$Λ$CDM, $Λ$DGP and extended phantom-like cosmologies

In this paper we compare outcomes of some extended phantom-like cosmologies with each other and also with $Λ$CDM\, and $Λ$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 $F(R,ϕ)$-DGP scenario is closer to the $Λ$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 $Λ$DGP model transits to the accelerating phase much earlier, the $F(R,ϕ)$-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 $Λ$CDM, but this age in $F(G,ϕ)$-DGP is smaller than $Λ$CDM.

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