Holographic induced gravity model with a Ricci dark energy: Smoothing the little rip and big rip through Gauss-Bonnet effects?

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 infra-red cutoff can describe the late-time acceleration of the universe. In addition, we show that the dimensionless holographic parameter is very important in characterising the DGP branches, and in determining the behaviour of the Ricci dark energy as well as the asymptotic behaviour of the brane. On the one hand, in the DGP scenario the Ricci dark energy will exhibit a phantom-like behaviour 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.

Why is the running vacuum energy more benign than the holographic Ricci dark energy?

“…III and Refs. [9,18]), separately, within the context of FLRW cosmology. Even though the Friedmann equation of both models looks pretty much similar [cf.…”

“…It can be checked that this event happens at an infinite cosmic time. Therefore, the universe undergoes a kind of smooth little rip singularity in the far future [17,18]. This kind of event was named by one of us ''the little sibling of the big rip singularity'' [19].…”

“…In summary, it is surprising that, in a HRDE model with ¼ 1=2, the presence of a positive cosmological constant can induce a bounce while the presence of a negative cosmological constant can induce a little sibling of the big rip singularity [19] (a smoother version of the little rip [17,18]). …”

“…[15][16][17][18]). The main purpose of this work is to point out the nature of the possible future singularities in the framework of the two recently proposed models of dark energy cosmology: the HRDE and the GRVE.…”

Eddington–Born–Infeld cosmology: a cosmographic approach, a tale of doomsdays and the fate of bound structures

“…The little rip has been previously analysed under four-dimensional (4D) standard cosmology [72], later on rediscovered in [59,62,85]. It can be found in dilatonic brane-world models [86] or other kinds of braneworld models [87,88]. Forty years after its discovery, the event has been baptised and named the "little rip" [89][90][91][92].…”