Exponential Lagrangian for the Gravitational Field and the problem of Vacuum Energy

TL;DR

This paper explores an exponential gravitational Lagrangian, highlighting its unique features, including a single fundamental scale and the necessity of a cancellation mechanism for vacuum energy, relevant to cosmological constant issues.

Contribution

It introduces an exponential Lagrangian for gravity with a focus on its parameters and implications for vacuum energy and the cosmological constant.

Findings

Only one fundamental scale emerges in the Einsteinian limit.

Vacuum energy in $f(R)$ theories requires a cancellation mechanism.

The model offers insights into the cosmological constant problem.

Abstract

We will analyze two particular features of an exponential gravitational Lagrangian. On the one hand, while this choice of the Lagrangian density allows for two free parameters, only one scale, the cosmological constant, arises as fundamental when the proper Einsteinian limit is to be recovered. On the other hand, the vacuum energy arising from $f(R)$ theories such that $f(0)\neq 0$ needs a cancellation mechanism, by which the present value of the cosmological constant can be recast.