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Regularized big bang singularity: Geodesic congruences

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 Added by Zi-Liang Wang
 Publication date 2021
  fields Physics
and research's language is English
 Authors Z.L. Wang




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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-Lema^itre-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.

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218 - F.R. Klinkhamer 2020
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.
105 - F.R. Klinkhamer , Z.L. Wang 2019
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108 - F. D. Albareti 2012
We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null geodesics. In particular, we focus on the space-time geometry contribution to this equation. By straightforward calculation from the metric of a Robertson-Walker cosmological model, it follows that in an accelerated expanding Universe the space-time contribution to the Raychaudhuri equation is positive for the fundamental congruence, favoring a non-focusing of the congruence of geodesics. However, the accelerated expansion of the present Universe does not imply a tendency of the fundamental congruence to diverge. It is shown that this is in fact the case for certain congruences of timelike geodesics without vorticity. Therefore, the focusing of geodesics remains feasible in an accelerated expanding Universe. Furthermore, a negative contribution to the Raychaudhuri equation from space-time geometry which is usually interpreted as the manifestation of the attractive character of gravity is restored in an accelerated expanding Robertson-Walker space-time at high speeds.
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