Belkacemi, Moulay-Hicham, Bouhmadi-Lopez, Mariam, Errahmani, Ahmed and Ouali, Taoufiq (2012), "Holographic induced gravity model with a Ricci dark energy: Smoothing
the little rip and big rip through Gauss-Bonnet effects?", PHYSICAL REVIEW D, 85, 8.
Abstract: We present an holographic brane-world model of the
Dvali-Gabadadze-Porrati (DGP) scenario with and without a Gauss-Bonnet
term (GB) in the bulk. We show that an holographic dark energy component
with the Ricci scale as the infrared cutoff can describe the late-time
acceleration of the Universe. In addition, we show that the
dimensionless holographic parameter is very important in characterizing
the DGP branches, and in determining the behavior of the Ricci dark
energy as well as the asymptotic behavior of the brane. On the one hand,
in the DGP scenario the Ricci dark energy will exhibit a phantomlike
behavior with no big rip if the holographic parameter is strictly larger
than 1/2. For smaller values, the brane hits a big rip or a little rip.
On the other hand, we have shown that the introduction of the GB term
avoids the big rip and little rip singularities on both branches but
cannot avoid the appearance of a big freeze singularity for some values
of the holographic parameter on the normal branch, however, these values
are very unlikely because they lead to a very negative equation of state
at the present and therefore we can speak in practice of singularity
avoidance. At this regard, the equation of state parameter of the Ricci
dark energy plays a crucial role, even more important than the GB
parameter, in rejecting the parameter space where future singularities
appear.
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