Recovering the effective cosmological constant in extended gravity theories

TL;DR

This paper investigates how extended gravity theories can produce an effective, time-dependent cosmological constant that approaches a true constant in the universe's late-time behavior, across various complex models.

Contribution

It introduces a set of conditions to recover asymptotic de Sitter behavior in extended gravity models, regardless of initial conditions, by defining a time-dependent effective cosmological constant.

Findings

Effective cosmological constant can be recovered in extended gravity models.

Conditions for asymptotic de Sitter behavior are established.

Applicable to scalar-tensor and higher-order theories.

Abstract

In the framework of extended gravity theories, we discuss the meaning of a time dependent "cosmological constant" and give a set of conditions to recover asymptotic de Sitter behaviour for a class of cosmological models independently of initial data. To this purpose we introduce a time-dependent (effective) quantity which asymptotically becomes the true cosmological constant. We will deal with scalar-tensor, fourth and higher than fourth-order theories.