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.