Gauss-Bonnet Coupling Research Articles

Realistic Compactification Models in Einstein–Gauss–Bonnet Gravity

We report the results of a study on the dynamical compactification of spatially flat cosmological models in Einstein–Gauss–Bonnet gravity. The analysis was performed in the arbitrary dimension in order to be more general. We consider both vacuum and Λ -term cases. Our results suggest that for vacuum case, realistic compactification into the Kasner (power law) regime occurs with any number of dimensions (D), while the compactification into the exponential solution occurs only for D ⩾ 2 . For the Λ -term case only compactification into the exponential solution exists, and it only occurs for D ⩾ 2 as well. Our results, combined with the bounds on Gauss–Bonnet coupling and the Λ -term ( α , Λ , respectively) from other considerations, allow for the tightening of the existing constraints and forbid α < 0 .

Greybody factors for a spherically symmetric Einstein-Gauss-Bonnet–de Sitter black hole

We study the greybody factors of the scalar fields in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black holes in higher dimensions. We derive the greybody factors analytically for both minimally and non-minimally coupled scalar fields. Moreover, we discuss the dependence of the greybody factor on various parameters including the angular momentum number, the non-minimally coupling constant, the spacetime dimension, the cosmological constant and the Gauss-Bonnet coefficient in detail. We find that the non-minimal coupling may suppress the Hawking radiation, while the Gauss-Bonnet coupling could enhance the radiation.

Entanglement entropy of singular surfaces under relevant deformations in holography

In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional CFT for singular entangling surface. We observe that in addition to the universal term due to the entangling surface, there is a new logarithmic term which corresponds to a relevant perturbation of the conformal field theory with a coefficient depending on the scaling dimension of the relevant operator. We also find a new power law divergence in the holographic entanglement entropy. In addition, we study the effect of a relevant perturbation in the Gauss-Bonnet gravity for a singular entangling surface. Again a logarithmic term shows up. This new term is proportional to both the dimension of the relevant operator and the Gauss-Bonnet coupling. We also introduce the renormalized entanglement entropy for a kink region which in the UV limit reduces to a universal positive finite term.

Exact inflation in Einstein–Gauss–Bonnet gravity

We study cosmological inflation in the Einstein gravity model, where additionally the Gauss-Bonnet term non-minimally coupled to a scalar field is included. We prove that inflationary solutions of exponential and power-law types are allowable and we found few examples of them. We also proposed the method of the exact inflationary solutions construction for a single scalar field with given scale factor and Gauss-Bonnet coupling term in the spatially flat Friedmann-Robertson-Walker Universe on the basis of connection with standard inflation and using special anzatses. With one special anzats we presented the system of equations in the form which allowed generation of exact solutions (at least in quadratures) of wide class by setting the scale factor.

Quasinormal modes of Einstein-Gauss-Bonnet-dilaton black holes

We study quasinormal modes of static Einstein-Gauss-Bonnet-dilaton black holes. Both axial and polar perturbations are considered and studied from $l=0$ to $l=3$. We emphasize the difference in the spectrum between the Schwarzschild solutions and dilatonic black holes. At large Gauss-Bonnet coupling constant a small secondary branch of black holes is present, when the dilaton coupling is sufficiently strong. The modes of the primary branch can differ from the Schwarzschild modes up to $10\%$. The secondary branch is unstable and possesses long-lived modes. We address the possible effects of these modes on future observations of gravitational waves emitted during the ringdown phase of astrophysical black holes.

Quasinormal modes of Gauss-Bonnet-AdS black holes: towards holographic description of finite coupling

Here we shall show that there is no other instability for the Einstein-Gauss-Bonnet-anti-de Sitter (AdS) black holes, than the eikonal one and consider the features of the quasinormal spectrum in the stability sector in detail. The obtained quasinormal spectrum consists from the two essentially different types of modes: perturbative and non-perturbative in the Gauss-Bonnet coupling α. The sound and hydrodynamic modes of the perturbative branch can be expressed through their Schwazrschild-AdS limits by adding a linear in α correction to the damping rates: ω≈ReωSAdS −ImωSAdS(1−α·((D+1)(D−4)/2R2))i, where R is the AdS radius. The non-perturbative branch of modes consists of purely imaginary modes, whose damping rates unboundedly increase when α goes to zero. When the black hole radius is much larger than the anti-de Sitter radius R, the regime of the black hole with planar horizon (black brane) is reproduced. If the Gauss-Bonnet coupling α (or used in holography λGB) is not small enough, then the black holes and branes suffer from the instability, so that the holographic interpretation of perturbation of such black holes becomes questionable, as, for example, the claimed viscosity bound violation in the higher derivative gravity. For example, D = 5 black brane is unstable at |λGB| > 1/8 and has anomalously large relaxation time when approaching the threshold of instability.

Holographic entanglement entropy in time dependent Gauss-Bonnet gravity

We investigate entanglement entropy in Gauss-Bonnet gravity following a global quench. It is known that in dynamical scenarios the entanglement entropy probe penetrates the apparent horizon. The goal of this work is to study how far behind the horizon can the entanglement probe reach in a Gauss-Bonnet theory. We find that the behavior is quite different depending on the sign of the Gauss-Bonnet coupling λGB. For λGB > 0 the behavior of the probes is just as in Einstein gravity; the probes do not reach the singularity but asymptote to a locus behind the apparent horizon. We calculate the minimum radial position rmin reached by the probes and show that for λGB > 0 they explore less of the spacetime behind the horizon than in Einstein gravity. On the other hand, for λGB < 0 the results are strikingly different; for early times a new family of solutions appears. These new solutions reach arbitrarily close to the singularity. We calculate the entanglement entropy for the two family of solutions with λGB < 0 and find that the ones that reach the singularity are the ones of less entanglement entropy. Thus, for λGB < 0 the holographic entanglement entropy probes further behind the horizon than in Einstein gravity. In fact, for early times it can explore all the way to the singularity.

Violating the quantum focusing conjecture and quantum covariant entropy bound in d ⩾ 5 dimensions

We study the quantum focussing conjecture (QFC) in curved spacetime. Noting that quantum corrections from integrating out massive fields generally induce a Gauss–Bonnet term, we study Einstein–Hilbert–Gauss–Bonnet gravity and show for spacetime dimensions that weakly-curved solutions can violate the associated QFC for either sign of the Gauss–Bonnet coupling. The nature of the violation shows that—so long as the Gauss–Bonnet coupling is non-zero—it will continue to arise for local effective actions containing arbitrary further higher curvature terms, and when gravity is coupled to generic theories of massive quantum fields. The argument also implies violations of a recently-conjectured form of the generalized covariant entropy bound. The possible validity of the QFC and covariant entropy bound in spacetime dimensions remains open.

Gravitational perfect fluid collapse in Gauss\u2013Bonnet gravity

The Einstein Gauss–Bonnet theory of gravity is the low-energy limit of heterotic super-symmetric string theory. This paper deals with gravitational collapse of a perfect fluid in Einstein–Gauss–Bonnet gravity by considering the Lemaitre–Tolman–Bondi metric. For this purpose, the closed form of the exact solution of the equations of motion has been determined by using the conservation of the stress-energy tensor and the condition of marginally bound shells. It has been investigated that the presence of a Gauss–Bonnet coupling term alpha >0 and the pressure of the fluid modifies the structure and time formation of singularity. In this analysis a singularity forms earlier than a horizon, so the end state of the collapse is a naked singularity depending on the initial data. But this singularity is weak and timelike, which goes against the investigation of general relativity.

Perturbation, non-Gaussianity, and reheating in a Gauss-Bonnet α -attractor model

Motivated by $\alpha$-attractor models, in this paper we consider a Gauss-Bonnet inflation with E-model type of potential. We consider the Gauss-Bonnet coupling function to be the same as the E-model potential. In the small $\alpha$ limit we obtain an attractor at $r=0$ as expected, and in the large $\alpha$ limit we recover the Gauss-Bonnet model with potential and coupling function of the form $\phi^{2n}$. We study perturbations and non-Gaussianity in this setup and we find some constraints on the model's parameters in comparison with PLANCK datasets. We study also the reheating epoch after inflation in this setup. For this purpose, we seek the number of e-folds and temperature during reheating epoch. These quantities depend on the model's parameter and the effective equation of state of the dominating energy density in the reheating era. We find some observational constraints on these parameters.

Reconstruction of the Scalar Field Potential in Inflationary Models with a Gauss-Bonnet term

We study inflationary models with a Gauss-Bonnet term to reconstruct the scalar field potentials and the Gauss-Bonnet coupling functions from the observable quantities. Using the observationally favored relations for both $n_s$ and $r$, we derive the expressions for both the scalar field potentials and the coupling functions. The implication of the blue-tilted spectrum, $n_t>0$, of the primordial tensor fluctuations is discussed for the reconstructed configurations of the scalar field potential and the Gauss-Bonnet coupling.

Boundary causality versus hyperbolicity for spherical black holes in Gauss–Bonnet gravity

We explore the constraints boundary causality places on the allowable Gauss–Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss–Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss–Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss–Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes.

Small dark energy and stable vacuum from Dilaton\u2013Gauss\u2013Bonnet coupling in TMT

In two measures theories (TMT), in addition to the Riemannian measure of integration, being the square root of the determinant of the metric, we introduce a metric-independent density Phi in four dimensions defined in terms of scalars varphi _a by Phi =varepsilon ^{mu nu rho sigma } varepsilon _{abcd} (partial _{mu }varphi _a)(partial _{nu }varphi _b) (partial _{rho }varphi _c) (partial _{sigma }varphi _d). With the help of a dilaton field phi we construct theories that are globally scale invariant. In particular, by introducing couplings of the dilaton phi to the Gauss–Bonnet (GB) topological density , {sqrt{-g}} , phi left( R_{mu nu rho sigma }^2 - 4 R_{mu nu }^2 + R^2 right) , we obtain a theory that is scale invariant up to a total divergence. Integration of the varphi _a field equation leads to an integration constant that breaks the global scale symmetry. We discuss the stabilizing effects of the coupling of the dilaton to the GB-topological density on the vacua with a very small cosmological constant and the resolution of the ‘TMT Vacuum-Manifold Problem’ which exists in the zero cosmological-constant vacuum limit. This problem generically arises from an effective potential that is a perfect square, and it gives rise to a vacuum manifold instead of a unique vacuum solution in the presence of many different scalars, like the dilaton, the Higgs, etc. In the non-zero cosmological-constant case this problem disappears. Furthermore, the GB coupling to the dilaton eliminates flat directions in the effective potential, and it totally lifts the vacuum-manifold degeneracy.

Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid

Gauss-Bonnet holographic fluid is a useful theoretical laboratory to study the effects of curvature-squared terms in the dual gravity action on transport coefficients, quasinormal spectra and the analytic structure of thermal correlators at strong coupling. To understand the behavior and possible pathologies of the Gauss-Bonnet fluid in 3 + 1 dimensions, we compute (analytically and non-perturbatively in the Gauss-Bonnet coupling) its second-order transport coefficients, the retarded two- and three-point correlation functions of the energy-momentum tensor in the hydrodynamic regime as well as the relevant quasinormal spectrum. The Haack-Yarom universal relation among the second-order transport coefficients is violated at second order in the Gauss-Bonnet coupling. In the zero-viscosity limit, the holographic fluid still produces entropy, while the momentum diffusion and the sound attenuation are suppressed at all orders in the hydrodynamic expansion. By adding higher-derivative electromagnetic field terms to the action, we also compute corrections to charge diffusion and identify the non-perturbative parameter regime in which the charge diffusion constant vanishes.

Holographic isotropisation in Gauss-Bonnet gravity

We study holographic isotropisation of homogeneous, strongly coupled, non-Abelian plasmas in Gauss-Bonnet gravity with a negative cosmological constant. We focus on small values of the Gauss-Bonnet coupling parameter λGB and linearise the equations of motion around a time-dependent background solution with λGB = 0. We numerically solve the linearised equations and show that the entire time evolution of the pressure anisotropy can be well approximated by the linear in λGB corrections to the quasinormal mode expansion, even in the cases of high anisotropy. We finally show that, quite generally, the time evolution of the pressure anisotropy with the Gauss-Bonnet term is approximately shifted with respect to the evolution without it, with the sign of the shift being directly related to the sign of the λGB parameter. Combined with the observation that negative λGB captures qualitative features of positive gauge coupling corrections, this suggests that the latter generically increase the isotropisation time of strongly coupled plasmas.

Constraining scalar-Gauss-Bonnet inflation by reheating, unitarity, and Planck data

We revisit the inflationary dynamics in detail for theories with Gauss-Bonnet gravity coupled to scalar functions, in light of the Planck data. Considering the chaotic inflationary scenario, we constrain the parameters of two models involving inflaton-Gauss-Bonnet coupling by current Planck data. For non zero inflaton-Gauss-Bonnet coupling $\beta$, an inflationary analysis provides us a big cosmologically viable region in the space of $(m,\beta)$, where $m$ is the mass of inflaton. However, we study further on constraining $\beta$ arising from reheating considerations and unitarity of tree-level amplitude involving we have studied the constraints on $\beta$ arising from reheating considerations and unitarity of tree level amplitude involving $2$ graviton $\rightarrow 2$ graviton ($h h\rightarrow hh$) scattering. Our analysis, particularly on reheating significantly reduces the parameter space of $(m,\beta)$ for all models. he quadratic Gauss-Bonnet coupling parameter turns out to be more strongly constrained than that of the linear coupling. For the linear Gauss-Bonnet coupling function, we obtain $\beta \lesssim 10^3$, with the condition $\beta (m/M_P)^2 \simeq 10^{-4}$. However, study of the Higgs inflation scenario in the presence of Gauss-Bonnet term turned out to be strongly disfavored.

Anisotopic inflation with a non-abelian gauge field in Gauss-Bonnet gravity

In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless SU(2) gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Gauss-Bonnet framework, a feature of the model for anisotropic inflation supported by a non-abelian gauge field but the effect of Gauss-Bonnet term further enhances or suppresses the generated anisotropy.

Warm-tachyon Gauss–Bonnet inflation in the light of Planck 2015 data

We study a warm-tachyon inflationary model non-minimally coupled to a Gauss-Bonnet term. The general conditions required for reliability of the model are obtained by considerations of a combined hierarchy of Hubble and Gauss-Bonnet flow functions. The perturbed equations are comprehensively derived in the longitudinal gauge in the presence of slow-roll and quasi-stable conditions. General expressions for observable quantities of interest such as the tensor-to-scalar ratio, scalar spectral index and its running are found in the high dissipation regime. Finally, the model is solved using exponential and inverse power-law potentials, which satisfy the properties of a tachyon potential, with parameters of the model being constrained within the framework of the Planck 2015 data. We show that the Gauss-Bonnet coupling constant controls termination of inflation in such a way as to be in good agreement with the Planck 2015 data.

Spherically symmetric brane in a bulk of f(R) and Gauss–Bonnet gravity

Effective gravitational field equations on a four-dimensional brane embedded in a five-dimensional bulk have been considered. Using the Einstein–Hilbert action along with the Gauss–Bonnet correction term, we have derived static spherically symmetric vacuum solution to the effective field equations, first order in the Gauss–Bonnet coupling parameter. The solution so obtained, has one part corresponding to general relativity with an additional correction term, proportional to the Gauss–Bonnet coupling parameter. The correction term modifies the spacetime structure, in particular, the location of the event horizon. Proceeding further, we have derived effective field equations for gravity with Gauss–Bonnet correction term and a static spherically symmetric solution has been obtained. In this case the Gauss–Bonnet term modifies both the event and cosmological horizon of the spacetime. There exists another way of obtaining the brane metric—expanding the bulk gravitational field equations in the ratio of bulk to brane curvature scale and assuming a separable bulk metric ansatz. It turns out that static, spherically symmetric solutions obtained from this perturbative method can be matched exactly, with the solutions derived earlier. This will hold for Einstein–Hilbert plus Gauss–Bonnet as well as for f(R) with the Gauss–Bonnet correction. Implications of these results are discussed.

Phase space analysis for a scalar-tensor model with kinetic and Gauss-Bonnet couplings

We study the phase space for a scalar-tensor string inspired model of dark energy with nonminimal kinetic and Gauss-Bonnet couplings. The form of the scalar potential and of the coupling terms is of the exponential type, which gives rise to appealing cosmological solutions. The critical points describe a variety of cosmological scenarios that go from a matter or radiation dominated universe to a dark energy dominated universe. Trajectories were found in the phase space departing from unstable or saddle fixed points and arriving at the stable scalar field dominated point corresponding to late-time accelerated expansion.