# The cosmology of minimal varying Lambda theories

## TL;DR

This paper explores a minimal varying Lambda theory in cosmology, showing how Lambda can be algebraically linked to matter density without additional scalar fields, and discusses its implications for dark matter and radiation.

## Contribution

It introduces a novel minimal theory where Lambda varies proportionally with matter density, avoiding scalar fields, and analyzes its cosmological consequences.

## Key findings

- Lambda is proportional to matter density with a state-dependent constant.
- Pure radiation case is incompatible with the minimal theory due to divergence.
- The generalized theory allows Lambda to coexist with radiation, consistent with Big Bang Nucleosynthesis.

## Abstract

Inserting a varying Lambda in Einstein's field equations can be made consistent with the Bianchi identities by allowing for torsion, without the need to add scalar field degrees of freedom. In the minimal such theory, Lambda is totally free and undetermined by the field equations in the absence of matter. Inclusion of matter ties Lambda algebraically to it, at least when homogeneity and isotropy are assumed, i.e. when there is no Weyl curvature. We show that Lambda is proportional to the matter density, with a proportionality constant depending on the equation of state. Unfortunately, the proportionality constant becomes infinite for pure radiation, ruling out the minimal theory prima facie despite of its novel internal consistency. It is possible to generalize the theory still without the addition of kinetic terms, leading to a new algebraically-enforced proportionality between Lambda and the matter density. Lambda and radiation may now coexist in a form consistent with Big Bang Nucleosynthesis, though this places strict constraints on the single free parameter of the theory, $\theta$. In the matter epoch Lambda behaves just like a dark matter component. Its density is proportional to the baryonic and/or dark matter, and its presence and gravitational effects would need to be included in accounting for the necessary dark matter in our Universe. This is a companion paper to Ref. [1] where the underlying gravitational theory is developed in detail.