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Register a new userNonsingular bouncing cosmology from general relativity: Scalar metric perturbations
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We derive the equations of motion for scalar metric perturbations in a particular nonsingular bouncing cosmology, where the big bang singularity is replaced by a spacetime defect with a degenerate metric. The adiabatic perturbation solution is obtained for nonrelativistic hydrodynamic matter. We get the same result by working with conformal coordinates. This last method is also valid for vector and tensor metric perturbations, and selected results are presented. We, finally, discuss several new effects from the linear perturbations of this nonsingular bouncing cosmology, such as across-bounce information transfer and the possible imprint on cosmological perturbations from a new phase responsible for the effective spacetime defect.
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We investigate a particular type of classical nonsingular bouncing cosmology, which results from general relativity if we allow for degenerate metrics. The simplest model has a matter content with a constant equation-of-state parameter and we get the modified Hubble diagrams for both the luminosity distance and the angular diameter distance. Based on these results, we present a Gedankenexperiment to determine the length scale of the spacetime defect which has replaced the big bang singularity. A possibly more realistic model has an equation-of-state parameter which is different before and after the bounce. This last model also provides an upper bound on the defect length scale.
We in this paper investigate the formation and evolution of primordial black holes (PBHs) in nonsingular bouncing cosmologies. We discuss the formation of PBH in the contracting phase and calculate the PBH abundance as a function of the sound speed and Hubble parameter. Afterwards, by taking into account the subsequent PBH evolution during the bouncing phase, we derive the density of PBHs and their Hawking radiation. Our analysis shows that nonsingular bounce models can be constrained from the backreaction of PBHs.
An old question surrounding bouncing models concerns their stability under vector perturbations. Considering perfect fluids or scalar fields, vector perturbations evolve kinematically as $a^{-2}$, where $a$ is the scale factor. Consequently, a definite answer concerning the bounce stability depends on an arbitrary constant, therefore, there is no definitive answer. In this paper, we consider a more general situation where the primeval material medium is a non-ideal fluid, and its shear viscosity is capable of producing torque oscillations, which can create and dynamically sustain vector perturbations along cosmic evolution. In this framework, one can set that vector perturbations have a quantum mechanical origin, coming from quantum vacuum fluctuations in the far past of the bouncing model, as it is done with scalar and tensor perturbations. Under this prescription, one can calculate their evolution during the whole history of the bouncing model, and precisely infer the conditions under which they remain linear before the expanding phase. It is shown that such linearity conditions impose constraints on the free parameters of bouncing models, which are mild, although not trivial, allowing a large class of possibilities. Such conditions impose that vector perturbations are also not observationally relevant in the expanding phase. The conclusion is that bouncing models are generally stable under vector perturbations. As they are also stable under scalar and tensor perturbations, we conclude that bouncing models are generally stable under perturbations originated from quantum vacuum perturbations in the far past of their contracting phase.
We present a dynamical model for a time-asymmetric nonsingular bounce with a post-bounce change of the effective equation-of-state parameter. Specifically, we consider a scalar-field model with a time-reversal-noninvariant effective potential.
We explore General Relativity solutions with stealth scalar hair in general quadratic higher-order scalar-tensor theories. Adopting the assumption that the scalar field has a constant kinetic term, we derive in a fully covariant manner a set of conditions under which the Euler-Lagrange equations allow General Relativity solutions as exact solutions in the presence of a general matter component minimally coupled to gravity. The scalar field possesses a nontrivial profile, which can be obtained by integrating the condition of constant kinetic term for each metric solution. We demonstrate the construction of the scalar field profile for several cases including the Kerr-Newman-de Sitter spacetime as a general black hole solution characterized by mass, charge, and angular momentum in the presence of a cosmological constant. We also show that asymptotically anti-de Sitter spacetimes cannot support nontrivial scalar hair.
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