Genuine Cosmic Hair

TL;DR

This paper introduces the concept of 'genuine cosmic hair' in asymptotically future deSitter spacetimes, defining new charges called cosmological tension that relate early universe properties to late-time observations.

Contribution

It defines cosmological tension charges as new asymptotic invariants in AFdS spacetimes, extending the analogy of ADM mass and tensions, and derives a Smarr relation linking early and late universe features.

Findings

Cosmological tension measures anisotropic expansion corrections.

Smarr relation connects early universe properties to late-time cosmic hair.

Kasner-deSitter spacetimes exemplify the application of these concepts.

Abstract

We show that asymptotically future deSitter (AFdS) spacetimes carry 'genuine' cosmic hair; information that is analogous to the mass and angular momentum of asymptotically flat spacetimes and that characterizes how an AFdS spacetime approaches its asymptotic form. We define new 'cosmological tension' charges associated with future asymptotic spatial translation symmetries, which are analytic continuations of the ADM mass and tensions of asymptotically planar AdS spacetimes, and which measure the leading anisotropic corrections to the isotropic, exponential deSitter expansion rate. A cosmological Smarr relation, holding for AFdS spacetimes having exact spatial translation symmetry, is derived. This formula relates cosmological tension, which is evaluated at future infinity, to properties of the cosmology at early times, together with a 'cosmological volume' contribution that is analogous to the thermodynamic volume of AdS black holes. Smarr relations for different spatial directions imply that the difference in expansion rates between two directions at late times is related in a simple way to their difference at early times. Hence information about the very early universe can be inferred from cosmic hair, which is potentially observable in a late time deSitter phase. Cosmological tension charges and related quantities are evaluated for Kasner-deSitter spacetimes, which serve as our primary examples.