Cosmological constant is a conserved charge

TL;DR

This paper demonstrates that the cosmological constant can be interpreted as a conserved gauge charge, introduces its conjugate potential, and extends thermodynamic laws to include variations of this charge, linking it to pressure.

Contribution

It provides a novel interpretation of the cosmological constant as a conserved gauge charge and extends thermodynamics to incorporate its variation as a conserved quantity.

Findings

Cosmological constant is a conserved gauge charge.

Introduces a conjugate chemical potential for the cosmological constant.

Extends the first law of thermodynamics to include the cosmological constant as a conserved charge.

Abstract

Cosmological constant can always be considered as the on-shell value of a top form in gravitational theories. The top form is field strength of a gauge field, and the theory enjoys a gauge symmetry. We show that cosmological constant is the charge of global part of the gauge symmetry, and is conserved irrespective of the dynamics of the metric and other fields. In addition, we introduce its conjugate chemical potential, and prove the generalized first law of thermodynamics which includes variation of cosmological constant as a conserved charge. We discuss how our new term in the first law is related to the volume-pressure term. In parallel with the seminal Wald entropy, this analysis suggests that pressure can also be considered as a conserved charge.