112 research outputs found
Modified Friedmann Equations from Tsallis Entropy
It was shown by Tsallis and Cirto that thermodynamical entropy of a
gravitational system such as black hole must be generalized to the non-additive
entropy, which is given by , where is the horizon
area and is the nonextensive parameter \cite{Tsa}. In this paper, by
taking the entropy associated with the apparent horizon of the
Friedmann-Robertson-Walker (FRW) Universe in the form of Tsallis entropy, and
assuming the first law of thermodynamics, , holds on the
apparent horizon, we are able to derive the corresponding Friedmann equations
describing the dynamics of the universe with any spatial curvature. We also
examine the time evolution of the total entropy and show that the generalized
second law of thermodynamics is fulfilled in a region enclosed by the apparent
horizon. Then, modifying the emergence proposal of gravity proposed by
Padmanabhan and calculating the difference between the surface degrees of
freedom and the bulk degrees of freedom in a region of space, we again arrive
at the modified Friedmann equation of the FRW Universe with any spatial
curvature which is the same as one obtained from the first law of
thermodynamics. We also study the cosmological consequences of Tsallis
cosmology. Interestingly enough, we find that this model can explain
simultaneously the late time acceleration in the universe filled with
pressureless matter without invoking dark energy, as well as the early
deceleration. Besides, the age problem can be circumvented automatically for an
accelerated universe and is estimated larger than age of the universe in
standard cosmology. For , we find Gyr Gyr,
which is consistent with recent observations. We also comment on the density
perturbation in the context of Tsallis cosmology.Comment: 11 pages, two columns. A new section regarding the cosmological
consequences of this model was added. Also text was revised and new
references adde
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