New explanation for accelerated expansion and flat galactic rotation curves

Understand

Employing the non-additive Tsallis entropy, $S\sim A^{\beta}$, for the large-scale gravitational systems, we disclose that in the cosmological scales both Friedmann equation and the equation of motion for the Newtonian cosmology get modified, accordingly.

• We then derive the modified Newton's law of gravitation which is valid on the 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 $\beta \lesssim1/2$.