We propose a gravitational model with a Brans-Dicke-type scalar field having, in the would-be action, a "wrong-sign" kinetic term and a quartic interaction term. In a cosmological context, we obtain, depending on the boundary conditions, either the Friedmann solution or a kink-bounce solution. The expanding-universe Friedmann solution has a big bang curvature singularity, whereas the kink-bounce solution has a nonsingular bouncing behavior of the cosmic scale factor. The bounce occurs precisely at the moment when the scalar field of the kink-type configuration goes through zero, making for a vanishing effective gravitational coupling.
The large-$N$ master field of the Lorentzian IIB matrix model can, in principle, give rise to a particular degenerate metric relevant to a regularized big bang. The length parameter of this degenerate metric is then calculated in terms of the IIB-matrix-model length scale.
The big bang singularity of the expanding-universe Friedmann solution of the Einstein gravitational field equation can be regularized by the introduction of a degenerate metric and a nonzero length scale $b$. The result is a nonsingular bounce of the cosmic scale factor with a contracting prebounce phase and an expanding postbounce phase. The corresponding maximum values of the curvature and the energy density occur at the moment of the bounce and are proportional to powers of $1/b$. This article presents a detailed calculation of the dynamics of such a nonsingular bounce. In addition, a compa…
Following up on earlier work on the regularization of the singular Schwarzschild solution, we now apply the same procedure to the singular Friedmann solution. Specifically, we are able to remove the divergences of the big bang singularity, at the price of introducing a 3-dimensional spacetime defect with a vanishing determinant of the metric. This particular regularization also suggests the existence of a "pre-big-bang" phase.
We present a simplified dynamic-vacuum-energy model for a time-symmetric Milne-like universe. The big bang singularity in this simplified model, like the one in a previous model, is just a coordinate singularity with finite curvature and energy density. We then calculate the dynamic behavior of scalar metric perturbations and find that these perturbations destabilize the big bang singularity.
We investigate a particular regularization of big bang singularity, which remains within the domain of 4-dimensional general relativity but allowing for degenerate metrics. We study the geodesics and geodesic congruences in the modified Friedmann-Lemaître-Robertson-Walker universe. In particular, we calculate the expansion of timelike and null geodesic congruences. Based on these results, we also briefly discuss the cosmological singularity theorems.
The Pre-Big Bang cosmology inspired generations of cosmologists in attempts to cure the initial Big Bang singularity using a fundamental length scale as proposed by String Theory. The existence of a phase of collapse/inflation with increasing curvature followed by a cosmic bounce has been proposed as an alternative to standard inflation in the solution of the horizon and curvature problems. However the generation of a nearly scale-invariant spectrum of perturbations is not an automatic prediction of such scenarios. In this paper I review some general statements about the evolution of perturbat…
After a brief review of current scenarios for the resolution and/or avoidance of the Big Bang, an alternative hypothesis is put forward implying an infinite increase in complexity towards the initial singularity. This may result in an effective non-calculability which would present an obstruction to actually reaching the beginning of time. This proposal is motivated by the appearance of certain infinite-dimensional duality symmetries of indefinite Kac--Moody type in attempts to unify gravity with the fundamental matter interactions, and deeply rooted in properties of Einstein's theory.
We present a short introduction to a non-standard cosmological scenario motivated by the duality symmetries of string theory, in which the big bang singularity is replaced with a "big bounce" at high but finite curvature. The bouncing epoch is prepared by a long (possibly infinitely extended) phase of cosmic evolution, starting from an initial state asymptotically approaching the string perturbative vacuum.
The necessary and sufficient condition for the absence of particle horizons in a big bang Friedmann-Robertson-Walker universe is provided. It happens to be a "smooth big bang" initial condition: the proper time derivative of the expansion factor $a(t)$ must be finite at the big bang. Equivalently, the energy density must not diverge faster than $a^{-2}$ at the big bang. This is just an initial condition: only the scale factor asymptotic behavior at the very moment of the big bang matters. The causal connection between remote space regions could then take place immediately after the big bang. E…
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…
A simple model for a scalar field and gravity admits homogeneous isotropic cosmological solutions which cross the Big Bang singularity. In the scaling frame with field dependent effective Planck mass these solutions are regular. They become singular in the Einstein frame with fixed Planck mass. This field singularity arises since the field transformation of the metric to the Einstein frame is singular at the crossing point of a vanishing scalar field. No physical singularity is present for these solutions. Within general models with no more than two derivatives we find that the possibility of …
A 5-dimensional gravity theory, motivated by the brane world picture, with factorisable metric and with Kaluza scalar $G_{55}(r)$, is shown to give rise to a positive contribution to the Raychaudhuri equation. This inhibits the focusing of geodesics and possibly cause non-focusing of the geodesics. This feature is translated into the situation in which the universe has an infinite age and hence no beginning avoiding the big bang singularity.
We show how to regularize the big bang singularity in the presence of random perturbations modeled by Brownian motion using stochastic methods. We prove that the physical variables in a contracting universe dominated by a scalar field can be continuously and uniquely extended through the big bang as a function of time to an expanding universe only for a discrete set of values of the equation of state satisfying special co-prime number conditions. This result significantly generalizes a previous result \cite{Xue:2014} that did not model random perturbations. This result implies that the extensi…
We argue that the Big Bang can be understood as a type of mirror. We show how reflecting boundary conditions for spinors and higher spin fields are fixed by local Lorentz and gauge symmetry, and how a temporal mirror (like the Bang) differs from a spatial mirror (like the AdS boundary), providing a possible explanation for the observed pattern of left- and right-handed fermions. By regarding the Standard Model as the limit of a minimal left-right symmetric theory, we obtain a new, cosmological solution of the strong $CP$ problem, without an axion.
