Abstract
In this paper, we show that a universe with a dynamical cosmological constant approaching pure de Sitter at timelike infinity, enjoys an infinite dimensional symmetry group at its horizon. This group is larger than the usual $SO(4,1)$ of pure de Sitter. The charges associated with the asymptotic symmetry generators are non-integrable, and we demonstrate that they promote an extended version of the first law of thermodynamics. This contains four pairs of conjugate variables. The pair $(\Theta,\Lambda)$ corresponding to the change in the cosmological constant and its conjugate volume $\Theta$. The contribution of the surface tension of the horizon and its conjugate parameter surface area make a pair $(\sigma, A)$. The usual conjugate variables $ (T, S) $, $ (\Omega, J) $ and a term $ \partial_v \delta S $ corresponding to entropy production, are included. In addition, this extended first law describes the non-conservative behaviour of the asymptotic charges in non-equilibrium.
Highlights
The extra symmetries of asymptotically flat spacetimes were first discussed by Bondi, van der Burg, Metzner and Sachs in the early 60’s [1,2,3]
Noting that the asymptotic symmetry generators are taken to be fixed to first order, they do not depend on the dynamical fields
We propose a process described by the equations of motion for the near-horizon geometry of a universe with a dynamical cosmological constant
Summary
The extra symmetries of asymptotically flat spacetimes were first discussed by Bondi, van der Burg, Metzner and Sachs in the early 60’s [1,2,3]. We show that the near-horizon geometry of a de Sitter– like spacetime admits asymptotic symmetries at its horizon In other words, this spacetime possesses a larger symmetry group than SOð4; 1Þ of pure de Sitter. For a nonstationary perturbation to the near-horizon geometry of a de Sitter– like spacetime generated by its asymptotic symmetries, the variation of the conserved charges can be calculated. This variation can be interpreted as an extended first law of thermodynamics that provides an insight into the nonconservation and apparent time-reversal symmetry breaking of this dynamical system.
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