New explanation for accelerated expansion and flat galactic rotation curves
Ahmad Sheykhi
Abstract
Abstract Employing the non-additive Tsallis entropy, $$S\sim A^{\beta }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mo>∼</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mi>β</mml:mi></mml:msup></mml:mrow></mml:math> , 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 $$\beta <1/2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi><mml:mo><</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> . 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 $$\beta \lesssim 1/2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi><mml:mo>≲</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> . Our study may be regarded as an alternative explanation for the “dark side of the universe”, through modification of the gravitational field equations.