More on the initial singularity problem in gravity’s rainbow cosmology

Abstract

Using a one-dimensional minisuperspace model with a dimensionless ratio E E P l , we study the initial singularity problem at the quantum level for the closed rainbow cosmology with a homogeneous, isotropic classical space-time background. We derive the classical Hamiltonian within the framework of Schutz's formalism for an ideal fluid with a cosmological constant. We characterize the behavior of the system at the early stages of the universe evolution through analyzing the relevant shapes for the potential sector of the classical Hamiltonian for various matter sources, each separately modified by two rainbow functions. We show that for both rainbow universe models presented here, there is the possibility of eliminating the initial singularity by forming a potential barrier and static universe for a non-zero value of the scale factor. We investigate their quantum stability and show that for an energy-dependent space-time geometry with energies comparable with the Planck energy, the non-zero value of the scale factor may be stable. It is shown that under certain constraints the rainbow universe model filled with an exotic matter as a domain wall fluid plus a cosmological constant can result in a non-singular harmonic universe. In addition, we demonstrate that the harmonically oscillating universe with respect to the scale factor is sensitive to E E P l and that at high energies it may become stable quantum mechanically. Through a Schrödinger-Wheeler-De Witt (SWD) equation obtained from the quantization of the classical Hamiltonian, we also extract the wave packet of the universe with a focus on the early stages of the evolution. The resulting wave packet supports the existence of a bouncing non-singular universe within the context of gravity's rainbow proposal.

Combined Rastall and rainbow theories of gravity with applications to neutron stars

“…In the literature, the choice of the these functions is theoretically and phenomenologically motivated. For example, in [38,39] the authors obtain solutions corresponding to a nonsingular universe through the choice of functions Ξ = 1 and Σ = √ 1 + x 2 . On the other hand, an exponential form of rainbow is applied in the study of gamma ray burst [39,40].…”

Dirac oscillator in the cosmic string spacetime in the context of gravity’s rainbow

“…where we shall consider a first order parameter for our purposes. These rainbow functions fit the requirement of a constant velocity of light and solves the horizon problem puzzle [9,10,12,22]. In this first scenario of gravity's rainbow, described by the rainbow functions in Eq.…”

“…Let us now construct a scenario of the cosmic string gravity's rainbow by using the following rainbow functions [9,10,12,22]:…”

“…The semi-classical approach of Gravity's Rainbow has been used, for instance, to investigate Cosmological and Astrophysical phenomena in a variety of contexts ranging from Friedmann-Robertson-Walker Universe [9][10][11][12], black hole thermodynamics [13][14][15][16][17] to neutron stars' properties [18], massive scalar field in the Schwarzschild metric [19][20][21] and Casimir effect [22]. These works show us a growing interest in the semi-classical approach of Rainbow's Gravity as to investigate quantum gravity effects through corrections to the dispersion relation of relativistic quantum fields.…”

Non-singular model universe from a perfect fluid scalar-metric cosmology

“…As an advantage, these canonical transformations let us to follow a dynamical system with more parameters [44,47].…”