A Scenario for a Singularity-free Generic Cosmological Solution

Abstract

We develop a scenario for the emergence of a non-singular generic cosmological solution based on the a WKB characterization of one of the two anisotropy degrees of freedom. We investigate the dynamics of the so-called inhomogeneous mixmaster in the "corner" configuration and inferring that one of the two anisotropic variables becomes small enough to explore the uncertainty principle.Then, we apply a standard WKB approximation to the dynamics of the Universe which has macroscopic volume, one macroscopic anisotropy and one microscopic quantum degree of freedom.Our study demonstrates the possibility that the Universe acquires a non-singular classical behavior, retaining the quantum degree of freedom as a small oscillating ripple on a stationary Universe. The role of the so-called "fragmentation process" is also taken into account in outlining the generality of such a behavior in independent local space regions.

Big-bounce and future time singularity resolution in Bianchi I: the projective invariant Nieh-Yan case

“…This, possibly, suggests a mechanism for circumventing the inconsistencies which usually arise when one tries to implement symmetries, like the projective invariance, in the presence of matter fields which couple to the connection [55]. Finally, we see that at the first order in perturbation (63) implies in vacuum δφ ∼ δψ, and the inspection of (60) suggests that in this case the Immirzi field could actually mimic the scalar polarization of gravitational waves in metric f (R) gravity (see [78,79] for details). On the other hand, observations on gravitational waves propagation [80] and Solar System dynamics [81,82] put severe constraints on the mass of additional scalar degrees of freedom, which for many purposes can be satisfactorily considered massless.…”

“…In this regard, then, consider for (37) the F (R)+N Y * model in vacuum (T = 0), identified by λ = 1 and the condition ∂V /∂ψ = 0 (or V 2 (ψ) = 0, see below). In this case equation (63) simply reads φ = φ(X). Direct substitution of the latter into (54) yields the equivalence at the Lagrangian level with (64), upon identification of the DHOST scalar field ϕ with the Immirzi field and considering the following functional choices:…”

“…For concreteness, we consider a quadratic correction (recall that the theory relies on a Palatini approach) because this choice is natural in the spirit of extending the GR Lagrangian to the f (R) domain and considering a Taylor series expansion. The main result provided by our semi-analytical study of the Bianchi I model consists on the emergence of a classical bouncing cosmology (see also [44,[63][64][65][66][67][68][69]) for negative values of the parameter controlling the quadratic correction to the Ricci scalar. However, the interest for the present case is due to the presence of three degrees of freedom, each of them contributing, with its own specific behavior, to the universe volume dynamics.…”

Quantum Dynamics of the Isotropic Universe in the Metric f(R) Gravity

“…The Bianchi IX model is of particular interest because it admits the isotropic limit and provides a valuable minisuperspace model for the generic inhomogeneous universe [30,31]. Thus, the present study suggests that the proposed dynamical paradigm must be extended to more general cosmological models, in order to understand if, adopting the non-minimally coupled scalar field of the f (R) gravity as physical clock, allows a tendency of the universe volume to a classical limit, even in the presence of anisotropy degrees of freedom.…”

Big bounce and future time singularity resolution in Bianchi I cosmologies: The projective invariant Nieh-Yan case

“…The main result provided by our semianalytical study of the Bianchi I model consists on the emergence of a classical bouncing cosmology (see also [43,[64][65][66][67][68][69][70]) for negative values of the parameter controlling the quadratic correction to the Ricci scalar. However, the interest for the present case is due to the presence of 3 degrees of freedom, each of them contributing, with its own specific behavior, to the universe volume dynamics.…”