Gauss-Bonnet Cosmology Research Articles

Gauss-Bonnet Cosmology: large-temperature behaviour and bounds from Gravitational Waves

We provide a transparent discussion of the high temperature asymptotic behaviour of Cosmology in a dilaton-Einstein-Gauss-Bonnet (dEGB) scenario of modified gravity with vanishing scalar potential. In particular, we show that it has a clear interpretation in terms of only three attractors (stable critical points) of a set of autonomous differential equations: w = -1/3, w = 1 and 1 < w < 7/3, where w ≡ p/ρ is the equation of state, defined as the ratio of the total pressure and the total energy density. All the possible different high-temperature evolution histories of the model are exhausted by only eight paths in the flow of the set of the autonomous differential equations. Our discussion clearly explains why five out of them are characterized by a swift transition of the system toward the attractor, while the remaining three show a more convoluted evolution, where the system follows a meta-stable equation of state at intermediate temperatures before eventually jumping to the real attractor at higher temperatures. Compared to standard Cosmology, the regions of the dEGB parameter space with w = -1/3 show a strong enhancement of the expected Gravitational Wave stochastic background produced by the primordial plasma of relativistic particles of the Standard Model. This is due to the very peculiar fact that dEGB allows to have an epoch when the energy density ρ rad of the relativistic plasma dominates the energy of the Universe while at the same time the rate of dilution with T of the total energy density is slower than what usually expected during radiation dominance. This allows to use the bound from Big Bang Nucleosynthesis (BBN) to put in dEGB a constraint T RH ≲ (108 – 109) GeV on the reheating temperature of the Universe T RH. Such BBN bound is complementary to late-time constraints from compact binary mergers.

Dynamics of a higher-dimensional Einstein–Scalar–Gauss–Bonnet cosmology

We study the dynamics of the field equations in a five-dimensional spatially flat Friedmann–Lemaître–Robertson–Walker metric in the context of a Gauss–Bonnet–Scalar field theory where the quintessence scalar field is coupled to the Gauss–Bonnet scalar. Contrary to the four-dimensional Gauss–Bonnet theory, where the Gauss–Bonnet term does not contribute to the field equations, in this five-dimensional Einstein–Scalar–Gauss–Bonnet model, the Gauss–Bonnet term contributes to the field equations even when the coupling function is a constant. Additionally, we consider a more general coupling described by a power-law function. For the scalar field potential, we consider the exponential function. For each choice of the coupling function, we define a set of dimensionless variables and write the field equations into a system of ordinary differential equations. We perform a detailed analysis of the dynamics for both systems and classify the stability of the equilibrium points. We determine the presence of scaling and super-collapsing solutions using the cosmological deceleration parameter. This means that our models can explain the Universe’s early and late-time acceleration phases. Consequently, this model can be used to study inflation or as a dark energy candidate.

4D Einstein–Gauss–Bonnet cosmology with Chameleon mechanism

4D Einstein–Gauss–Bonnet cosmology with Chameleon mechanism

The Fate of the Universe Evolution in the Quadratic Form of Ricci–Gauss–Bonnet Cosmology

The Fate of the Universe Evolution in the Quadratic Form of Ricci–Gauss–Bonnet Cosmology

WIMPs in dilatonic Einstein Gauss-Bonnet cosmology

We use the Weakly Interacting Massive Particle (WIMP) thermal decoupling scenario to probe Cosmologies in dilatonic Einstein Gauss-Bonnet (dEGB) gravity, where the Gauss-Bonnet term is non-minimally coupled to a scalar field with vanishing potential.We put constraints on the model parameters when the ensuing modified cosmological scenario drives the WIMP annihilation cross section beyond the present bounds from DM indirect detection searches. In our analysis we assumed WIMPs that annihilate to Standard Model particles through an s-wave process. For the class of solutions that comply with WIMP indirect detection bounds, we find that dEGB typically plays a mitigating role on the scalar field dynamics at high temperature, slowing down the speed of its evolution and reducing the enhancement of the Hubble constant compared to its standard value. For such solutions, we observe that the corresponding boundary conditions at high temperature correspond asymptotically to a vanishing deceleration parameter q, so that the effect of dEGB is to add an accelerating term that exactly cancels the deceleration predicted by General Relativity.The bounds from WIMP indirect detection are nicely complementary to late-time constraints from compact binary mergers. This suggests that it could be interesting to use other Early Cosmology processes to probe the dEGB scenario.

Late-time constraints on modified Gauss-Bonnet cosmology

In this paper, we consider a gravitational action containing a combination of the Ricci scalar, R, and the topological Gauss-Bonnet term, G. Specifically, we study the cosmological features of a particular class of modified gravity theories selected by symmetry considerations, namely the $$f(R,G)= R^n G^{1-n}$$ model. In the context of a spatially flat, homogeneous and isotropic background, we show that the currently observed acceleration of the Universe can be addressed through geometry, hence avoiding de facto the shortcomings of the cosmological constant. We thus present a strategy to numerically solve the Friedmann equations in presence of pressureless matter and obtain the redshift behavior of the Hubble expansion rate. Then, to check the viability of the model, we place constraints on the free parameters of the theory by means of a Bayesian Monte Carlo method applied to late-time cosmic observations. Our results show that the f(R, G) model is capable of mimicking the low-redshift behavior of the standard $$\Lambda $$ CDM model. Finally, we investigate the energy conditions and show that, under suitable choices for the values of the cosmographic parameters, they are all violated when considering the mean value of n obtained from our analysis, as occurs in the case of a dark fluid.

Primordial perturbations and inflation in a holography inspired Gauss-Bonnet cosmology

We consider an action for gravity that, in addition to the Einstein-Hilbert term, contains a function of the Ricci scalar and the Gauss-Bonnet invariant. The specific form of the function considered is motivated by holographic cosmology. At background level the field equations imply modified Friedmann equations of the same form as those in the holographic cosmology. We calculate the cosmological perturbations and derive the corresponding power spectra assuming a general $k$-inflation. We find that the resulting power spectra differ substantially from those obtained in both holographic and standard cosmology. The estimated spectral index and tensor-to-scalar ratio are confronted with the Planck results.

Autonomous dynamical system of Einstein–Gauss–Bonnet cosmologies

In this paper, we study the phase space of cosmological models in the context of Einstein–Gauss–Bonnet theory. More specifically, we consider a generalized dynamical system that encapsulates the main features of the theory and for the cases that this is rendered autonomous, we analyze its equilibrium points and stable and unstable manifolds corresponding to several distinct cosmological evolutions. As we demonstrate, the phase space is quite rich and contains invariant structures, which dictate the conditions under which the theory may be valid and viable in describing the evolution Universe during different phases. It is proved that a stable equilibrium point and two invariant manifolds leading to the fixed point, have both physical meaning and restrict the physical aspects of such a rich in structure modified theory of gravity. More important we prove the existence of a heteroclinic orbit which drives the evolution of the system to a stable fixed point. However, while on the fixed point the Friedman constraint corresponding to a flat Universe is satisfied, the points belonging to the heteroclinic orbit do not satisfy the Friedman constraint. We discuss the origin of this intriguing issue in some detail.

Splitting Into Two Isotropic Subspaces as a Result of Cosmological Evolution in Einstein—Gauss—Bonnet Gravity

We consider numerically dynamics of a flat anisotropic Universe in Einstein-Gauss-Bonnet gravity with positive $\Lambda$ in dimensionalities 5+1 and 6+1. We identify three possible outcomes of the evolution, one singular and two nonsingular. First nonsingular outcome is oscillatory. Second is the known exponential solution. The simplest version of it is the isotropic de Sitter solution. In Gauss-Bonnet cosmology there exist also anisotropic exponential solutions. When an exponential solution being an outcome of cosmological evolution has two different Hubble parameters, the evolution leads from initially totally anisotropic stage to a sum of two isotropic subspaces. We show that such type of evolution is rather typical and possible even in the case when de Sitter solution also exists.

Generalized Noether theorem for Gauss–Bonnet cosmology

Generalized Noether’s theory is a useful method for researching the modified gravity theories about the conserved quantities and symmetries. A generally Gauss-Bonnet gravity f(R,G) theory was proposed as an alternative gravity model. Through the generalized Noether symmetry, polynomial and product forms of the f(R,G) theory with corresponding conserved quantities and symmetries are researched. Then suitable general forms of the polynomial form f(R,G)=k1Rn+(6)n2(−1)n+1k1Gn2 and the product form f(R,G)=k(R/G)nG are found out, to contain the solution of accelerated expansion cosmology. Both forms of f(R,G) concerned in this paper only possess time translational symmetry. And energy condition of these solutions are also checked. To some extent, the consistency of conservation of symmetry and energy condition is demonstrated. For the specific form of different n, it needs further detailed study. Noting that, the corresponding conserved quantities are both zero, and the only conservation relation is conservation of energy.

Observational constraints on Gauss–Bonnet cosmology

We analyze a fully geometric approach to dark energy in the framework of [Formula: see text] theories of gravity, where [Formula: see text] is the Ricci curvature scalar and [Formula: see text] is the Gauss–Bonnet topological invariant. The latter invariant naturally exhausts, together with [Formula: see text], the whole curvature content related to curvature invariants coming from the Riemann tensor. In particular, we study a class of [Formula: see text] models with power law solutions and find that, depending on the value of the geometrical parameter, a shift in the anisotropy peaks position of the temperature power spectrum is produced, as well as an increasing in the matter power spectrum amplitude. This fact could be extremely relevant to fix the form of the [Formula: see text] model. We also perform an MCMC analysis using both Cosmic Microwave Background data by the Planck (2015) release and the Joint Light-Curve Analysis of the SNLS–SDSS collaborative effort, combined with the current local measurements of the Hubble value, [Formula: see text], and galaxy data from the Sloan Digital Sky Survey (BOSS CMASS DR11). We show that such a model can describe the CMB data with slightly high [Formula: see text] values, and the prediction on the amplitude matter spectrum value is proved to be in accordance with the observed matter distribution of the universe. At the same time, the value constrained for the geometric parameter implies a density evolution of such a component that is growing with time.

Erratum: On stable exponential solutions in the Einstein–Gauss–Bonnet cosmology with zero variation of G [Gravitation and Cosmology 22 (4), 329–332 (2016)

Erratum: On stable exponential solutions in the Einstein–Gauss–Bonnet cosmology with zero variation of G [Gravitation and Cosmology 22 (4), 329–332 (2016)

Friedmann Dynamics Recovered from Compactified Einstein–Gauss–Bonnet Cosmology

In this paper cosmological dynamics in Einstein-Gauss-Bonnet gravity with a perfect fluid source in arbitrary dimension is studied. A systematic analysis is performed for the case that the theory does not admit maximally symmetric solutions. Considering two independent scale factors, namely one for the three dimensional space and one for the extra dimensional space, is found that a regime exists where the two scale factors tend to a constant value via damped oscillations for not too negative pressure of the fluid, so that asymptotically the evolution of the $(3+1)$-dimensional Friedmann model with perfect fluid is recovered. At last, it is worth emphasizing that the present numerical results strongly support a 't Hooft-like interpretation of the parameter $1/D$ (where $D$ is the number of extra dimensions) as a small expansion parameter in very much the same way as it happens in the large $N$ expansion of gauge theories with $1/N$. Indeed, the dependence on $D$ of many of the relevant physical quantities computed here manifests a clear WKB-like pattern, as expected on the basis of large $N$ arguments.

A Gauss–Bonnet Cosmology with an Effective Time-Dependent Scalar Potential

Abstract A special class of a Gauss–Bonnet minimal power-law cosmology characterised by an effective time-dependent scalar field potential is explored in this communication. Some new features related to the late-time cosmological dynamics are observed and discussed accordingly.

On stable exponential solutions in Einstein–Gauss–Bonnet cosmology with zero variation of G

A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term Lambda is considered. Assuming diagonal cosmological metrics, we find, for certain non-zero Lambda new examples of solutions with an exponential time dependence of two scale factors, governed by two Hubble-like parameters H > 0 and h < 0, corresponding to submanifolds of dimensions m and l, respectively, with (m,l) = (4,2), (5,2), (5,3), (6,7), (7,5), (7,6) and D = 1 + m + l. Any of these solutions describes an exponential expansion of "our" 3-dimensional factor-space with Hubble parameter H and zero variation of the effective gravitational constant G. We also prove the stability of these solutions in the class of cosmological solutions with diagonal metrics.

On exponential solutions in the Einstein–Gauss–Bonnet cosmology, stability and variation of G

A D-dimensional gravitational model with Gauss–Bonnet and cosmological terms is considered. When an ansatz with a diagonal cosmological metric is adopted, we find new examples of solutions for Λ Λ ≠ 0 and D = 8 with an exponential dependence of the scale factors, which describe expansion of our 3D factor-space and contraction of 4D internal space. We also study the stability of the solutions with static Hubble-like parameters hi and prove that two solutions with Λ = 0 in dimensions D = 22, 28, which were found earlier, are stable. For both solutions we find asymptotic relations for the effective gravitational constant.

Gauss-Bonnet cosmology unifying late and early-time acceleration eras with intermediate eras

In this paper we demonstrate that with vacuum $F(G)$ gravity it is possible to describe the unification of late and early-time acceleration eras with the radiation and matter domination era. The Hubble rate of the unified evolution contains two mild singularities, so called Type IV singularities, and the evolution itself has some appealing features, such as the existence of a deceleration-acceleration transition at late times. We also address quantitatively a fundamental question related to modified gravity models description of cosmological evolution: Is it possible for all modified gravity descriptions of our Universe evolution, to produce a nearly scale invariant spectrum of primordial curvature perturbations? As we demonstrate, the answer for the $F(G)$ description is no, since the resulting power spectrum is not scale invariant, in contrast to the $F(R)$ description studied in the literature. Therefore, although the cosmological evolution can be realized in the context of vacuum $F(G)$ gravity, the evolution is not compatible with the observational data, in contrast to the $F(R)$ gravity description of the same cosmological evolution.

Noether symmetry approach in Gauss–Bonnet cosmology

We discuss the Noether Symmetry Approach in the framework of Gauss–Bonnet cosmology showing that the functional form of the F(R, 𝒢) function, where R is the Ricci scalar and 𝒢 is the Gauss–Bonnet topological invariant, can be determined by the presence of symmetries. Besides, the method allows to find out exact solutions due to the reduction of cosmological dynamical system and the presence of conserved quantities. Some specific cosmological models are worked out.

Higher-order Gauss-Bonnet cosmology by Lagrange multipliers

We study cosmological models derived from higher-order Gauss-Bonnet gravity $F(R,G)$ by using the Lagrange multiplier approach without assuming the presence of additional fields with the exception of standard perfect fluid matter. The presence of Lagrange multipliers reduces the number of allowed solutions. We need to introduce compatibility conditions of the FRW equations, which impose strict restrictions on the metric or require the introduction of additional exotic matter. Several classes of $F(R,G)$ models are generated and discussed.

On the stability of power-law solutions in multidimensional Gauss-Bonnet cosmology

We consider dynamics of a flat anisotropic multidimensional cosmological model in Gauss-Bonnet gravity in the presence of a homogeneous magnetic field. In particular, we find conditions under which the known power-law vacuum solution can be an attractor for the case with non-zero magnetic field. We also describe a particular class of numerical solution in $(5+1)$-dimensional case which does not approach the power-law regime.