Fluid interpretation of some models of f(R) theory of gravity

Abstract

In the modified theory of gravity, the equivalence of \(\frac{1}{R}\) or \(R^2\) or \(R^{3/2}\) interaction with an ideal fluid in Friedmann–Lemaitre–Robertson–Walker background reduces the field equations to a set of second order equations in terms of density \(\rho \) and pressure p of the fluid with \(p=p(\rho )\). The second order equations yield the evolution identical to the solution obtained from higher derivative gravity. The universe is radiation dominated at sufficiently large densities, while at smaller densities it is accelerating. The \(R^2\) term also shows a deSitter solution.