A Cyclic Cosmological Model Based on the <i>f(ρ)</i> Modified Theory of Gravity

Abstract

We consider FLRW cosmological models for perfect fluid (with ρ as the energy density) in the frame work of the f ( ρ ) modified theory of gravity [V. N. Tunyak, Russ. Phys. J. 21, 1221 (1978); J. R. Ray, L. L. Smalley, Phys. Rev. D. 26, 2615 (1982)]. This theory, with total Lagrangian R - f ( ρ ), can be considered as a cousin of the F ( R ) theory of gravity with total Lagrangian F ( R )- ρ . We can pick proper function forms f ( ρ ) to achieve, as the F ( R ) theory does, the following 4 specific goals, 1) producing a non-singular cosmological model (Ricci scalar and Ricci tensor curvature are bounded); 2) explaining the cosmic early inflation and late acceleration in a unified fashion; 3) passing the solar system tests; 4) unifying the dark matter with dark energy. In addition we also achieve goal number 5) unify the regular matter/energy with dark matter/energy in a seamless fashion. The mathematics is simplified because in the f ( ρ ) theory the leading terms in Einstein ’ s equations are linear in second order derivative of metric wrt coordinates but in the F ( R ) theory the leading terms are linear in fourth order derivative of metric wrt coordinates.