Abstract
In this work, we present some cosmologically relevant solutions using the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in metric f ( R ) gravity where the form of the gravitational Lagrangian is given by 1 α e α R . In the low curvature limit this theory reduces to ordinary Einstein-Hilbert Lagrangian together with a cosmological constant term. Precisely because of this cosmological constant term this theory of gravity is able to support nonsingular bouncing solutions in both matter and vacuum background. Since for this theory of gravity f ′ and f ″ is always positive, this is free of both ghost instability and tachyonic instability. Moreover, because of the existence of the cosmological constant term, this gravity theory also admits a de-Sitter solution. Lastly we hint towards the possibility of a new type of cosmological solution that is possible only in higher derivative theories of gravity like this one.
Highlights
Investigation of non-singular bouncing cosmological solutions to Einstein field equations has a history that dates back to first half of the twentieth century, and can be attributed to various works of Lemaitre, Tolman, Friedmann and even Einstein himself
We present a bounce mechanism and not a full description of cosmology which includes how physics much prior to bounce is related to the bouncing period, our model can have a transition to low energy general relativity (GR) for small values of the Ricci scalar but we presume such a cross-over to low energy theory may require new physics
It was shown in Ref. [18] that no polynomial f ( R) gravity can simultaneously void both ghost and tachyonic instability for all R. All these examples show that it is very difficult to find a f ( R) which gives rise to a stable cosmological bounce. In this regard we show that the exponential f ( R) gravity theory, as chosen in the present article, can produce perfectly stable cosmological bounces
Summary
Investigation of non-singular bouncing cosmological solutions to Einstein field equations has a history that dates back to first half of the twentieth century, and can be attributed to various works of Lemaitre, Tolman, Friedmann and even Einstein himself (see, e.g., Ref. [1] for early histories of bouncing cosmology). The motivation of the present paper is to present a metric f ( R) theory of gravity, which is free of the above mentioned instabilities, and which can produce a successful cosmological bounce in the early universe. We present a new solution of f ( R) gravity theories which admits a cosmological bounce. Unlike GR, f ( R) theories depend on the second time derivative of the Hubble parameter and one can tune the cosmological development of a model by specifying various values of Ḧ at some specific time These new solutions can produce interesting new model universes. The section concludes the article by summarizing the results obtained
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