We discuss about the speed of sound squared in the Mass Varying Neutrinos scenario (MaVaNs). Recently, it was argued that the MaVaNs has a catastrophic instability which is the emergence of an imaginary speed of sound at the non-relativistic limit of neutrinos.As the result of this instability, the neutrino-acceleron fluid cannot act as the dark energy.However, it is found that the speed of sound squared in the neutrino-acceleron fluid could be positive in our model. We examine the speed of sound in two cases of the scalar potential.One is the small fractional power-law potential and another is the logarithmic one. The power-law potential model with the right-handed neutrinos gives a stable one. † e-mail: takahasi@muse.sc.niigata-u.ac.jp ‡ e-mail: tanimoto@muse.sc.niigata-u.ac.jp
I INTRODUCTIONOne of the most challenging questions in both cosmological and particle physics is the nature of the dark energy in the Universe. At the present epoch, the energy density of the Universe is dominated by a dark energy component, whose negative pressure causes the expansion of the Universe to accelerate. In order to clarify the origin of the dark energy, one has tried to understand the connection of the dark energy with particle physics. MaVaNs scenario leads to interesting phenomenological results. The neutrino oscillations may be a probe of the dark energy [6,7,8]. The leptogenesis [9,10], the cosmo MSW effect of neutrinos [11] and the solar neutrino [12,13] have been studied in the context of this scenario. Cosmological discussions of the scenario are also presented [14,15,16,17,18,19].The extension to the supersymmetry have been presented in ref. [20,21]. This scenario is also discussed in the context of the texture of the neutrino mass matrix with three families [22].Despite many implications of this scenario, ref. [23] showed that this scenario contains a catastrophic instability which occurs when neutrinos become non-relativistic. As neutrinos become non-relativistic, the speed of sound squared in the neutrino-acceleron fluid turns to be negative. As the result of this instability, neutrinos condense into neutrino nuggets, and 2 thus cannot act as the dark energy. However, we have found that the speed of sound squared in this fluid could be positive even though neutrinos are not enough relativistic. In order to realize the positive speed of sound squared, a constraint for the scalar potential is required.The paper is organized as follows: in Sec.II, we summarize the MaVaNs scenario with three families. Sec.III presents discussions for the speed of sound in the hydrodynamic picture. Sec.IV presents a stable model in the MaVaNs scenario. Sec.V devotes to the summary.