Static configurations of dark energy and dark matter

Abstract

We study static configurations of dark matter coupled to a scalar field responsible for thedark energy of the Universe. The dark matter is modelled as a Fermi gas within theThomas–Fermi approximation. The mass of the dark matter particles is a function ofthe scalar field. We analyse the profile of the dark matter haloes in galaxies.In this case our framework is equivalent to the model of the isothermal sphere.In the presence of a scalar field, the velocity of a massive object orbiting thegalaxy is not of the order of the typical velocity of the dark matter particles, as inthe conventional picture. Instead, it is reduced by a factor that quantifies thedependence of the dark matter mass on the scalar field. This has implications fordark matter searches. We derive new solutions of the Einstein equations whichdescribe compact objects composed of dark matter. Depending on the scale ofthe dark matter mass, the size of these objects can vary between microscopicscales and cosmological distances. We determine the mass to radius relation anddiscuss similarities with conventional neutron stars and exotic astrophysical objects.