Oscillating universe in massive bigravity

Abstract

In this paper, in the framework of massive bigravity, we study all possible cosmic evolutions by using a method in which the modified Friedmann equation is written in a form in which the scale factor evolves like the motion of a particle under a ``potential.'' Massive bigravity provides this potential with the most general mass interaction term, which can create new circumstances to find different kinds of cosmological evolutions in the early Universe. We classify all possible cosmic evolutions according to the classifications of the energy density as dust, radiation, and dust with phantom. The oscillating universe and Einstein static state that exist initially may show a useful property of the early Universe, obtained in this model, in which the initial singularity is avoided. The bouncing universe extracted in the massive bigravity model can present a reasonable cosmic evolutionary behavior having a big bang initial point with the expansion phase and switching to the contraction phase, leading to a final big crunch point. The large-valued graviton mass $m$ in the early times causes a very small ${a}_{\mathrm{S}}$ (the Einstein static state scale factor), and $\ensuremath{\lambda}={\ensuremath{\rho}}_{0}{a}_{0}^{3}$ is a constant parameter constructed of the present-day energy density and scale factor.