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In this paper we present a modified localization landscape theory to calculate localized/confined electron and hole states and the corresponding energy eigenvalues without solving a (large) eigenvalue problem. We motivate and demonstrate the benefit of solving $\hat{H}^2u=1$ in the modified localization landscape theory in comparison to $\hat{H}u=1$, solved in the localization landscape theory. We detail the advantages by fully analytic considerations before targeting the numerical calculation of electron and hole states and energies in III-N heterostructures. We further discuss how the solution of $\hat{H}^2u=1$ is used to extract an effective potential $W$ that is comparable to the effective potential obtained from $\hat{H}u=1$, ensuring that it can for instance be used to introduce quantum corrections to drift-diffusion transport calculations. Overall, we show that the proposed modified localization landscape theory keeps all the benefits of the recently introduced localization landscape theory but further improves factors such as convergence of the calculated energies and the robustness of the method against the chosen integration region for $u$ to obtain the corresponding energies. We find that this becomes especially important for here studied $c$-plane InGaN/GaN quantum wells with higher In contents. All these features make the proposed approach very attractive for calculation of localized states in highly disordered systems, where partitioning the systems into different subregions can be difficult., Comment: 14 pages, 6 figures

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_eff, 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 x 10^-23 Gev on the scalar decay constant, corresponding to a reheating temperature of about 3.3 Mev., Comment: 13 pages, to appear in PRD

Late-time entropy production from scalar decay arises in scenarios like thermal inflation, proposed to dilute long-lived, massive fields like the gravitino and the moduli. The scalar decay may continue into Mev-scale temperatures and affect BB nucleosynthesis. The effect of such entropy production on electron neutrino decoupling is studied. A lower bound of about 10^(-22) Gev is estimated for the scalar decay constant, such that, for higher values of the decay constant, standard electron neutrino decoupling is unaffected., Comment: 7 pages, Latex, no figures, one reference added

Small Recent theories have proposed a variety of massive particles, like the moduli, whose abundance or decay endangers standard cosmological results. To dilute them, thermal inflation has been proposed, with its own massive scalar flaton field which goes on decaying in the era of Mev-scale temperatures. In this paper, the effect of late-time entropy production on neutrino decoupling during such reheating is investigated by including a term, arising from the rate of entropy production due to scalar decay, in the Boltzmann equation for the neutrino number density. The effect on the decoupling temperature of massless neutrinos is studied. It is found that a lower bound to the scalar decay rate constant can be set at 10^{-22} Gev., Comment: 17 pages, Latex, No figures

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 WR+ - WR- 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., Comment: Latex, 16 pages, No figures. Some additions in the text and references. Conclusions unaffected. To appear in Eur. Phys. J. C

We investigate the effect of B+L - violating anomalous generation of massive right-handed neutrinos on their decoupling, when the right-handed 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 of the order of 100 Tev., Comment: 28 Pages, Latex, 2 figures

Starting from an initial state of thermal equilibrium, we derive an expression for the quantum fluctuation in the energy density during the inflationary epoch in terms of the mode functions for the inflaton field. The effect of this particular initial state is not washed out in the final formula, contrary to what is usually believed. Numerically, however, the effect is completely negligible, validating the use of the two point function in the vacuum state. We also point out the requirement of conventional quantum field theory during inflation, that the quantum fluctuation in a wavelength must be evaluated, at the latest, when the wavelength crosses the Hubble length, in contrast to the usual practice in the literature., Comment: 12 pages, latex, 1 figure, axodraw

We examine the calculation of density perturbation at large scales in the inflationary scenario. The formula for its magnitude is reviewed from first principles and applied to the original model of extended inflation. Our estimate is an order of magnitude bigger than the earlier ones due to the difference in the time at which the primordial fluctuation is evaluated and to the inclusion of terms neglected earlier in the standard formula for density perturbation., Comment: 11 pages, Latex, no figures