$\Lambda$CDM, $\Lambda$DGP and extended phantom-like cosmologies

TL;DR

This paper compares various extended phantom-like cosmologies with $ ext{Lambda}$CDM and $ ext{Lambda}$DGP, analyzing their effects on cosmic acceleration, universe age, and transition redshifts using dynamical system methods.

Contribution

It introduces and compares extended $F(R,\, ext{phi})$-DGP models with existing cosmologies, highlighting their stability and proximity to $ ext{Lambda}$CDM.

Findings

The $f(R)$-DGP scenario's acceleration phase is stable with a phantom scalar field.

The $F(R, ext{phi})$-DGP model closely resembles $ ext{Lambda}$CDM.

Transition redshifts to acceleration differ among models.

Abstract

In this paper we compare outcomes of some extended phantom-like cosmologies with each other and also with $\Lambda$CDM\, and $\Lambda$DGP. We focus on the variation of the luminosity distances, the age of the universe and the deceleration parameter versus the redshift in these scenarios. In a dynamical system approach, we show that the accelerating phase of the universe in the $f(R)$-DGP scenario is stable if one consider the \emph{curvature fluid} as a phantom scalar field in the equivalent scalar-tensor theory, otherwise it is a transient and unstable phenomenon. Up to the parameters values adopted in this paper, the extended $F(R,\phi)$-DGP scenario is closer to the $\Lambda$CDM scenario than other proposed models. All of these scenarios explain the late-time cosmic speed-up in their normal DGP branches, but the redshift at which transition to the accelerating phase occurs are different: while the $\Lambda$DGP model transits to the accelerating phase much earlier, the $F(R,\phi)$-DGP model transits to this phase much later than other scenarios. Also, within the parameter spaces adopted in this paper, the age of the universe in the $f(R)$-DGP model is larger than $\Lambda$CDM, but this age in $F(G,\phi)$-DGP is smaller than $\Lambda$CDM.