Late-Time Entropy Production and Relic Abundances of Neutralinos

Many models possess unwanted relics, which should be diluted by entropy production just before the big-bang nucleosynthesis. A field responsible for the entropy production may produce stable weakly interacting massive particles, if kinematically accessible. We compute their relic abundances by integrating out coupled equations numerically. Applying our results to supersymmetric standard models, we argue that the neutralino lightest superparticles will overclose the universe in most of the parameter space if the reheat temperature is of the order of 10 MeV. Many models beyond the standard model predict unwanted relics, which should be diluted by entropy production such as inflation and subsequent reheating. Among other things, weakly interacting massive scalar fields will be the most problematic, as they can store their energy density in the form of coherent oscillation, which may not be diluted by inflation because the coherent mode during the inflationary epoch is generally displaced from its value in the true vacuum. An example is a problem associated with moduli fields of string theory, named the cosmological moduli problem [1]. In string theory coupling constants are determined dynamically by vacuum expectation values of the moduli (and dilaton) fields. These fields generically acquire masses comparable to the gravitino mass, which should be in the TeV range in gravity mediated supersymmetry breaking. Damped coherent oscillation and subsequent decay of the fields would spoil the standard big-bang nucleosynthesis (BBN). Late-time entropy production before the BBN should operate to dilute the energy density of the problematic scalar fields. Indeed thermal inflation was proposed [2, 3], for which reheat temperature should be much lower than the electroweak scale for a successful dilution. Another example of the problematic scalar fields is an invisible axion with decay constant larger than 10 GeV, whose coherent oscillation would exceed the critical density of the universe [4]. Entropy production may be able to dilute the energy density of the axion field [5]. Since the oscillation of the axion field starts around the QCD phase transition, the reheat temperature at the entropy production should be lower than 100 MeV. Interestingly it has been argued that strongly coupled E8 × E8 heterotic string theory (Mtheory) possesses such an axion candidate with the decay constant ∼ 10 GeV, provided that non-perturbative effects to generate the superpotential for the axion field are suppressed [6, 7]. To dilute the energy density of the M-theory axion to a harmless level, the reheat temperature of the entropy production should be at its lowest value allowed by the BBN, 1–10 MeV. The requisite entropy production is provided by decays of massive unstable particles. The decays, however, may produce too many stable particles as well if the production is kinematically allowed. In a supersymmetric theory, the lightest superparticle (LSP), which is likely to be a neutralino, is stable under the assumption of R-parity conservation. Indeed it was argued that the neutralinos produced by the decays of the massive particles tend to overclose the universe, if the reheat temperature is much lower than 1 GeV [8, 9]. Motivated by the aforementioned demands for the late-time entropy pro-