On planetary orbits, ungravity and entropic gravity

TL;DR

The paper evaluates whether ungravity and entropic gravity can account for dark energy or dark matter by computing their effects on planetary orbits and confronting them with solar-system data. It derives the ungravity-modified Schwarzschild solution with a characteristic scale $R_G$ and quantifies the induced perihelion precession, obtaining a stringent bound $|R_G|\lesssim 0.005$ m from Mercury and additional bounds from light bending, redshift, and Shapiro delay. It then analyzes entropic-gravity corrections from modified entropy–area relations, deriving a perturbative perihelion shift with a tight constraint $|\epsilon|\leq 2.8\times10^{-58}$, and surveys several generalized entropies; many models fail to simultaneously fit solar-system and galactic observations. The results strongly disfavor ungravity as the origin of the cosmological constant and place tight limits on entropic-gravity scenarios, especially when galactic rotation curves are also considered, highlighting the value of combining solar-system and galactic data to test modified gravity proposals.

Abstract

In previous works, entropic gravity and ungravity have been considered as possible solutions to the dark energy and dark matter problems. To test the viability of these models, modifications to planetary orbits are calculated for ungravity and different models of entropic gravity. Using the gravitational sector of unparticles, an equation for the contribution to the effect of orbital precession is obtained. We conclude that the estimated values for the ungravity parameters from planetary orbits are inconsistent with the values needed for the cosmological constant. The same ideas are explored for entropic gravity arising from a modified entropy--area relationship.