Bouncing universes with varying constants

We investigate the behaviour of exact closed bouncing Friedmann universes in theories with varying constants. We show that the simplest BSBM varying-alpha theory leads to a bouncing universe. The value of alpha increases monotonically, remaining approximately constant during most of each cycle, but increasing significantly around each bounce. When dissipation is introduced we show that in each new cycle the universe expands for longer and to a larger size. We find a similar effect for closed bouncing universes in Brans-Dicke theory, where G also varies monotonically in time from cycle to cycle. Similar behaviour occurs also in varying speed of light theories. Bouncing Universes with Varying Constants 2 The ”bouncing universe ” is a modern cosmological reincarnation of an ancient fascination with the cyclic patterns of nature and the myth of the ”eternal return” [1, 2, 3]. Gravitation theories like general relativity allow us to make precise models of this popular conception of a “phoenix ” cosmology, in which a universe periodically collapses to a Big Crunch, only to rebound into a new state of expansion, as if emerging from a unique Big Bang [4]. Multiple bounces are possible but each cycle lasts longer