Relic Abundance of Mass-Varying Cold Dark Matter Particles

In models of coupled dark energy and dark matter the mass of the dark matter particle depends on the cosmological evolution of the dark energy field. In this note we exemplify in a simple model the effects of this mass variation on the relic abundance of cold dark matter. We still do not know the origin and composition of the cold dark matter (CDM) in the universe. Recent precision measurements of the cosmological microwave background and of the large scale structure of the universe put a strict bound on the abundance of non-baryonic CDM [1]: ΩCDMh 2 = 0.113± 0.008, (1) resulting from a fit of several measurements combined in the framework of a ΛCDM model with a running spectral index. Most probably CDM is made of particles (even though there are alternatives where dark matter is the manifestation of a fluid with a non-standard equation of state, such as the Chaplygin gas and quartessence models [2]) and the default candidate is the lightest supersymmetric particle (LSP) of supersymmetric (SUSY) extensions of the standard model of electroweak interactions, which is stable if R-parity is conserved. The calculation of the LSP abundance in the universe has reached a very sophisticated level. Computer codes are now publicly available that take into account all the several LSP annihilation and co-annihilation processes that enter in the evaluation of its abundance today [3]. The comparison of the results of the computer codes with recent observations are placing strong constraints in the parameters of SUSY (actually, minimal supergravity models) [4]. In fact, accuracies of the order of 10% among differents codes are being sought [5]. We also know that the universe is accelerating today. There should exist a form of dark energy, comprising roughly 70% of the energy density of the universe, responsible for its acceleration. The simplest possibility, still consistent with cosmological data, is a cosmological constant. One tantalizing problem that arises in these models is the so-called coincidence problem: why dark energy starts to dominate the universe only at recent times? This has motivated the study of models in which dark energy is coupled to dark matter . In these models of coupled dark energy, the mass of the dark matter particle depends on the dark energy field and therefore it varies on a cosmological time scale. In this letter we point out in a general way what consequences this effect may have in the calculations of the cosmological abundance of cold dark matter, illustrating them with a particular simple model. There are several different models of coupled dark energy, sometimes referred to as VAMPs (VAriable-Mass Particles) in the literature. The mass of the dark matter particles evolves according to some function of the dark energy field φ, as, for example, a linear function of the field [7, 8, 9, 10] with a inverse power law dark energy potential or an exponential function [11, 12, 13, 14, 15, 16] with an exponential dark energy potential. For instance, if the dark matter is a fermion one could have an interaction like g(φ)m0χ̄χ, where the fermion mass mχ = g(φ)m0 is a function of the dark energy field. Since the dark energy field is dynamically evolving with time, one would have mχ = mχ(φ(a)) = mχ(a). In order to have a rough idea of the possible magnitude of the mass-varying effect, we will follow a more phenomenological approach and assume that the dark matter particle mass There are also recent models that couples dark energy to neutrinos so that the energy density of neutrinos tracks the dark energy density [6]