Does the universe obey the energy conservation law by a constant mass or an increasing mass with radius during its evolution?

Abstract

How the energy conservation law is obeyed by the universe during its evolution is an important but not yet unanimously resolved question. Does the universe have a constant mass during its evolution or has its mass been increasing with its radius? Here, we evaluate the two contending propositions within the context of the Friedmann equations and the standard big bang theory. We find that though both propositions appeal to the Friedmann equations for validity, an increasing mass with increasing radius is more in harmony with the thermal history of the big bang model. In addition, temperature and flatness problems that plague the constant mass proposal are mitigated by the increasing mass with radius proposal. We conclude that the universe has been increasing in mass and radius in obedience to the energy conservation law.