Variational Principle in an Expanding Universe

In this paper we complete the relativistic cosmological theory because we extend the variational principle including variations of metric induced by expansion of the space. We will show that the mass not only curves Space and Time but also generates them: we’ll speak of the principle of mass-space equivalence. Then the increasing mass generates variations of metric as also the space increasing or expansion. So, the dark component of the mass generates additional gravity around galaxies as well as additional space, which generates a pressure (dark energy) accelerating the galaxies in their move away. All this could explain the cosmic coincidence (Ωdm/Ωde ≈ 1). To talk about the increasing mass is equivalent to speak of mass creation in universe, causing the variation of the tensor (T) mass-energy tensor of all component fields. We conjecture that its variation is caused by mass-energy flow comes out from a physical system (Θ) composed by set of uncoupled quantum oscillators (structure of no-field) in vacuum state. All this allows formulating a variational principle which generates the cosmological equation with the (Λ) parameter and a tensor T* with variable mass density, where T*(T, Θ).