Brown-Teitelboim instantons and thermodynamics of de Sitter and anti-de Sitter space

Abstract

We study the instantons (or bounces) in the Brown-Teitelboim (BT) mechanism of relaxation of the cosmological constant which is a cosmological version of the Schwinger mechanism. The BT mechanism is a false vacuum decay of (anti-)de Sitter [(A)dSd+1] (and R1,d) spaces via spontaneous nucleations of spherical (d-1)-branes and thus ostensibly has bearings on (A)dSd+1/CFTd holography. In this paper, we focus on the four-dimensional case, although the higher- or lower-dimensional generalization is straightforward. As is the case with pair productions near black hole and de Sitter horizons, we show that the BT instanton action for a membrane nucleation encodes the thermodynamics of (anti-)de Sitter space. In particular, the membrane instanton precisely accounts for the change of entropy of (A)dS space before and after nucleation, in good accordance with AdSd+1/CFTd in which the (d-1)-branes make up all degrees of freedom of AdSd+1 space. In light of this lesser-known perspective presented here, we also make remarks on 1) (A)dS/CFT and 2) complexity. For the complexity, we observe that the Lorentzian bounce action may have a close connection to complexity.