Entropy production from scalar decay in the era of low temperatures after neutrino decoupling will change the ratio of the relic neutrino temperature to the CMB temperature, and, hence, the value of N ef f , the effective number of neutrino species. Such scalar decay is relevant to reheating after thermal inflation, proposed to dilute massive particles, like the moduli and the gravitino, featuring in supersymmetric and string theories. The effect of such entropy production on the relic neutrino temperature ratio is calculated in a semi-analytic manner, and a recent lower bound on this ratio, obtained from the WMAP satellite and 2dF galaxy data, is used to set a lower bound of ∼ 1.5 × 10 −23 Gev on the scalar decay constant, corresponding to a reheating temperature of about 3.3 Mev.

We investigate the effect of B+L−violating anomalous generation of massive right-handed neutrinos on their decoupling, when the righthanded neutrino mass is considerably greater than the right-handed gauge boson masses. Considering normal annihilation channels, the Lee-Weinberg type of calculation, in this case, gives an upper bound of about 700 Gev, which casts doubt on the existence of such a right-handed neutrino mass greater than right-handed gauge boson masses. We examine the possibility that a consideration of anomalous effects related to the SU (2)R gauge group may turn this into a lower bound ∼ 10 2 Tev. PACS number(s) : 18.80.-k, 14.60.St, 11.10.Wx. I. INTRODUCTIONNeutrino oscillation interpretation of recent observations of solar and atmospheric neutrino fluxes, although presenting some inconsistencies, may be taken to strengthen the idea of non-zero neutrino masses. In this situation, in addition to the standard model left-handed neutrinos, the existence and masses of right-handed neutrinos assume topical interest.The contribution of massive neutrinos to the mass-density of the universe 1 allows the setting of a lower bound to such a neutrino mass from the usual cosmological constraints on the age and mass-density of the universe [1,2,3]. The standard calculations consider a neutrino mass less than gauge boson masses.In the present paper, working in a L-R symmetric extension of the standard model [4,5,6], we investigate how the nature of the bound is altered when the right-handed neutrino mass is greater than gauge boson masses.In these L-R symmetric models, the breaking of SU (2) R gauge symmetry is associated with a critical temperature. This may, typically, be of the order of 1-10 Tev [7,8,9], and right-handed electron neutrino masses ≈ 10 Tev have been considered, yielding a left-handed electron neutrino mass ≈ 10 −10 Gev, by a see-saw mechanism [9]. Now, B+L is not conserved in standard electroweak theory due to an anomaly involving the SU (2)

Heavy right-handed neutrinos are of current interest. The interactions and decay of such neutrinos determine their decoupling epoch during the evolution of the universe. This in turn affects various observable features like the energy density, nucleosynthesis, CMBR spectrum, galaxy formation, and baryogenesis. Here, we consider reduction of right-handed electron-type Majorana neutrinos, in the left-right symmetric model, by the W + R W − R channel and the channel originating from an anomaly, involving the SU (2) R gauge group, as well as decay of such neutrinos. We study the reduction of these neutrinos for different ranges of left-right model parameters, and find that, if the neutrino mass exceeds the right-handed gauge boson mass, then the neutrinos never decouple for realistic values of the parameters, but, rather, decay in equilibrium. Because there is no out-of-equilibrium decay, no mass bounds can be set for the neutrinos.

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