Abstract
The Big Bang initial singularity problem can be solved by means of bouncing solutions. In the context of extended theories of gravity, we will look for covariant effective actions whose field equations contain up to fourth-order derivatives of the metric tensor. In finding such bouncing solutions, we will make use of an order reduction technique based on a perturbative approach. Reducing the order of the field equations to second-order, we are able to find solutions which are perturbatively close to General Relativity. We will build the covariant effective actions of the resulting order reduced theories.
Highlights
The classical theory of Big Bang describes the beginning of the Universe as an initial singularity wherein the temperature and the density assume an infinite value
In the framework of f (R, P, Q) extended theory of gravity, we provide specific cosmological model reproducing the effective Friedmann equation of Loop Quantum Cosmology (LQC)
We are able to find additive contributions to the Ricci scalar building a theory which is perturbatively close to General Relativity (GR)
Summary
The classical theory of Big Bang describes the beginning of the Universe as an initial singularity wherein the temperature and the density assume an infinite value. The most interesting case is for w = 1, which correspond to a massless scalar field in LQC In this framework, we can write the second effective Friedmann equation as follows a = − 1 κ (ρ + 3p) 1 − 2 2ρ + 3p ρ a6 ρ + 3p ρc. We can connect the LQC correction of Equation (1) to the additional contributions coming from the curvature energy-momentum tensor (characterizing extended theories of gravity) by requiring that the modified Friedmann equation mimics Equation (1) This connection is done by using a perturbative approach, having GR as zeroth o. Once the perturbation parameter has been introduced, we compare the term −κρ2/3ρc of Equation (1) to T0(0φ), where T0(0φ) is the 0-0 component of the effective energy-momentum tensor evaluated at the zeroth perturbative order in , in a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) background. To better understand what happens when φ is a multivariable function, we apply the method to a general fourth-order theory of gravity, which represents the generalization of all the works present in literature, until today
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