Constructing a Classically Stable Non-singular Cyclic Cosmology

Abstract

Bouncing cosmology is a mechanism for flattening, isotropizing, and homogenizing the universe. A scalar field with a deeply negative potential causes the universe to slowly contract and dilutes any initial anisotropy, inhomogeneity, or curvature. Then by violating the null energy condition (NEC) the universe is brought back to expansion. This is achieved using Horndeski gravity to deviate from Einstein gravity for a relatively short period. We propose two kinds of cyclic cosmology scenarios in which the above mechanism occurs periodically in perpetuity. In the first, the scalar field $\phi$ oscillates between two positive potential plateaus: starting from one plateau, rolling into a negative potential well, enabling the bouncing mechanism, then climbing onto the other plateau. Eventually, the field stops and rolls back towards the well, restarting the cycle and returning to the original position. In the second, the scalar field periodically enters a region of $\phi$ space in which the bouncing mechanism can occur: starting from one plateau, rolling into a negative potential well, enabling the bouncing mechanism, climbing up a positive potential barrier until $\phi$ turns around, and returning back to the original plateau. Again, the field eventually stops and rolls towards the well to restart the cycle. These models call for Horndeski coupling functions that allow the field and the potential to behave as prescribed, enable $H(t)$ to go through contraction$\rightarrow$NEC violation$\rightarrow$expansion, and maintain a stable subluminal speed of perturbation propagation. One set of Horndeski coupling functions constructed strongly suggests the feasibility of the first kind. Another set of Horndeski coupling functions constructed demonstrates the possibility of the second kind.