Debye entropic force and modified Newtonian dynamics

TL;DR

This paper explores how Verlinde's entropic gravity framework can be modified at low temperatures using Debye's law, leading to a connection between modified Newtonian dynamics (MOND) and cosmology, especially regarding the Hubble constant.

Contribution

It introduces a Debye-based modification to entropic force, linking MOND parameters to cosmological constants within Verlinde's entropic gravity model.

Findings

Modified entropic force proportional to acceleration squared at low temperatures

Returns to Newtonian gravity at high temperatures

Connects MOND parameter $a_0$ with Debye frequency and Hubble constant

Abstract

Verlinde has suggested that the gravity has an entropic origin, and a gravitational system could be regarded as a thermodynamical system. It is well-known that the equipartition law of energy is invalid at very low temperature. Therefore, entropic force should be modified while the temperature of the holographic screen is very low. It is shown that the modified entropic force is proportional to the square of the acceleration, while the temperature of the holographic screen is much lower than the Debye temperature $T_D$. The modified entropic force returns to the Newton's law of gravitation while the temperature of the holographic screen is much higher than the Debye temperature. The modified entropic force is connected with modified Newtonian dynamics (MOND). The constant $a_0$ involved in MOND is linear in the Debye frequency $\omega_D$, which can be regarded as the largest frequency of the bits in screen. We find that there do have a strong connection between MOND and cosmology in the framework of Verlinde's entropic force, if the holographic screen is taken to be bound of the Universe. The Debye frequency is linear in the Hubble constant $H_0$.