutions can be rendered stable, making them appealing models for the early universe.

Generalized multi-Galileons, covariantized new terms, and the no-go theorem for nonsingular cosmologies

It has been pointed out that non-singular cosmological solutions in second-order scalar-tensor theories generically suffer from gradient instabilities. We extend this no-go result to second-order gravitational theories with an arbitrary number of interacting scalar fields. Our proof follows directly from the action of generalized multi-Galileons, and thus is different from and complementary to that based on the effective field theory approach. Several new terms for generalized multi-Galileons on a flat background were proposed recently. We find a covariant completion of them and confirm that they do not participate in the no-go argument.

Spin-2 fields from torsion: Dark energy and bouncing cosmology

We study a modified theory of gravitation built on a restricted Riemann–Cartan space-time, characterized by reduction in the number of degrees of freedom of torsion. The dynamics is defined by the Einstein–Cartan action of the Einstein–Cartan–Sciama–Kibble (ECSK) theory, while the kinematical structure is defined in such a way that the general-relativistic kinematics is recovered in the associated Riemannian space-time. In this case, the torsion is automatically decomposed into two spin-2 fields with energies of opposite sign. Investigated is the special case where these spin-2 fields are “sterile” (i.e., only interact with other matter fields through gravitation) and have their number of degrees of freedom further reduced to only one. When these fields are furnished with a conservative self-interaction potential, the spatially homogeneous and isotropic cosmological solution obtained via numerical integration of the field equations exhibits accelerated expansion compatible with the current observational data, while the equation of state of both spin-2 fields have values confined in the interval between −1 and −1/3 during the whole cosmic history. Moreover, the present model exhibits nonsingular (bouncing) cosmological solutions.

Born-Infeld-likef(R)gravity

Several features of an $f(R)$ theory in which there is a maximum value for the curvature are analyzed. The theory admits all the vacuum solutions of General Relativity, and also the radiation evolution for the scale factor of the standard cosmological model. Working in the Jordan frame, a complete analysis of the phase space is performed, and shown to be in agreement with examples obtained by numerical integration. In particular, nonsingular cosmological solutions were obtained, which after the bounce enter a phase of de Sitter expansion and subsequently relax to a GR-like radiation-dominated evolution.

Quantum cosmology: expectations and results

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 a dark energy universe and show several interesting possibilities of the avoidance of future singularities.

Cosmologies from higher‐order string corrections

AbstractWe 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 a dark energy universe and show several interesting possibilities of the avoidance of future singularities.