Unimodular Supergravity

TL;DR

This paper develops a supergravity theory with a fixed metric determinant, eliminating the need for fine-tuning the cosmological constant and suggesting its zero value as most probable, while maintaining supersymmetry consistency.

Contribution

It formulates unimodular supergravity in various dimensions, integrating the unimodular constraint with supersymmetry and analyzing its implications for the cosmological constant.

Findings

Cosmological constant is naturally zero as the most probable configuration.

Supersymmetry algebra remains consistent under the unimodular condition.

The formulation extends supergravity to fixed-volume metrics in multiple dimensions.

Abstract

We present the locally supersymmetric formulation of unimodular gravity theory in D (1\le D \le 11) dimensions, namely supergravity theory with the metric tensor whose determinant is constrained to be unity. In such a formulation, the usual fine-tuning of cosmological constant is no longer needed, but its value is understood as an initial condition. Moreover, the zero-ness of the cosmological constant is concluded as the most probable configuration, based on the effective vacuum functional. We also show that the closure of supersymmetry gauge algebra is consistent with the unimodular condition on the metric.