Cosmology and gravitational waves in the Nordstrom-Vlasov system, a laboratory for Dark Energy

Abstract

We discuss a cosmological solution of the system which was originally introduced by Calogero and is today popularly known as "Nordstrom-Vlasov system". Although the model is un-physical, its cosmological solution results interesting for the same reasons for which the Nordstrom-Vlasov system was originally introduced in the framework of galactic dynamics. In fact, it represents a theoretical laboratory where one can rigorously study some problems, like the importance of the gravitational waves in the dynamics, which at the present time are not well understood within the physical model of the Einstein-Vlasov system. As the cosmology of the Nordstrom-Vlasov system is founded on a scalar field, a better understanding of the system is important also in the framework of the Dark Energy problem. In fact, various attempts to achieve Dark Energy by using scalar fields are present in the literature. In the solution an analytical expression for the time dependence of the cosmological evolution of the Nordstrom's scalar field is also released.This analytical expression is unknown in the literature of the Nordstrom-Vlasov system. Based on their importance, the propagation of gravitational waves in the Nordstrom-Vlasov system and their effects on test masses are also discussed.