General Relativity & Quantum Cosmology

Gibbons and Hawking proposed that the Euclidean gravity path integral with periodic boundary conditions in time computes the thermal partition sum of gravity. As a corollary, they argued that a derivative of the associated free energy with respect to the Euclidean time period computes gravitational entropy. Why is this interpretation correct?  That is, why does this path integral compute a trace over the Hilbert space of quantum gravity?   I will show that the quantity computed by the Gibbons-Hawking path integral is equal to an a priori different object -- an explicit thermal trace over the Hilbert space spanned by states produced by the Euclidean gravity path integral. I will explain that this follows if the Hilbert space with two boundaries factorizes into a product of two single boundary Hilbert spaces.  To show the latter I will develop a basis for the nonperturbative Hilbert space of quantum gravity with one asymptotic boundary. I will use this basis to show that the Hilbert space for gravity with two disconnected boundaries factorizes into a product of two copies of the single boundary Hilbert space, from which our main result will follow.

Tidal disruption events — where an unfortunate star is destroyed by a previously quiescent supermassive black hole — offer a unique probe of the low mass end of the supermassive black hole population. Recent observational advances have lead to the discovery of ~100 such events, many of which are comprehensively followed up across the entire electromagnetic spectrum. I will discuss how time-dependent relativistic accretion theory can be used to understand this multi wavelength emission from optical through X-ray energies, and how this theory allows tidal disruption events to act as probes of the massive black hole population. I will present current constraints on the occupation fraction of intermediate mass black holes, and look forward to what can be expected in the LSST era.

Suppose our universe really had a huge cosmological constant.  What would this mean observationally?  For a homogeneous universe the answer is clear, but if the universe is inhomogeneous at the Planck scale the question becomes more subtle.  At the level of initial data, $\Lambda$ can be "hidden" in spacetime foam, rapidly expanding and contracting regions that coexist and give an average expansion near zero.  Classically, such data develop singularities, and we need a quantum description of their evolution.  I describe results from a spherically symmetric midisuperspace model in which the wave function can become "trapped" for long periods in regions in which the average expansion remains small, effectively hiding a large cosmological constant.