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Register a new userGauss-Bonnet-Chern approach to the averaged Universe
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The standard model of cosmology with postulated dark energy and dark matter sources may be considered as a fairly successful fitting model to observational data. However, this model leaves the question of the physical origin of these dark components open. Fully relativistic contributions that act like dark energy on large scales and like dark matter on smaller scales can be found through generalization of the standard model by spatially averaging the inhomogeneous Universe within general relativity. The spatially averaged 3+1 Einstein equations are effective balance equations that need a closure condition. Heading for closure we here explore topological constraints. Results are straightforwardly obtained for averaged 2+1 model universes. For the relevant 3+1 case, we employ a method based on the Gauss-Bonnet-Chern theorem generalized to Lorentzian spacetimes and implement a sandwich approach to obtain spatial average properties. The 3+1 topological approach supplies us with a new equation linking evolution of scalar invariants of the expansion tensor to the norm of the Weyl tensor. From this we derive general evolution equations for averaged scalar curvature and kinematical backreaction, and we discuss related evolution equations on this level of the hierarchy of averaged equations. We also discuss the relation between topological properties of cosmological manifolds and dynamical topology change, e.g. as resulting from the formation of black holes.
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We construct boson stars in (4+1)-dimensional Gauss-Bonnet gravity. We study the properties of the solutions in dependence on the coupling constants and investigate these in detail. While the thick wall limit is independent of the value of the Gauss-Bonnet coupling, we find that the spiraling behaviour characteristic for boson stars in standard Einstein gravity disappears for large enough values of the Gauss-Bonnet coupling. Our results show that in this case the scalar field can not have arbitrarily high values at the center of the boson star and that it is hence impossible to reach the thin wall limit. Moreover, for large enough Gauss-Bonnet coupling we find a unique relation between the mass and the radius (qualitatively similar to those of neutron stars) which is not present in the Einstein gravity limit.
We propose a novel $k$-Gauss-Bonnet model, in which a kinetic term of scalar field is allowed to non-minimally couple to the Gauss-Bonnet topological invariant in the absence of a potential of scalar field. As a result, this model is shown to admit an isotropic power-law inflation provided that the scalar field is phantom. Furthermore, stability analysis based on the dynamical system method is performed to indicate that this inflation solution is indeed stable and attractive. More interestingly, a gradient instability in tensor perturbations is shown to disappear in this model.
Inflationary era of our Universe can be characterized as semi-classical because it can be described in the context of four-dimensional Einsteinss gravity involving quantum corrections. These string motivated corrections originate from quantum theories of gravity such as superstring theories and include higher gravitational terms as, Gauss-Bonnet and Chern-Simons terms. In this paper we investigated inflationary phenomenology coming from a scalar field, with quadratic curvature terms in the view of GW170817. Firstly, we derived the equations of motion, directly from the gravitational action. As a result, formed a system of differential equations with respect to Hubbles parameter and the inflaton field which was very complicated and cannot be solved analytically, even in the minimal coupling case. Based on the observations from GW170817, which have shown that the speed of the primordial gravitational wave is equal to the speed of light, our equations of motion where simplified after applying this constraint, the slow-roll approximations and neglecting the string corrections. We described the dynamics of inflationary phenomenology and proved that theories with Gauss-Bonnet term can be compatible with recent observations. Also, the Chern-Simons term leads to asymmetric generation and evolution of the two circular polarization states of gravitational wave. Finally, viable inflationary models are presented, consistent with the observational constraints. The possibility of a blue tilted tensor spectral index is briefly investigated.
In this paper, we study the thermodynamics especially the $P$-$V$ criticality of the Friedmann-Robertson-Walker (FRW) universe in the novel 4-dimensional Gauss-Bonnet gravity, where we define the thermodynamic pressure $P$ from the cosmological constant $Lambda$ as $P=-frac{Lambda}{8pi}$. We obtain the first law of thermodynamics and equation of state of the FRW universe. We find that, if the Gauss-Bonnet coupling constant $alpha$ is positive, there is no $P$-$V$ phase transition. If $alpha$ is negative, there are $P$-$V$ phase transitions and critical behaviors within $-1/3leqomegaleq1/3$. Particularly, there are two critical points of the $P$-$V$ criticality in the case $alpha<0,~-1/3<omega<1/3$. We investigate these $P$-$V$ criticality around the critical points, and calculate the critical exponents. We find that these critical exponents in the $-1/3<omegaleq1/3$ case are consistent with those in the mean field theory, and hence satisfy the scaling laws.
The effect of the Gauss-Bonnet term on the existence and dynamical stability of thin-shell wormholes as negative tension branes is studied in the arbitrary dimensional spherically, planar, and hyperbolically symmetric spacetimes. We consider radial perturbations against the shell for the solutions which have the Z${}_2$ symmetry and admit the general relativistic limit. It is shown that the Gauss-Bonnet term shrinks the parameter region admitting static wormholes. The effect of the Gauss-Bonnet term on the stability depends on the spacetime symmetry. For planar symmetric wormholes, the Gauss-Bonnet term does not affect their stability. If the coupling constant is positive but small, the Gauss-Bonnet term tends to destabilize spherically symmetric wormholes, while it stabilizes hypebolically symmetric wormholes. The Gauss-Bonnet term can destabilize hypebolically symmetric wormholes as a non-perturbative effect, however, spherically symmetric wormholes cannot be stable.
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