We present a new cosmological event, which we named the little sibling of the big rip. This event is much smoother than the big rip singularity. When the little sibling of the big rip is reached, the Hubble rate and the scale factor blow up but the cosmic derivative of the Hubble rate does not. This abrupt event takes place at an infinite cosmic time where the scalar curvature explodes. We show that a doomsday \'a la little sibling of the big rip is compatible with an accelerating universe, indeed at present it would mimic perfectly a LCDM scenario. It turns out that eventhough the event seems to be harmless as it takes place in the infinite future, the bound structures in the universe would be unavoidably destroyed on a finite cosmic time from now. The model can be motivated by considering that the weak energy condition should not be abusibely violated in our Universe, and it could give us some hints about the status of recently formulated nonlinear energy conditions.Comment: 20 pages, 4 figures, clarifications include

We present an holographic model of the Dvali-Gabadadze-Porrati scenario with a Gauss-Bonnet term in the bulk. We concentrate on the solution that generalises the normal Dvali-GabadadzePorrati branch. It is well known that this branch cannot describe the late-time acceleration of the universe even with the inclusion of a Gauss-Bonnet term. Here, we show that this branch in the presence of a Gauss-Bonnet curvature effect and an holographic dark energy with the Hubble scale as the infra-red cutoff can describe the late-time acceleration of the universe. It is worthwhile to stress that such an energy density component cannot do the same job on the normal Dvali-GabadadzePorrati branch (without Gauss-Bonnet modifications) nor in a standard 4-dimensional relativistic model. The acceleration on the brane is also presented as being induced through an effective dark energy which corresponds to a balance between the holographic one and geometrical effects encoded through the Hubble parameter.

We address three genuine phantom dark energy models where each of them induces the particular future events known as Big Rip, Little Rip and Little Sibling of the Big Rip. The background models are fully determined by a given dark energy equation of state. We first observationally constrain the corresponding model parameters that characterise each paradigm using the available data of supernova type Ia, Cosmic Microwave Background and Baryonic Acoustic Oscillations by using a Markov Chain Monte Carlo method. The obtained fits are used to solve numerically the first order cosmological perturbations. We compute the evolution of the density contrast of (dark) matter and DE, from the radiation dominated era till a totally DE dominated universe. Then, the obtained results are compared with respect to ΛCDM. We obtain the predicted current matter power spectrum and the evolution of f σ8 given by the models studied in this work. Finally, the models are tested by computing the reduced χ 2 for the "Gold2017" f σ8 dataset. * aminebouali smp@yahoo.com †

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.

We consider a Brans-Dicke cosmology in five-dimensional space-time. Neglecting the quadratic and the mixed Brans-Dicke terms in the Einstein equation, we derive a modified wave equation of the Brans-Dicke field. We show that, at high energy limit, the 3-brane Brans-Dicke cosmology could be described as the standard one by changing the equation of state. Finally as an illustration of the purpose, we show that the dark energy component of the universe agrees with the observations data.