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arXiv · 1602.04397

Cosmological singularity theorems for $f(R)$ gravity theories

Ivo Alani·Osvaldo Santillan
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Abstract

In the present work some generalizations of the Hawking singularity theorems in the context of $f(R)$ theories are presented. The assumptions are of these generalized theorems is that the matter fields satisfy the conditions $\bigg(T_{ij}-\frac{g_{ij}}{2} T\bigg)k^i k^j\geq 0$ for any generic unit time like field, that the scalaron takes bounded positive values during its evolution, and that the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper surface $Σ$ for which the expansion parameter $θ$ of the geodesic congruence emanating orthogonally from $Σ$ satisfies some specific conditions, it may be shown that the resulting space time is geodesically incomplete. Some mathematical results of reference \cite{fewster} are very important for proving this. The generalized theorems presented here apply directly some specific models such as the Hu-Sawicki or Starobinsky ones \cite{especif3}, \cite{capoziello4}. However, for other scenarios, some extra assumptions should be implemented for the geodesic incompleteness to take place. However, the negation of the hypothesis of these results does not necessarily imply that a singularity is absent, but that other mathematical results should be considered to prove that.

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BibTeXRIS

Ivo Alani, Osvaldo Santillan. 2016-05-13. Cosmological singularity theorems for $f(R)$ gravity theories. https://doi.org/10.1088/1475-7516%2F2016%2F05%2F023

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