Abstract
We study the instantons (or bounces) in the Brown-Teitelboim (BT) mechanism of relaxation of cosmological constant which is a cosmological version of the Schwinger mechanism. The BT mechanism is a false vacuum decay of (A)dS$_{d+1}$ (and $R^{1, d}$) spaces via spontaneous nucleations of spherical $(d-1)$-branes and thus ostensibly has bearings on (A)dS$_{d+1}$/CFT$_d$ 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 first law of 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 AdS$_{d+1}$/CFT$_d$ in which the $(d-1)$-branes make up all degrees of freedom of AdS$_{d+1}$ 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 close connection to complexity.
Highlights
The Brown-Teitelboim (BT) mechanism is a cosmological version of the Schwinger mechanism [1] in which the cosmological constant relaxes to a smaller value via nucleations of spherical membranes [2]
As is the case with pair productions near black hole and de Sitter horizons [11,12,13,14], the BT instanton action encodes the thermodynamics ofde Sitter space
II, we provide a refreshing review on BT instanton solutions of the membrane nucleation 1) in the conformally flat metric of four-dimensional de Sitter space and 2) in the dS3 slice of four-dimensional de Sitter, flat, and anti–de Sitter spaces
Summary
The Brown-Teitelboim (BT) mechanism is a cosmological version of the Schwinger mechanism [1] in which the cosmological constant relaxes to a smaller value via nucleations of spherical membranes [2] This is a false vacuum decay of (anti–)de Sitter [ðAÞdSdþ1] and R1;d spaces [3,4], more generally, via spontaneous nucleations of spherical (d − 1)-branes. II, we provide a refreshing review on BT instanton (or bounce) solutions of the membrane nucleation 1) in the conformally flat metric of four-dimensional de Sitter space and 2) in the dS3 slice of four-dimensional de Sitter, flat, and anti–de Sitter spaces The former manifests itself as being the most intuitive as false vacuum decay and can be regarded as a direct and apparent higher-dimensional generalization of the twodimensional Schwinger mechanism in a uniform electric flux. In string/M-theory compactifications, the bare cosmological constant λbare is typically negative, because typical six-/seven-dimensional internal manifolds have positive curvatures
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