Hydrogen atom in Palatini theories of gravity

TL;DR

This paper investigates how certain Palatini $f(R)$ gravity theories affect hydrogen atom stability, revealing that some models incompatible with observed atomic and cosmic stability due to gravitational backreaction.

Contribution

It demonstrates that low-curvature $f(R)$ models in Palatini formalism cause atomic instabilities, challenging their viability for explaining cosmic acceleration.

Findings

Hydrogen disintegrates in less than two hours in 1/R gravity model.

High curvature correction models do not produce such instabilities.

Gravity significantly influences atomic states in specific $f(R)$ theories.

Abstract

We study the effects that the gravitational interaction of $f(R)$ theories of gravity in Palatini formalism has on the stationary states of the Hydrogen atom. We show that the role of gravity in this system is very important for lagrangians $f(R)$ with terms that grow at low curvatures, which have been proposed to explain the accelerated expansion rate of the universe. We find that new gravitationally induced terms in the atomic Hamiltonian generate a strong backreaction that is incompatible with the very existence of bound states. In fact, in the 1/R model, Hydrogen disintegrates in less than two hours. The universe that we observe is, therefore, incompatible with that kind of gravitational interaction. Lagrangians with high curvature corrections do not lead to such instabilities.