Gas of Baby Universes in JT Gravity and Matrix Models

It has been shown recently by Saad, Shenker and Stanford that the genus expansion of a certain matrix integral generates partition functions of Jackiw-Teitelboim (JT) quantum gravity on Riemann surfaces of arbitrary genus with any fixed number of boundaries. We use an extension of this integral for studying gas of baby universes or wormholes in JT gravity. To investigate the gas nonperturbatively we explore the generating functional of baby universes in the matrix model. The simple particular case when the matrix integral includes the exponential potential is discussed in some detail. We argue that there is a phase transition in the gas of baby universes.