An ansatz for spacetimes of zero gravitational mass : global monopoles and textures

We propose a geometric ansatz, a restriction on Euclidean / Minkowski distance in the embedding space being propotional to distance in the embedded space, to generate spacetimes with vanishing gravitational mass ($R_{ik} u^i u^k = 0, u_i u^i = 1$). It turns out that these spacetimes can represent global monopoles and textures. Thus the ansatz is a prescription to generate zero mass spacetimes that could describe topological defects, global monopoles and textures.Comment: 9 pages, LaTeX versio

Momentum-dependent contributions to the gravitational coupling of neutrinos in a medium

When neutrinos travel through a normal matter medium, the electron neutrinos couple differently to gravity compared to the other neutrinos, due to the presence of electrons in the medium and the absence of the other charged leptons. We calculate the momentum-dependent part of the matter-induced gravitational couplings of the neutrinos under such conditions, which arise at order $g^2/M^4_W$, and determine their contribution to the neutrino dispersion relation in the presence of a gravitational potential $\phi^{\mathrm{ext}}$. These new contributions vanish for the muon and tau neutrinos. For electron neutrinos with momentum $K$, they are of the order of the usual Wolfenstein term times the factor $(K^2/M^2_W)\phi^{\mathrm{ext}}$, for high energy neutrinos. In environments where the gravitational potential is substantial, such as those in the vicinity of Active Galactic Nuclei, they could be the dominant term in the neutrino dispersion relation. They must also be taken into account in the analysis of possible violations of the Equivalence Principle in the neutrino sector, in experimental settings involving high energy neutrinos traveling through a matter background.Comment: Minor corrections in the references; one reference adde

Coherent Neutrino Interactions in a Dense Medium

Motivated by the effect of matter on neutrino oscillations (the MSW effect) we study in more detail the propagation of neutrinos in a dense medium. The dispersion relation for massive neutrinos in a medium is known to have a minimum at nonzero momentum p \sim (G_F\rho)/\sqrt{2}. We study in detail the origin and consequences of this dispersion relation for both Dirac and Majorana neutrinos both in a toy model with only neutral currents and a single neutrino flavour and in a realistic "Standard Model" with two neutrino flavours. We find that for a range of neutrino momenta near the minimum of the dispersion relation, Dirac neutrinos are trapped by their coherent interactions with the medium. This effect does not lead to the trapping of Majorana neutrinos.Comment: 28 pages, 6 figures, Latex; minor changes, one reference added; version to appear in Phys. Rev.

O(4) texture with a cosmological constant

We investigate O(4) textures in a background with a positive cosmological constant. We find static solutions which co-move with the expanding background. There exists a solution in which the scalar field is regular at the horizon. This solution has a noninteger winding number smaller than one. There also exist solutions in which scalar-field derivatives are singular at the horizon. Such solutions can complete one winding within the horizon. If the winding number is larger than some critical value, static solutions including the regular one are unstable under perturbations.Comment: 25 pages, revtex, 6 eps figure

Maximum lepton asymmetry from active-sterile neutrino oscillations in the Early Universe

A large lepton asymmetry could be generated in the Early Universe by oscillations of active to sterile neutrinos with a small mixing angle sin 2 \theta < 10^-2. The final order of magnitude of the lepton asymmetry \eta is mainly determined by its growth in the last stage of evolution when the MSW resonance dominates the kinetic equations. In this paper we present a simple way of calculating the maximum possible lepton asymmetry which can be created. Our results are in good agreement to previous calculations. Furthermore, we find that the growth of asymmetry does not obey any particular power law. We find that the maximum possible asymmetry at the freeze-out of the n/p ratio at T \sim 1 MeV strongly depends on the mass-squared difference \delta m^2: the asymmetry is negligible for \delta m^2 \ll 1 eV^2 and reaches asymptotically large values for \delta m^2 \ge 50 eV^2.Comment: 14 pp, 4 figure

Electron-, Mu-, and Tau-Number Conservation in a Supernova Core

We study if the neutrino mixing parameters suggested by the atmospheric neutrino anomaly imply chemical equilibrium between mu- and tau-flavored leptons in a supernova (SN) core. The initial flavor-conversion rate would indeed be fast if the nu_mu-nu_tau-mixing angle were not suppressed by second-order refractive effects. The neutrino diffusion coefficients are different for nu_mu, anti-nu_mu, nu_tau and anti-nu_tau so that neutrino transport will create a net mu and tau lepton number density. This will typically lead to a situation where the usual first-order refractive effects dominate, further suppressing the rate of flavor conversion. Altogether, neutrino refraction has the nontrivial consequence of guaranteeing the separate conservation of e, mu, and tau lepton number in a SN core on the infall and cooling time scales, even when neutrino mixing angles are large.Comment: Slightly expanded version with improved presentation, no changes of substanc

Neutrino-Neutrino Scattering and Matter-Enhanced Neutrino Flavor Transformation in Supernovae

We examine matter-enhanced neutrino flavor transformation ($\nu_{\tau(\mu)}\rightleftharpoons\nu_e$) in the region above the neutrino sphere in Type II supernovae. Our treatment explicitly includes contributions to the neutrino-propagation Hamiltonian from neutrino-neutrino forward scattering. A proper inclusion of these contributions shows that they have a completely negligible effect on the range of $\nu_e$-$\nu_{\tau(\mu)}$ vacuum mass-squared difference, $\delta m^2$, and vacuum mixing angle, $\theta$, or equivalently $\sin^22\theta$, required for enhanced supernova shock re-heating. When neutrino background effects are included, we find that $r$-process nucleosynthesis from neutrino-heated supernova ejecta remains a sensitive probe of the mixing between a light $\nu_e$ and a $\nu_{\tau(\mu)}$ with a cosmologically significant mass. Neutrino-neutrino scattering contributions are found to have a generally small effect on the $(\delta m^2,\ \sin^22\theta)$ parameter region probed by $r$-process nucleosynthesis. We point out that the nonlinear effects of the neutrino background extend the range of sensitivity of $r$-process nucleosynthesis to smaller values of $\delta m^2$.Comment: 38 pages, tex, DOE/ER/40561-150-INT94-00-6

Further studies on relic neutrino asymmetry generation II: a rigorous treatment of repopulation in the adiabatic limit

We derive an approximate relic neutrino asymmetry evolution equation that systematically incorporates repopulation processes from the full quantum kinetic equations (QKEs). It is shown that in the collision dominant epoch, the said equation reduces precisely to the expression obtained previously from the static/adiabatic approximation. The present treatment thus provides a rigorous justification for the seemingly incongruous assumptions of a negligible repopulation function and instantaneous repopulation sometimes employed in earlier works.Comment: RevTeX, 11 pages, no figure

Textures and Newtonian Gravity

Newtonian theory is used to study the gravitational effects of a texture, in particular the formation of massive structures.Comment: 4 pages, 4 ps figures, REVTEX, accepted for publication in PR

Neutrino-Mixing-Generated Lepton Asymmetry and the Primordial 4^4He Abundance

It has been proposed that an asymmetry in the electron neutrino sector may be generated by resonant active-sterile neutrino transformations during Big Bang Nucleosynthesis (BBN). We calculate the change in the primordial $^4$He yield $Y$ resulting from this asymmetry, taking into account both the time evolution of the $\nu_e$ and $\bar\nu_e$ distribution function and the spectral distortions in these. We calculate this change in two schemes: (1) a lepton asymmetry directly generated by $\nu_e$ mixing with a lighter right-handed sterile neutrino $\nu_s$; and (2) a lepton asymmetry generated by a $\nu_\tau\leftrightarrow\nu_s$ or $\nu_\mu\leftrightarrow\nu_s$ transformation which is subsequently partially converted to an asymmetry in the $\nu_e\bar\nu_e$ sector by a matter-enhanced active-active neutrino transformation. In the first scheme, we find that the percentage change in $Y$ is between -1% and 9% (with the sign depending on the sign of the asymmetry), bounded by the Majorana mass limit m_{\nu_e}\la 1 eV. In the second scheme, the maximal percentage reduction in $Y$ is 2%, if the lepton number asymmetry in neutrinos is positive; Otherwise, the percentage increase in $Y$ is \la 5% for m^2_{\nu_\mu,\nu_\tau}-m^2_{\nu_s}\la 10^4 eV. We conclude that the change in the primordial $^4$He yield induced by a neutrino-mixing-generated lepton number asymmetry can be substantial in the upward direction, but limited in the downward direction.Comment: 15 pages, 7 figures, submitted to PR