Erschienen:
Springer Science and Business Media LLC, 2024
Erschienen in:
Journal of High Energy Physics, 2024 (2024) 1
Sprache:
Englisch
DOI:
10.1007/jhep01(2024)132
ISSN:
1029-8479
Entstehung:
Anmerkungen:
Beschreibung:
<jats:title>A<jats:sc>bstract</jats:sc>
</jats:title><jats:p>We obtain solutions of the Wheeler-DeWitt equation with positive cosmological constant for a closed universe in the large-volume limit. We argue that this space of solutions provides a complete basis for the Hilbert space of quantum gravity in an asymptotically de Sitter spacetime. Our solutions take the form of a universal phase factor multiplied by distinct diffeomorphism invariant functionals, with simple Weyl transformation properties, that obey the same Ward identities as a CFT partition function. The Euclidean vacuum corresponds to a specific choice of such a functional but other choices are equally valid. Each functional can be thought of as specifying a “theory” and, in this sense, the space of solutions is like “theory space”. We describe another basis for the Hilbert space where all states are represented as excitations of the vacuum that have a specific constrained structure. This gives the finite <jats:italic>G</jats:italic><jats:sub><jats:italic>N</jats:italic></jats:sub> generalization of the basis proposed by Higuchi in terms of group averaging, which we recover in the nongravitational limit.</jats:p>