We extend our previous study on the effects of an information-theoretically motivated nonlinear correction to the Wheeler-deWitt equation in the minisuperspace scheme for FRW universes. Firstly we show that even when the geometry is hyperbolic, and matter given by a cosmological constant, the nonlinearity can still provide a barrier to screen the initial singularity, just as in the case for flat universes. Secondly, in the flat case we show that singularity avoidance in the presence of a free massless scalar field is perturbatively possible for a very large class of initially unperturbed quantum states, generalising our previous discussion using Gaussian states.
We extend recent discussions of singularity avoidance in quantum gravity from isotropic to anisotropic cosmological models. The investigation is done in the framework of quantum geometrodynamics (Wheeler-DeWitt equation). We formulate criteria of singularity avoidance for general Bianchi class A models and give explicit and detailed results for Bianchi I models with and without matter. We find that the classical singularities can generally be avoided in these models.
We consider the fourth-order differential theory of gravitation to treat the problem of singularity avoidance: studying the short-distance behaviour in the case of black-holes and the big-bang we are going to see a way to attack the issue from a general perspective.
The purpose of this work is to investigate the consequences of quantum gravity for the singularity problem. We study the higher-derivative terms that invariably appear in any quantum field theoretical model of gravity, handling them both non-perturbatively and perturbatively. In the former case, by computing the contributions of the additional degrees of freedom to a congruence of geodesics, we show that the appearance of singularities is no longer a necessity. In the latter, which corresponds to treating the quantised general relativity as an effective field theory, we generalise the Hawking-…
We investigate the fate of the classical singularity in a collapsing dust cloud. For this purpose, we quantize the marginally bound Lemaitre-Tolman-Bondi model for spherically-symmetric dust collapse by considering each dust shell in the cloud individually, taking the outermost shell as a representative. Because the dust naturally provides a preferred notion of time, we can construct a quantum mechanical model for this shell and demand unitary evolution for wave packets. It turns out that the classical singularity can generically be avoided provided the quantization ambiguities fulfill some we…
We propose a new version of the $AdS/CFT$ correspondence, where polymer structures similar to Loop Quantum Cosmology spin networks can be induced on an isotropic and homogeneous flat Randall-Sundrum II brane, corresponding to the holographic duals of closed string states living in the bulk. Such polymer structures drive a discrete evolution of the braneworld spacetime that leads to the regularization of the Big Bang singularity. The present results show that the $AdS/CFT$ conjecture can be a possible bridge between String theory and Loop Quantum Gravity.
Using a new procedure based on Kummer's Confluent Hypergeometric Functions, we investigate the question of singularity avoidance in loop quantum gravity (LQG) in the context of U$(1)^3$ complexifier coherent states and compare obtained results with already existing ones. Our analysis focuses on the dynamical operators, denoted by q(r), whose products are the analogue of the inverse scale factor in LQG and also play a pivotal role for other dynamical operators such as matter Hamiltonians or the Hamiltonian constraint. For graphs of cubic topology and linear powers in q(r), we obtain the correct…
Models of the universe with arbitrary (non gravitational) interaction between the components of the cosmic fluid: the phantom energy and the background, are investigated. A general form of the interaction that is inspired in scalar-tensor theories of gravity is considered. No specific model for the phantom fluid is assumed. We concentrate our investigation on solutions that are free of the coincidence problem. We found a wide region in the parameter space where the solutions are free of the big rip singularity also. Physical arguments, together with arguments based on the analysis of the obser…
In a previous paper, some of us studied general relativistic homogeneous gravitational collapses for dust and radiation, in which the density profile was replaced by an effective density justified by some quantum gravity models. It was found that the effective density introduces an effective pressure that becomes negative and dominant in the strong-field regime. With this set-up, the central singularity is replaced by a bounce, after which the cloud starts expanding. Motivated by the fact that in the classical case homogeneous and inhomogeneous collapse models have different properties, here w…
We present a quantum model of the vacuum Bianchi-IX dynamics. It is based on four main elements. First, we use a compound quantization procedure: an affine coherent state quantization for isotropic variables and a Weyl quantization for anisotropic ones. Second, inspired by standard approaches in molecular physics, we make an adiabatic approximation (Born-Oppenheimer-like approximation). Third, we expand the anisotropy potential about its minimum in order to deal with its harmonic approximation. Fourth, we develop an analytical treatment on the semiclassical level. The resolution of the classic…
We present a class of cosmological solutions for a generalized teleparallel gravity with, $f(T)=T+\tildeα(-T)^n$, where $\tildeα$ is some parameter and $n$ is an integer or half-integer. Choosing $\tildeα \sim G^{n-1}$, where $G$ is the gravitational constant, and working with an equation of state $p=w\, ρ$, one obtains a cosmological solution with multiple branches. The dynamics of the solution describes standard cosmology at late times, but the higher-torsion correction changes the nature of the initial singularity from big bang to a sudden singularity. The milder behavior of the sudden sing…
The standard $Λ$CDM model despite its agreement with observational data still has some issues unaddressed, lie the problem of initial singularity. Solving that problem usually requires modifications of general relativity. However, there appeared the Hořava-Lifshitz (HL) theory of gravity, in which equations governing cosmological evolution include a new term scaling similarly as dark radiation term in the Friedmann equations, enabling a bounce of the universe instead of initial singularity. This review describes past works on a stability of such a bounce in different formulations of HL theory,…
We evaluate the physical viability and logical strength of an array of putative criteria for big bang singularity resolution in quantum cosmology. Based on this analysis, we propose a mutually consistent set of constitutive conditions, which we argue should be taken to jointly define `global' and `local' big bang singularity resolution in this context. Whilst the present article will focus exclusively on evaluating resolution criteria for big bang singularities in the context of finite dimensional models of quantum cosmology, it is also hoped that the core features of our analysis will be exte…
Interest in cosmological singularities has remarkably grown in recent times, particularly on future singularities with the discovery of late-time acceleration of the universe and dark energy. While such explorations have previously been done in various modified gravity and quantum gravitationally inspired cosmologies (besides standard general relativistic cosmology), no such an endeavour has been taken up till now in the realms of renormalization group approaches to cosmology and we have hence took up on this journey. In this work, we consider the formation of cosmological singularities in an …
