Abstract
Employing the non-additive Tsallis entropy, Ssim A^{beta }, for the large-scale gravitational systems, we disclose that in the cosmological scales both the Friedmann equation and the equation of motion for Newtonian cosmology get modified, respectively. We then derive the modified Newton’s law of gravitation which is valid on large scales. We show that, in the relativistic regime, the modified Friedmann equation admits an accelerated expansion, for a universe filled with ordinary matter, without invoking any kind of dark energy, provided the non-extensive parameter is chosen beta <1/2. In the non-relativistic regime, however, the modified Newton’s law of gravitation can explain the flat galactic rotation curves without invoking particle dark matter provided beta lesssim 1/2. Our study may be regarded as an alternative explanation for the “dark side of the universe”, through modification of the gravitational field equations.
Highlights
Another attempt for explanation of the dark matter puzzle, through a non-relativistic model, is modified Newtonian dynamics (MOND) [18,19], which proposed to address the flat rotation curves of spiral galaxies through modifying Newton’s law of gravitation
In the relativistic regime, the modified Friedmann equation admits an accelerated expansion, for a universe filled with ordinary matter, without invoking any kind of dark energy, provided the non-extensive parameter is chosen β < 1/2
We would like to propose an alternative perspective for tackling the problem of accelerated expansion as well as the flat galactic rotation curves through modifying the Friedmann equation and Newton’s law of gravitation, using a thermodynamic argument
Summary
It is problematic to embed MOND theory within a more comprehensive relativistic theory of gravity and, its theoretical origin remains unclear. It predicts that the individual halo associated with a galaxy is infinite in extent, while recent galaxy–galaxy lensing results suggest that galaxy halos may have a maximum extent of about 0.5 Mpc [20]. We would like to propose an alternative perspective for tackling the problem of accelerated expansion as well as the flat galactic rotation curves through modifying the Friedmann equation and Newton’s law of gravitation, using a thermodynamic argument. In 1988 Tsallis generalized standard thermodynamics to non-extensive thermody-
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