Gravitino Dark Matter and Non-Gaussianity

We investigate density fluctuations in a scenario with gravitino dark matter in the framework of modulated reheating, which is known to generate large nonGaussianity. We show that gravitino dark matter is disfavored if primordial fluctuations have large local-type non-Gaussianity in this framework. We also briefly discuss the case with the curvaton mechanism and some other possible dark matter scenarios. Recent progress in high-precision observational cosmology with cosmic microwave background (CMB) radiation has motivated us to study the tiny nonlinear effects in the very early stage of the Universe when the amplitude of fluctuations was much smaller than unity. Among various observables to quantify non-Gaussianity of primordial fluctuations, the so-called non-linearity parameter fNL, which is a stunted parameter to quantify the degrees of freedom of actual non-Gaussianity, has been widely discussed recently because observations of CMB is becoming to be able to measure its possible deviation from zero. From the recent result from WMAP5, the so-called local-type non-linearity parameter fNL is constrained as −9 < fNL < 111 [1] and −4 < fNL < 80 [2] at 95 % confidence level (CL). Although purely Gaussian fluctuation with fNL = 0 is perfectly consistent with the data, its observed central value is so much deviated from zero that future higher-precision observations may well confirm this local-type non-Gaussianity. Then the simplest models of single-field inflation [3] would be ruled out as a generation mechanism of primordial density/curvature fluctuations [4]. We can think of two mechanisms as an alternative to the inflaton to generate primordial fluctuations, modulated reheating [5] and the curvaton [6, 7], which are motivated in particle physics because there are many light fields in generic supersymmetric theories. Neither of them is necessary as long as the inflaton can be responsible for the generation of primordial fluctuations. But if the presence of large non-Gaussianity was established, they would be a target of serious study. In fact, non-Gaussianity in these alternative scenarios has been studied already in [9,10] for modulated reheating and in [11,12] for the curvaton, and it has been shown that in both scenarios large local-type non-Gaussianity is possible depending on the values of model parameters and/or initial conditions. The purpose of this Letter is to argue that confirmation of non-Gaussianity of localtype would not only rule out the simplest single-field slow-roll inflation models but also constrain the identity of the dark matter. That is, we show that the gravitino dark matter would confront difficulty in the two representative generation mechanisms of fluctuations mentioned above. Before proceeding to this main topic, for completeness, let us mention the relevance of the other type of non-Gaussianity, namely the equilateral-type, to the nature of the dark matter. It is generated due to nonlinear interactions during inflation. Typical models generating such non-Gaussianity are those making use of scalar fields with non-canonical kinetic terms [13]. They do not give us any information on the nature of the dark matter, because the inflaton is responsible for the fluctuation in this case. Observationally, the non-linearity parameter of the equilateral-type, f equil NL , has been much less constrained than the local-type, and as long as the former is concerned, there is no hint of non-Gaussianity so far. We therefore concentrate on the local-type non-Gaussianity which we denote simply by fNL as above. In models with a supersymmetric extension of the standard model, the gravitino, the spin-3/2 superpartner of the graviton, arises when the global supersymmetry is promoted to a local symmetry. If it is the lightest supersymmetric particle (LSP) and stable be#1 Other phenomenological generation mechanisms of large local-type non-Gaussianity include Refs. [8].