Cosmology of the Baby Universe in Coupled SYK

Abstract

We analyze the structure of the baby universe which arises in the coupled SYK realization of the AS$^2$ geometry. To do this, we develop and leverage combinatorial arguments about traces of many Majoranas which remain valid at finite $N$ and $p$ and thus furnish the finite $λ$ completion of the chord rules found in [1]. We find that there is a first order phase transition which persists in the $β\rightarrow\infty$ limit between the thermal AdS and AS$^2$ phases parameterized by the mass of the heavy particle insertion and the ratio between the SYK and Maldacena-Qi coupling constants. We then explore Lorentzian time evolution in the baby universe and find a cosine scale factor confirming the big bang / big crunch nature of the bulk cosmology.