Causal horizons in a bouncing universe

Abstract: As our understanding of the past in a bouncing universe is limited, it becomes difficult to propose a cosmological model which can give some understanding of the causal structure of the bouncing universe. In this article we address the issue related to the particle horizon problem in the bouncing universe models. It is shown that in many models the particle horizon does not exist, and consequently the horizon problem is trivially solved. In some cases a bouncing universe can have a particle horizon and we specify the conditions for its existence. In the absence of a particle horizon the Hubble surface specifies the causal structure of a bouncing universe. We specify the complex relationship between the Hubble surface and the particle horizon when the particle horizon exists. The article also address the issue related to the event horizon in a bouncing universe. A toy example of a bouncing universe is first presented where we specify the conditions which dictate the presence of a particle horizon. Next we specify the causal structures of three widely used bouncing models. The first case is related to quintom matter bounce model, the second one is loop quantum cosmology based bounce model and lastly $f(R)$ gravity induced bounce model. We present a brief discussion on the horizon problem in bouncing cosmologies. We point out that the causal structure of the various bounce models fit our general theoretical predictions.