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.
Bianchi-I cosmology with scale dependent $G$ and $Λ$ in asymptotically safe gravity
National Central University（中央大学）；Center for High Energy and High Field Physics (CHiP), National Central University（国立中央大学高能高场物理中心）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）；Nagoya University（名古屋大学）；Department of Physics and Kobayashi-Maskawa Institute, Nagoya University（名古屋大学物理系及小林-益川研究所）；Osaka Metropolitan University（大阪公立大学）；Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University（大阪公立大学南部阳一郎理论与实验物理研究所）
