Homogeneous cosmological solutions are obtained in five dimensional space time assuming equations of state p = kρ and p 1 = γρ where p is the isotropic 3 -pressure and p 1 , that for the fifth dimension. Using different values for the constants k and γ many known solutions are rediscovered. Further the current acceleration of the universe has led us to investigate higher dimensional gravity theory, which is able to explain acceleration from a theoretical view point without the need of introducing dark energy by hand. We also extend a recent work of Mohammedi where using a special form of the extra dimensional scale factor a new interpretation of the higher dimensional equations of motion is given and the concept of an effective four dimensional pressure is introduced. Interestingly the 5D matter field remains regular while the effective negative pressure is responsible for the inflation. Relaxing the assumptions of two equations of state we also present a class of solutions which provide early deceleration followed by a late acceleration in a unified manner. Relevant to point out that in this case our cosmology apparently mimics the well known quintessence scenario fuelled by a generalised Chaplygin-type of fluid where a smooth transition from a dust dominated model to a de Sitter like one takes place. Depending on the relative magnitude of the different constants appearing in our solutions we show that some of the cases are amenable to the desirable property of dimensional reduction.
We present a simple higher dimensional FRW type of model where the acceleration is apparently caused by the presence of the extra dimensions. Assuming an ansatz in the form of the deceleration parameter we get a class of solutions some of which shows the desirable feature of dimensional reduction as well as reasonably good physical properties of matter. Interestingly we do not have to invoke an extraneous scalar field or a cosmological constant to account for this acceleration. One argues that the terms containing the higher dimensional metric coefficients produces an extra negative pressure that apparently drives the inflation of the 4D space with an accelerating phase. It is further found that in line with the physical requirements our model admits of a decelerating phase in the early era along with an accelerating phase at present.Further the models asymptotically mimic a steady state type of universe although it starts from a big type of singularity.Correspondence to Wesson's induced matter theory is also briefly discussed and in line with it it is argued that the terms containing the higher dimensional metric coefficients apparently creates a negative pressure which drives the inflation of the 3-space with an accelerating phase.
We discuss a Weyl-type theory which was considered by Utiyama and Nishioka. We point out that the vanishing of the trace of the energy-momentum tensor in the space-time with QPy = v, + is not an inevitable outcome of the theory, but follows from an incorrect treatment.
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