Solvable potentials in a FLRW+Scalar universe and Fits to type Ia supernovae data

Abstract

FLRW equations are analyzed in a universe with a cosmic scalar background that is spatially uniform but time-varying. Some solvable potentials to the combined dynamics in such a universe are presented, that are consistent with the scalar dynamics as a consequence of energy momentum conservation. Certain potentials are found to provide very good fits to type Ia supernovae data, with the kinetic and potential energies of the scalar providing the source for dark matter and dark energy. The scalar rolls down the potential as the universe expands with the potential playing the role of a time-varying cosmological constant, modeling a scenario recently discussed in the literature.