Gauss–Bonnet dark energy on Hořava–Lifshitz cosmology

We investigate the Gauss–Bonnet dark energy model and its deformed version on Ho?ava–Lifshitz cosmology, which belongs to the class of cosmologies obtained from the so-called projectable version of Ho?ava–Lifshitz gravity. In particular, we investigate the bulk/boundary interaction in this scenario through the Q function, which we interpret as a measure of the energy transference between the bulk and the spacetime boundary. Then we discuss whether the thermal equilibrium will be stable or not, once it is reached, and the validity of the generalized second law. We show that the Q function can exhibit sign changes along the cosmic evolution and the Universe reaches the thermal equilibrium as a transient phenomenon.     

Ricci dark energy in braneworld models with a Gauss–Bonnet term in the bulk

We investigate the Ricci Dark Energy (RDE) in the braneworld models with a Gauss–Bonnet term in the Bulk. We analytically solve the generalized Friedmann equation on the brane and find that the universe will finally enter into a pure de Sitter spacetime in stead of the big rip that appears in the usual 4D Ricci dark energy model with parameter α<1/2$\alpha <1/2$. We also consider the Hubble horizon as the IR cutoff in holographic dark energy model and find it cannot accelerate the universe as in the usual case without interacting.     

Thermodynamics of Gauss–Bonnet black holes revisited

We investigate the Gauss–Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss–Bonnet coupling c and mass M, comparing with those of the Born–Infeld-AdS (BIAdS), Reissner–Norstr?m-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For c<0 we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy, because the entropy does not satisfy the area law. On the other hand, for c>0, we find the BIAdS-like black hole, showing that the coupling c plays the role of a pseudo-charge. Importantly, we could not obtain the SAdS in the limit of c→0, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasi-normal modes may take on analytic expressions.     

More on the dilatonic Einstein–Gauss–Bonnet gravity

Einstein–Gauss–Bonnet gravity coupled to a dynamical dilaton is examined from the viewpoint of Einstein’s equivalence principle. We point out that the usual frame change that applies to the action without curvature correction does not cure the problem of nonminimal couplings by the dynamical nature of a dilaton field. Thus a modification of the Einstein frame is required. It is proposed that the kinetic term of a dilaton should be brought to a canonical form, which completely fixes the additional terms associated with the frame transformation.     

Transient crossing of phantom divide line w Λ = − 1 under Gauss–Bonnet interaction

Smooth double crossing of the phantom barrier w _Λ = − 1 has been found possible in cosmological model with Gauss–Bonnet-scalar interaction, in the presence of background cold dark matter. Such crossing has been observed to be a sufficiently late time phenomena and independent of the sign of Gauss–Bonnet-scalar interaction. The luminosity distance versus redshift curve shows a perfect fit with the Λ CDM model up to z = 3.5.     

Gravastars in modified Gauss–Bonnet gravity

This paper aims to discuss the viable and analytic solution of the spherically symmetric gravastar model under the influence of modification of Gauss–Bonnet gravity, i.e., f(G) gravity, where G is the Gauss–Bonnet curvature term. For this purpose, we evaluate the field equations in corresponding theory and conservation equation with the help of an effective energy–momentum tensor. A mathematical formalism of the gravastar’s three regions, i.e., interior de-Sitter region, thin shell, and the exterior Schwarzschild vacuum region have been discussed. We, then analyze different realistic features, in particular energy, entropy, and length of the shell. The viability of these physical features is then examined through the graphical representations separately. Within the framework of an alternative theory, we have obtained the exact and singularity free model of gravastar.     

Accelerated expansion of an anisotropic Brans–Dicke cosmology from nonlinear derivative interaction and Gauss–Bonnet invariant

The study of Brans–Dicke cosmology has attracted considerable attention in the recent years since it explains most of the important features of the progress of the universe. We discuss in this letter a homogeneous and anisotropic cosmological model in the framework of Brans–Dicke theory including together a non-linear derivative interaction which appears in theory with the Galilean shift symmetry, a Gauss–Bonnet invariant motivated from heterotic string theory which plays an important role in numerous alternatives cosmological frameworks, two scalar fields and their interactions to fit easier with universe history expansion. Several particular cases are studied and the properties related to scaling solutions and asymptotic behaviour are discussed in some details.     

Gauss–Bonnet term on vacuum decay

We study the effect of the Gauss–Bonnet term on vacuum decay process in the Coleman–De Luccia formalism. The Gauss–Bonnet term has an exponential coupling with the real scalar field, which appears in the low energy effective action of string theories. We calculate numerically the instanton solution, which describes the process of vacuum decay, and obtain the critical size of bubble. We find that the Gauss–Bonnet term has a nontrivial effect on the false vacuum decay, depending on the Gauss–Bonnet coefficient.     

Generalized second law of thermodynamics in Gauss–Bonnet braneworld

We investigate the validity the generalized second law of thermodynamics in a general braneworld model with curvature correction terms on the brane and in the bulk, respectively. Employing the derived entropy expression associated with the apparent horizon, we examine the time evolution of the total entropy, including the derived entropy of the apparent horizon and the entropy of the matter fields inside the apparent horizon. We show that the generalized second law of thermodynamics is fulfilled on the 3-brane embedded in the 5D spacetime with curvature corrections.     

Some solutions of the Gauss–Bonnet gravity with scalar field in four dimensions

We give all exact solutions of the Einstein–Gauss–Bonnet Field Equations coupled with a scalar field in four dimensions under certain assumptions. The main assumption we make in this work is to take the second covariant derivative of the coupling function proportional to the spacetime metric tensor. Although this assumption simplifies the field equations considerably, to obtain exact solutions we assume also that the spacetime metric is conformally flat. Then we obtain a class of exact solutions.     

The geometry of the higher dimensional black hole thermodynamics in Einstein–Gauss–Bonnet theory

In this paper, we have studied the geometry of the five-dimensional black hole solutions in (a) Einstein–Yang–Mills–Gauss–Bonnet theory and (b) Einstein–Maxwell–Gauss–Bonnet theory with a cosmological constant for spherically symmetric space time. Formulating the Ruppeiner metric, we have examined the possible phase transition for both the metrics. It is found that depending on some restrictions phase transition is possible for the black holes. Also for Λ = 0 in Einstein–Gauss–Bonnet black hole, the Ruppeiner metric becomes flat and hence the black hole becomes a stable one.     

Emergent universe scenario in the Einstein–Gauss–Bonnet gravity with dilaton

We obtain cosmological solutions which admit emergent universe (EU) scenario in the framework of Einstein Gauss–Bonnet (GB) gravity coupled with a dilaton field in 4-dimensions. The coupling parameter of the GB terms and the dilaton in the theory are determined for obtaining an EU scenario. The corresponding dilaton potential which admits such scenario is determined. It is found that the GB terms coupled with a dilaton field plays an important role in describing the dynamics of the evolution of the early as well as the late universe. We note an interesting case where the GB term dominates initially in the asymptotic past regime, subsequently it decreases and thereafter its contribution in determining the dynamics of the evolution dominates once again. We note that the Einstein’s static universe solution permitted here is unstable which the asymptotic EU might follow. We also compare our EU model with supernova data.     

Intermediate inflation in Gauss–Bonnet brane world

In this article we study an intermediate inflationary universe models using the Gauss–Bonnet brane. General conditions required for these models to be realizable are derived and discussed. We use recent astronomical observations to constraint the parameters appearing in the model.     

On the possibility of dark energy from corrections to the Wheeler–DeWitt equation

We present a method for approximating the effective consequence of generic quantum gravity corrections to the Wheeler–DeWitt equation. We show that in many cases these corrections can produce departures from classical physics at large scales and that this behaviour can be interpreted as additional matter components. This opens up the possibility that dark energy (and possible dark matter) could be large scale manifestations of quantum gravity corrections to classical general relativity. As a specific example we examine the first order corrections to the Wheeler–DeWitt equation arising from loop quantum cosmology in the absence of lattice refinement and show how the ultimate breakdown in large scale physics occurs.     

Viscous fluids and Gauss–Bonnet modified gravity

We study effects of cosmic fluids on finite-time future singularities in modified f (R, G)-gravity, where R and G are the Ricci scalar and the Gauss–Bonnet invariant, respectively. We consider the fluid equation of state in the general form, ω = ω(ρ), and we suppose the existence of a bulk viscosity. We investigate quintessence region (ω > −1) and phantom region (ω < −1) and the possibility to change or avoid the singularities in f (R, G)-gravity. Finally, we study the inclusion of quantum effects in large curvature regime.     

Geometrothermodynamics of five dimensional black holes in Einstein–Gauss–Bonnet theory

We investigate the thermodynamic properties of 5D static and spherically symmetric black holes in (i) Einstein–Maxwell–Gauss–Bonnet theory, (ii) Einstein–Maxwell–Gauss–Bonnet theory with negative cosmological constant, and in (iii) Einstein–Yang–Mills–Gauss–Bonnet theory. To formulate the thermodynamics of these black holes we use the Bekenstein–Hawking entropy relation and, alternatively, a modified entropy formula which follows from the first law of thermodynamics of black holes. The results of both approaches are not equivalent. Using the formalism of geometrothermodynamics, we introduce in the manifold of equilibrium states a Legendre invariant metric for each black hole and for each thermodynamic approach, and show that the thermodynamic curvature diverges at those points where the temperature vanishes and the heat capacity diverges.