# A Zero-Parameter Extension of General Relativity with Varying Cosmological Constant

## TL;DR

This paper introduces a novel extension of general relativity where the cosmological constant varies dynamically via torsion, reducing free parameters and potentially offering new insights into cosmology and gravitational physics.

## Contribution

It proposes a zero-parameter extension of GR with a dynamical cosmological constant encoded in torsion, implemented through a quasi-topological term in the Einstein action.

## Key findings

- The theory has fewer free parameters than standard GR with a cosmological constant.
- The dynamical $\\Lambda$ is fixed by the matter content in homogeneous and isotropic models.
- The model is formulated using the Palatini approach and satisfies Bianchi identities automatically.

## Abstract

We provide a new extension of general relativity (GR) which has the remarkable property of being more constrained than GR plus a cosmological constant, having one less free parameter. This is implemented by allowing the cosmological constant to have a consistent space-time variation, through coding its dynamics in the torsion tensor. We demonstrate this mechanism by adding a `quasi-topological' term to the Einstein action, which naturally realizes a dynamical torsion with an automatic satisfaction of the Bianchi identities. Moreover, variation of the action with respect to this dynamical $\Lambda$ fixes it in terms of other variables, thus providing a scenario with less freedom than general relativity with a cosmological constant. Once matter is introduced, at least in the homogeneous and isotropic reduction, $\Lambda$ is uniquely determined by the field content of the model. We make an explicit construction using the Palatini formulation of GR and describe the striking properties of this new theory. We also highlight some possible extensions to the theory. A companion paper [1] explores the Friedmann--Robertson--Walker reduction for cosmology, and future work will study Solar System tests of the theory.