Cosmology in a certain vector-tensor theory of gravitation

Abstract

We study relevant cosmological topics in the framework of a certain vector-tensor theory of gravitation (hereafter VT). This theory is first compared with the so-called extended electromagnetism (EE). These theories have a notable resemblance and both explain the existence of a cosmological constant. It is shown that, in EE, a positive dark energy density requires a Lagrangian leading to quantum ghosts, whereas VT is free from these ghosts. On account of this fact, the remainder of the paper is devoted to study cosmology in the framework of VT. Initial conditions, at high redshift, are used to solve the evolution equations of all the VT scalar modes. In particular, a certain scalar mode characteristic of VT—which does not appear in general relativity (GR)—is chosen in such a way that it evolves separately. In other words, the scalar modes of the standard model based on GR do not affect the evolution of the VT characteristic mode; however, this scalar mode influences the evolution of the standard GR ones. Some well known suitable codes (CMBFAST and COSMOMC) have been modified to include our VT initial conditions and evolution equations, which are fully general. One of the resulting codes—based on standard statistical methods—has been used to fit VT predictions and observational evidence about both Ia supernovae and cosmic microwave background anisotropy. Seven free parameters are used in this fit. Six of them are often used in GR cosmology, and the seventh one is characteristic of VT. From the statistical analysis it follows that VT seems to be advantageous against GR in order to explain cosmological observational evidences.