Abstract:
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The gravitational path integral suggests a striking result: the Hilbert space of closed universes in each superselection sector, a so-called alpha-sector, is one-dimensional. We develop an abstract formalism encapsulating recent proposals that modify the gravitational path integral in the presence of observers and allow larger Hilbert spaces to be associated with closed universes. Our formalism regards the gravitational path integral as a map from abstract objects called sources to complex numbers, and introduces additional objects called partial sources, which form sources when glued together. We apply this formalism to treat, on equal footing, universes with spatial boundaries, closed universes with prescribed observer worldlines, and closed universes containing observers entangled with external systems. In these contexts, the relevant gravitational Hilbert spaces contain states prepared by partial sources and can consequently have nontrivial alpha-sectors supporting noncommuting operators.

Depending on the audience and time, I may elaborate on aspects not emphasized in previous versions of this talk given elsewhere: a bound on the size of alpha-sectors derived from the positivity of the inner product; the relation to prescriptions for tracing out subregions in closed universes; and connections to cosmological models where holographic CFTs play the role of observers.

This talk is mostly based on arXiv:2505.15892 [hep-th].