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We use $(4+1)$ split to derive the 4D induced energy density $rho $ and pressure $p$ of the $5D$ Ricci-flat cosmological solutions which are characterized by having a bounce instead of a bang. The solutions contain two arbitrary functions of time $t$ and, therefore, are mathematically rich in giving various cosmological models. By using four known energy conditions (null, weak, strong, and dominant) to pick out and study physically meaningful solutions, we find that the 4D part of the $5D$ solutions asymptotically approach to the standard 4D FRW models and the expansion of the universe is decelerating for normal induced matter for which all the four energy conditions are satisfied. We also find that quintessence might be normal or abnormal, depending on the parameter $w$ of the equation of state. If $-1leqslant w<-1/3$, the expansion of the universe is accelerating and the quintessence is abnormal because the strong energy condition is violated while other three are satisfied. For phantom, all the four energy conditions are violated. Before the bounce all the four energy conditions are violated, implying that the cosmic matter before the bounce could be explained as a phantom which has a large negative pressure and makes the universe bouncing. In the early times after the bounce, the dominant energy condition is violated while the other three are satisfied, and so the cosmic matter could be explained as a super-luminal acoustic matter.
Current universe (assumed here to be normal matter on the brane) is pressureless from observations. In this case the energy condition is $rho_0geq0$ and $p_0=0$. By using this condition, brane models can be distinguished. Then, assuming arbitrary com
We discuss the correspondence between the DGP brane cosmology and 5D Ricci-flat cosmology by letting their metrics equal each other. By this correspondence, a specific geometrical property of the arbitrary integral constant I in DGP metric is given a
The exactly solvable quantum model of the homogeneous, isotropic and closed universe in the matter-energy production epoch is considered. It is assumed that the universe is originally filled with a uniform scalar field and a perfect fluid which defin
Within a first-order framework, we comprehensively examine the role played by boundary conditions in the canonical formulation of a completely general two-dimensional gravity model. Our analysis particularly elucidates the perennial themes of mass an
Phenomenological implications of the Mimetic Tensor-Vector-Scalar theory (MiTeVeS) are studied. The theory is an extension of the vector field model of mimetic dark matter, where a scalar field is also incorporated, and it is known to be free from gh