Cosmological functions and their relation

TL;DR

This paper explores a modified gravity theory where the cosmological constant becomes a variable function dependent on canonical variables, linking different formalisms through the Ricci scalar.

Contribution

It demonstrates the relationship between cosmological functions in different formalisms via the three-dimensional Ricci scalar within Krasnov's non-metric gravity.

Findings

Cosmological functions are related through the Ricci scalar.

The theory generalizes GR by replacing the constant with a variable function.

Connections between Ashtekar and ADM formalisms are established.

Abstract

In the non-metric gravity proposed by K. Krasnov, this is a theory in which the scalar constraint of the Ashtekar's formalism is modified in such way that the cosmological constant is replaced by a cosmological function that depends of the canonical variables $A_{a}{}^{i}$ and $E_{i}{}^{a}$, the General Relativity (GR) is the particular case when the cosmological function is a constant. Some years ago inspired by this theory Rosas-Rodr\'iguez proposed two cosmological functions, one for the Ashtekar's formalism and the other for the ADM formalism. In this paper we show that this cosmological functions are related thought the three-dimensional Ricci scalar.