Gauss-Bonnet Cosmology Research Articles

Stable analytic bounce in non-local Einstein–Gauss–Bonnet cosmology

We consider the most general quadratic in curvature stringy-motivated non-local action for the modified Einstein's gravity. We present exact analytic cosmological solutions including the bouncing ones and develop the relevant techniques for the further study of these types of models. We also elaborate on the perturbation formalism and argue that the found bouncing solution is stable during the bounce phase.

Interacting Tachyon Dark Energy Model in Gauss-Bonnet Cosmology

We investigate the tachyon scalar filed model of dark energy in the framework of Gauss-Bonnet cosmology. We consider a spatially non-flat universe containing interacting tachyon dark energy with pressureless dark matter. We obtain the equation of state and deceleration parameters. We also reconstruct the potential and the dynamics for the tachyon scalar field model, which describe accelerated expansion of the universe.

The nature of singularity in multidimensional anisotropic Gauss–Bonnet cosmology with a perfect fluid

We investigate dynamics of (4+1) and (5+1) dimensional flat anisotropic Universe filled by a perfect fluid in the Gauss-Bonnet gravity. An analytical solutions valid for particular values of the equation of state parameter $w=1/3$ have been found. For other values of $w$ structure of cosmological singularity have been studied numerically. We found that for $w > 1/3$ the singularity is isotropic. Several important differences between (4+1) and (5+1) dimensional cases are discussed.

On anisotropic Gauss-Bonnet cosmologies in (n + 1) dimensions, governed by an n-dimensional Finslerian 4-metric

The (n +1)-dimensional Einstein-Gauss-Bonnet (EGB) model is considered. For diagonal cosmological metrics, the equations of motion are written as a set of Lagrange equations with the effective Lagrangian containing two "minisuperspace" metrics on R^n: a 2-metric of pseudo-Euclidean signature and a Finslerian 4-metric proportional to the n-dimensional Berwald-Moor 4-metric. For the case of the "pure" Gauss-Bonnet model, two exact solutions are presented, those with power-law and exponential dependences of the scale factors (w.r.t. the synchronous time variable). (The power-law solution was considered earlier by N. Deruelle, A. Toporensky, P. Tretyakov, and S. Pavluchenko.) In the case of EGB cosmology, it is shown that for any non-trivial solution with an exponential dependence of scale factors, a_i(\tau) = A_i exp(v^i \tau), there are no more than three different numbers among v^1, ..., v^n.

Non-minimal Maxwell-modified Gauss–Bonnet cosmologies: inflation and dark energy

In this paper we show that power-law inflation can be realized in non-minimal gravitational coupling of electromagnetic field with a general function of the Gauss–Bonnet invariant. Such a non-minimal coupling may appear due to quantum corrections. We also consider modified Maxwell-F(G) gravity in which non-minimal coupling between electromagnetic field and f(G) occurs in the framework of modified Gauss–Bonnet gravity. It is shown that inflationary cosmology and late-time accelerated expansion of the universe are possible in such a theory.

Interacting Holographic Dark Energy in the Scalar Gauss–Bonnet Gravity

We study cosmological application of interacting holographic dark energy density in the scalar Gauss–Bonnet framework. We employ the interacting holographic model of dark energy to obtain the equation of state for the interacting holographic energy density in a spatially flat universe. Our calculations show that taking ΩΛ = 0.73 for the present time, it is possible to have wΛeff crossing –1. This implies that one can generate a phantom-like equation of state from the interacting holographic dark energy model in flat universe in the scalar Gauss–Bonnet cosmology framework. Then we reconstruct the potential of the scalar field.

Gauss–Bonnet cosmology with induced gravity and a non-minimally coupled scalar field onthe brane

We construct a cosmological model with a non-minimally coupled scalar field on the brane,where Gauss–Bonnet and induced gravity effects are taken into account. This model has 5Dcharacter at both high and low energy limits but reduces to 4D gravity for intermediatescales. While induced gravity is a manifestation of the IR limit of the model, theGauss–Bonnet term and non-minimal coupling of the scalar field and induced gravity areessentially related to the UV limit of the scenario. We study the cosmologicalimplications of this scenario focusing on the late time behavior of the solutions. In thissetup, non-minimal coupling plays the role of an additional fine-tuning parameterthat controls the initial density of the predicted finite density big bang. Also,non-minimal coupling has important implications for the bouncing nature of thesolutions.

A note on the viability of Gauss–Bonnet cosmology

In this Letter, we analyze the viability of a vacuum Gauss–Bonnet cosmology by examining the dynamics of the homogeneous and anisotropic background in 4+1 dimensions. The trajectories of the system either originate from the standard singularity or from non-standard type, the later is characterized by the divergence of time derivative of the Hubble parameters for its finite value. At the onset, the system should relax to Einstein phase at late times as the effect of Gauss–Bonnet term becomes negligible in the low energy regime. However, we find that most of the trajectories emerging from the standard big-bang singularity lead to future re-collapse whereas the system beginning its evolution from the non-standard singularity enters the Kasner regime at late times. This leads to the conclusion that the measure of trajectories giving rise to a smooth evolution from a standard singularity to the Einstein phase is negligibly small for generic initial conditions.

Gauss–Bonnet cosmologies: crossing the phantom divide and the transition from matterdominance to dark energy

Dark energy cosmologies with an equation of state parameterw lessthan −1 are often found to violate the null energy condition and show unstable behaviour. A solution tothis problem may require the existence of a consistent effective theory that violates the nullenergy condition only momentarily and does not develop any instabilities or other pathologicalfeatures for a late time cosmology. A model which incorporates a dynamical scalar fieldφ coupled to the quadratic Riemann invariant of the Gauss–Bonnet form is a viable proposal.Such an effective theory is shown to admit non-singular cosmological evolutions for a widerange of scalar–Gauss–Bonnet coupling. We discuss the conditions for which our modelyields observationally supported spectra of scalar and tensor fluctuations, undercosmological perturbations. The model can provide a reasonable explanation for thetransition from matter dominance to dark energy regime and the late time cosmicacceleration, offering an interesting testing ground for investigations of the cosmologicalmodified gravity.

Ghost conditions for Gauss–Bonnet cosmologies

We investigate the stability against inhomogeneous perturbations and the appearance of ghost modes in Gauss–Bonnet gravitational theories with a non-minimally coupled scalar field, which can be regarded as either the dilaton or a compactification modulus in the context of string theory. Through cosmological linear perturbations we extract four no-ghost and two sub-luminal constraint equations, written in terms of background quantities, which must be satisfied for consistency. We also argue that, for a general action with quadratic Riemann invariants, homogeneous and inhomogeneous perturbations are, in general, inequivalent, and that attractors in the phase space can have ghosts. These results are then generalized to a two-field configuration. Single-field models as candidates for dark energy are explored numerically and severe bounds on the parameter space of initial conditions are placed. A number of cases proposed in the literature are tested and most of them are found to be unstable or observationally unviable.

Cosmological solutions in Kaluza–Klein theories of quadratic Lagrangians

We present a new class of solutions in a five-dimensional Gauss–Bonnet cosmology. The space-time consists of one time-like direction and two maximally symmetric space-like subspaces, the external space and the internal one. The universe is filled with matter in the form of a one-component perfect fluid and the analysis is carried out for various equations of state. The solutions to the field equations are based on a new approximation technique that determines the scales of the ordinary universe, in terms of the cosmological redshift parameter, at which the error between the exact and the approximate description becomes minimum, at each order of approximation. In this case, the four-dimensional Friedmann models of General Relativity result as external space solutions in the first-order approximation of the quadratic theory. Conditions for the existence of the resulting five-dimensional models are derived and discussed, together with their cosmological behavior. In this context, it is shown that under certain conditions, some of the models may be geodesically complete.