What is the gravitational mass when energy and inertial mass are not equivalent?

Laboratoire des écoulements géophysiques et industriels - Domaine Universitaire, CS 40700, 38058 Grenoble Cedex 9, France

Received: 16 July 2018
Accepted: 31 July 2018

Abstract

In this paper, we discuss some consequences of the existence in the Universe of particles for which energy minimum happens at a finite momentum (like rotons in superfluid ⁴He). The most striking consequence for a gas of such particles is that its inertial mass is not related to its energy. Thus, a natural question is the value of its gravitational mass. Assuming the equivalence of inertial and gravitational masses, we find that this gas contributes increasingly to the total mass of the expanding Universe. However, it implies to modify the Einstein equations of General Relativity. Using a simple example borrowed from condensed matter, we show why such a modification has to be expected. Looking for a possible outcome of such particles in the observations, we compare the behavior of the gas they would form with the behavior of Dark Energy.