 2138 Vaibhav R. Kalvakota
 Investigating f(R) gravity and cosmologies
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Jul 11, 21

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Abstract. The f (R) theory of gravity is an extended theory of gravity that is based on general relativity in the simplest case of $f(R) = R$. This theory extends such a function of the Ricci scalar into arbitrary functions that are not necessarily linear, i.e. could be of the form $f(R) = lpha R^{2}$. The action for such a theory would be $S_{EH} = rac{1}{2k} \int f(R) + L^{m}\; d^{4}x\sqrt{−g}$, where $S_{EH}$ is the EinsteinHilbert action for our theory, $g$ is the determinant of the metric tensor $g_{\mu
u}$ and $L^{m}$ is the Lagrangian density for matter. In this paper, we will look at some of the physical implications of such a theory, and the importance of such a theory in cosmology and in understanding the geometric nature of such f (R) theories of gravity.
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