Gauss–Bonnet cosmology with induced gravity and a non-minimally coupled scalar field on the brane (original) (raw)
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Causal cosmology with braneworld gravity including Gauss Bonnet coupling
Modern Physics Letters A, 2020
Causal cosmological evolutions in Randall Sundrum type II (RS) braneworld gravity with Gauss Bonnet coupling and dissipative effects are discussed here. Causal theory of dissipative effects are illustrated by Full Israel Stewart theory are implemented. We consider the numerical solutions of evolutions and analytic solutions as a special case for extremely non-linear field equation in Randall Sundrum type II braneworld gravity with Gauss Bonnet coupling. Cosmological models admitting Power law expansion, Exponential expansion and evolution in the vicinity of the stationary solution of the universe are investigated for Full Israel Stewart theory. Stability of equilibrium or fixed points related to the dynamics of evolution in Full Israel Stewart theory in Randall Sundrum type II braneworld gravity together with Gauss Bonnet coupling are disclosed here.
International Journal of Theoretical Physics, 2012
We study a model of scalar field with kinetic terms non-minimally coupled to to the curvature, and the scalar field coupled to the Gauss Bonnet 4-dimensional invariant. A variety of solutions are found, giving rise to different cosmological scenarios. A unified description of early time matter (radiation) dominance with transitions to late time quintessence and phantom phases have been made. Among others, we found solutions unifying asymptotically the early power law behavior and late time cosmological constant. Solutions of Chaplygin gas and generalized Chaplygin gas cosmologies have also been found.
Journal of Cosmology and Astroparticle Physics, 2007
The Gauss-Bonnet (GB) curvature invariant coupled to a scalar field φ can lead to an exit from a scaling matter-dominated epoch to a late-time accelerated expansion, which is attractive to alleviate the coincident problem of dark energy. We derive the condition for the existence of cosmological scaling solutions in the presence of the GB coupling for a general scalar-field Lagrangian density p(φ, X), where X = −(1/2)(∇φ) 2 is a kinematic term of the scalar field. The GB coupling and the Lagrangian density are restricted to be in the form f (φ) ∝ e λφ and p = Xg(Xe λφ ), respectively, where λ is a constant and g is an arbitrary function. We also derive fixed points for such a scaling Lagrangian with a GB coupling f (φ) ∝ e µφ and clarify the conditions under which the scaling matter era is followed by a de-Sitter solution which can appear in the presence of the GB coupling. Among scaling models proposed in the current literature, we find that the models which allow such a cosmological evolution are an ordinary scalar field with an exponential potential and a tachyon field with an inverse square potential, although the latter requires a coupling between dark energy and dark matter.
Gauss-Bonnet Gravity in D=4 Without Gauss-Bonnet Coupling to Matter - Cosmological Implications
2018
We propose a new model of D=4 Gauss-Bonnet gravity. To avoid the usual property of the integral over the standard D=4 Gauss-Bonnet scalar becoming a total derivative term, we employ the formalism of metric-independent non-Riemannian spacetime volume elements which makes the D=4 Gauss-Bonnet action term non-trivial without the need to couple it to matter fields unlike the case of ordinary D=4 Gauss-Bonnet gravity models. The non-Riemannian volume element dynamically triggers the Gauss-Bonnet scalar to be an arbitrary integration constant M on-shell, which in turn has several interesting cosmological implications: (i) It yields specific solutions for the Hubble parameter and the Friedmann scale factor as functions of time, which are completely independent of the matter dynamics, i.e., there is no back reaction by matter on the cosmological metric; (ii) For M>0 it predicts a "coasting"-like evolution immediately after the Big Bang, and it yields a late universe with dynami...
Emergent Universe Scenario in Modified Gauss-Bonnet Gravity
arXiv: Cosmology and Nongalactic Astrophysics, 2020
We present modified Gauss-Bonnet gravity without matter in four dimensions which accommodates flat emergent universe (EU) obtained in Einstein's general theory of gravity with a non-linear equation of state. The EU model is interesting which is free from big-bang singularity with other observed features of the universe. It is assumed that the present universe emerged out from a static Einstein universe phase exists in the infinite past. To obtain a flat EU model we reconstructed mimetic modified f(G)f(G)f(G)-gravity ($G$ representing Gauss-Bonnet terms) without matter. The functional form of f(G)-gravity is determined which accommodates the early inflation and late accelerating phases without matter.
2011
We consider warped five-dimensional thick braneworlds with four-dimensional Poincaré invariance originated from bulk scalar matter non-minimally coupled to gravity plus a Gauss-Bonnet term. The background field equations as well as the perturbed equations are investigated. A relationship between 4D and 5D Planck masses is studied in general terms. By imposing finiteness of the 4D Planck mass and regularity of the geometry, the localization properties of the tensor modes of the perturbed geometry are analysed to first order, for a wide class of solutions. In order to explore the gravity localization properties for this model, the normalizability condition for the lowest level of the tensor fluctuations is analysed. It is found that for the examined class of solutions, gravity in four dimensions is recovered if the curvature invariants are regular and the 4D Planck mass is finite. It turns out that both the addition of the Gauss-Bonnet term and the non-minimal coupling between the scalar field and gravity reduce the value of the 4D Planck mass compared to its value when the scalar field and gravity are minimally coupled and the Gauss-Bonnet term is absent. The above discussed analysis depends on the explicit form of the scalar field (through its non-minimal coupling to gravity), making necessary the construction of explicit solutions in order to obtain results in closed form, and is illustrated with some examples which constitute smooth generalizations of the so-called Randall-Sundrum braneworld model. These solutions were obtained by making use of a detailed singular perturbation theory procedure with respect to the non-minimal coupling parameter between the scalar field and gravity, a difficult task that we managed to perform in such a way that all the physically meaningful conditions for the localization of gravity are fully satisfied. From the obtained explicit solutions, we found an interesting effect: when we consider a non-minimally coupled scalar-tensor theory, there arise solutions for which the symmetries of the background geometry are not preserved by the scalar matter energy density distribution. In particular, the value of the ‘5D cosmological constant’ of the asymptotically AdS5 spacetime (which is even with respect to the extra coordinate) gets different contributions at -∞ and +∞ from the asymptotic values of the self-interaction potential of the scalar field. Thus, an asymmetric energy density distribution of scalar matter gives rise to a spacetime which is completely even with respect to the fifth coordinate, in contrast to braneworld models derived from minimally coupled scalar-tensor theories, where both entities possess the same symmetry.
Physical Review D, 2007
We extend the covariant analysis of the brane cosmological evolution in order to take into account, apart from a general matter content and an induced-gravity term on the brane, a Gauss-Bonnet term in the bulk. The gravitational effect of the bulk matter on the brane evolution can be described in terms of the total bulk mass as measured by a bulk observer at the location of the brane. This mass appears in the effective Friedmann equation through a term characterized as generalized dark radiation that induces mirage effects in the evolution. We discuss the normal and self-accelerating branches of the combined system. We also derive the Raychaudhuri equation that can be used in order to determine if the cosmological evolution is accelerating.
Towards inflation and dark energy cosmologies from modified Gauss–Bonnet theory
Journal of Cosmology and Astroparticle Physics - JCAP, 2006
We consider a physically viable cosmological model that has a field dependent Gauss–Bonnet coupling in its effective action, in addition to a standard scalar field potential. The presence of such terms in the four dimensional effective action gives rise to several novel effects, such as a four dimensional flat Friedmann–Robertson–Walker universe undergoing a cosmic inflation at the early epoch, as well as a cosmic acceleration at late times. The model predicts, during inflation, spectra of both density perturbations and gravitational waves that may fall well within the experimental bounds. Furthermore, this model provides a mechanism for reheating of the early universe, which is similar to a model with some friction terms added to the equation of motion of the scalar field, which can imitate energy transfer from the scalar field to matter.
Cosmological perturbations from braneworld inflation with a Gauss-Bonnet term
Physical Review D, 2004
Braneworld inflation is a phenomenology related to string theory that describes high-energy modifications to general relativistic inflation. The observable universe is a braneworld embedded in 5-dimensional anti de Sitter spacetime. When the 5-dimensional action is Einstein-Hilbert, we have a Randall-Sundrum type braneworld. The amplitude of tensor and scalar perturbations from inflation is strongly increased relative to the standard results, although the ratio of tensor to scalar amplitudes still obeys the standard consistency relation. If a Gauss-Bonnet term is included in the action, as a high-energy correction motivated by string theory, we show that there are important changes to the Randall-Sundrum case. We give an exact analysis of the tensor perturbations. They satisfy the same wave equation and have the same spectrum as in the Randall-Sundrum case, but the Gauss-Bonnet change to the junction conditions leads to a modified amplitude of gravitational waves. The amplitude is no longer monotonically increasing with energy scale, but decreases asymptotically after an initial rise above the standard level. Using an approximation that neglects bulk effects, we show that the amplitude of scalar perturbations has a qualitatively similar behaviour to the tensor amplitude. In addition, the tensor to scalar ratio breaks the standard consistency relation.
Higher-dimensional cosmology with Gauss-Bonnet terms and the cosmological-constant problem
Physical Review D, 1990
Cosmological solutions of field equations derived from a ten-dimensional (10D) action containing higher-derivative terms in the Gauss-Bonnet combination have been studied. An attempt has been made to construct a scenario which includes a spontaneous compactification and an inflationary epoch followed by a four-dimensional radiation-dominated stage. It is noted that one can have a realistic scenario, provided there is an inflationary stage of the early 10D universe. A mechanism is suggested which makes the 4D cosmological constant small. The action considered is different from the superstring-corrected action. The study reveals a rich structure of the theory due to the presence of Gauss-Bonnet terms, although one gets back the usual Einstein equation in 4D at a large time.