Electromagnetic duality in general relativity

By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action implies the Einstein vacuum equation without the cosmological term. The vacuum equation is invariant under interchange of active and passive electric parts giving rise to the same vacuum solutions but the gravitational constant changes sign. Further by modifying the equation it is possible to construct interesting dual solutions to vacuum as well as to flat spacetimes.Comment: 18 pages, LaTEX versio

Beyond the Small-Angle Approximation For MBR Anisotropy from Seeds

In this paper we give a general expression for the energy shift of massless particles travelling through the gravitational field of an arbitrary matter distribution as calculated in the weak field limit in an asymptotically flat space-time. It is {\it not} assumed that matter is non-relativistic. We demonstrate the surprising result that if the matter is illuminated by a uniform brightness background that the brightness pattern observed at a given point in space-time (modulo a term dependent on the oberver's velocity) depends only on the matter distribution on the observer's past light-cone. These results apply directly to the cosmological MBR anisotropy pattern generated in the immediate vicinity of of an object like a cosmic string or global texture. We apply these results to cosmic strings, finding a correction to previously published results for in the small-angle approximation. We also derive the full-sky anisotropy pattern of a collapsing texture knot.Comment: 23 pages, FERMILAB-Pub-94/047-

On the sign of the neutrino asymmetry induced by active-sterile neutrino oscillations in the early Universe

We deal with the problem of the final sign of the neutrino asymmetry generated by active-sterile neutrino oscillations in the Early Universe solving the full momentum dependent quantum kinetic equations. We study the parameter region $10^{-2} \stackrel{<}{\sim} |\delta m^2|/eV^2\le 10^3$. For a large range of $\sin^2 2\theta_0$ values the sign of the neutrino asymmetry is fixed and does not oscillate. For values of mixing parameters in the region $10^{-6}\stackrel{<}{\sim}\sin^{2}2\theta_{0}\stackrel{<}{\sim} 3\times 10^{-4} ({\rm eV}^{2}/|\delta m^{2}|)$, the neutrino asymmetry appears to undergo rapid oscillations during the period where the exponential growth occurs. Our numerical results indicate that the oscillations are able to change the neutrino asymmetry sign. The sensitivity of the solutions and in particular of the final sign of lepton number to small changes in the initial conditions depends whether the number of oscillations is high enough. It is however not possible to conclude whether this effect is induced by the presence of a numerical error or is an intrinsic feature. As the amplitude of the statistical fluctuations is much lower than the numerical error, our numerical analysis cannot demonstrate the possibility of a chaotical generation of lepton domains. In any case this possibility is confined to a special region in the space of mixing parameters and it cannot spoil the compatibility of the $\nu_{\mu}\leftrightarrow\nu_{s}$ solution to the neutrino atmospheric data obtained assuming a small mixing of the $\nu_{s}$ with an ${\rm eV}-\tau$ neutrino.Comment: Typo's corrected, accepted for publication in Phys.Rev.

Active-sterile neutrino oscillations in the early Universe: asymmetry generation at low |delta m^2| and the Landau-Zener approximation

It is well established that active-sterile neutrino oscillations generate large neutrino asymmetries for very small mixing angles ($\sin^2 2\theta_0\lesssim 10^{-4}$), negative values of $\delta m^2$ and provided that $|\delta m^2|\gtrsim 10^{-4} {\rm eV^2}$. By numerically solving the quantum kinetic equations, we show that the generation still occurs at much lower values of $|\delta m^2|$. We also describe the borders of the generation at small mixing angles and show how our numerical results can be analytically understood within the framework of the Landau-Zener approximation thereby extending previous work based on the adiabatic limit. This approximate approach leads to a fair description of the MSW dominated regime of the neutrino asymmetry evolution and is also able to correctly reproduce its final value. We also briefly discuss the impact that neutrino asymmetry generation could have on big bang nucleosynthesis, CMBR and relic neutrinos.Comment: 29 pages, 8 figures; to appear on Phys. ReV. D; figure 7 added, new curves in figure 5a, new figure

Detailed study of BBN implications of neutrino oscillation generated neutrino asymmetries in some four neutrino models

We re-examine the evolution of neutrino asymmetries in several four neutrino models. The first case involves the direct creation of $L_{\nu_e}$ by $\nu_e \leftrightarrow \nu_s$ oscillations. In the second case, we consider the mass hierarchy $m_{\nu_\tau} \gg m_{\nu_\mu}, m_{\nu_e}, m_{\nu_s}$ where $\nu_\tau \leftrightarrow \nu_s$ oscillations generate a large $L_{\nu_\tau}$ and some of this asymmetry is converted into $L_{\nu_e}$ by $\nu_{\tau} \leftrightarrow \nu_{e}$ oscillations. We estimate the implications for BBN for a range of cosmologically interesting $\delta m^2$ values. The present paper improves on previous published work by taking into account the finite repopulation rate and the time dependence of the distortions to the neutrino momentum distributions. The treatment of chemical decoupling is also improved.Comment: Expanded discussion on the sign of the neutrino asymmetr

How precisely can we reduce the three-flavor neutrino oscillation to the two-flavor one only from (\delta m^2_{12})/(\delta m^2_{13}) <~ 1/15 ?

We derive the reduction formula, which expresses the survival rate for the three-flavor neutrino oscillation by the two-flavor one, to the next-to-leading order in case there is one resonance due to the matter effect. We numerically find that the next-to-leading reduction formula is extremely accurate and the improvement is relevant for the precision test of solar neutrino oscillation and the indirect measurment of CP violation in the leptonic sector. We also derive the reduction formula, which is slightly different from that previously obtained, in case there are two resonances. We numerically verify that this reduction formula is quite accurate and is valid for wider parameter region than the previously obtained ones are.Comment: 28pages, 8figures, revtex4. to appear in PR

Electromagnetic properties of a neutrino stream

In a medium that contains a neutrino background in addition to the matter particles, the neutrinos contribute to the photon self-energy as a result of the effective electromagnetic vertex that they acquire in the presence of matter. We calculate the contribution to the photon self-energy in a dense plasma, due to the presence of a gas of charged particles, or neutrinos, that moves as a whole relative to the plasma. General formulas for the transverse and longitudinal components of the photon polarization tensor are obtained in terms of the momentum distribution functions of the particles in the medium, and explicit results are given for various limiting cases of practical interest. The formulas are used to study the electromagnetic properties of a plasma that contains a beam of neutrinos. The transverse and longitudinal photon dispersion relations are studied in some detail. Our results do not support the idea that neutrino streaming instabilities can develop in such a system. We also indicate how the phenomenon of optical activity of the neutrino gas is modified due to the velocity of the neutrino background relative to the plasma. The general approach and results can be adapted to similar problems involving relativistic plasmas and high-temperature gauge theories in other environments.Comment: Revtex, 19 pages and 3 included ps file

Stringent Constraints on Cosmological Neutrino-Antineutrino Asymmetries from Synchronized Flavor Transformation

We assess a mechanism which can transform neutrino-antineutrino asymmetries between flavors in the early universe, and confirm that such transformation is unavoidable in the near bi-maximal framework emerging for the neutrino mixing matrix. We show that the process is a standard Mikheyev-Smirnov-Wolfenstein flavor transformation dictated by a synchronization of momentum states. We also show that flavor ``equilibration'' is a special feature of maximal mixing, and carefully examine new constraints placed on neutrino asymmetries. In particular, the big bang nucleosynthesis limit on electron neutrino degeneracy xi_e < 0.04 does not apply directly to all flavors, yet confirmation of the large-mixing-angle solution to the solar neutrino problem will eliminate the possibility of degenerate big bang nucleosynthesis.Comment: 11 pages, 6 figures; minor changes to match PRD versio

On the Evolution of the Neutrino State inside the Sun

We reexamine the conventional physical description of the neutrino evolution inside the Sun. We point out that the traditional resonance condition has physical meaning only in the limit of small values of the neutrino mixing angle, theta<<1. For large values of theta, the resonance condition specifies neither the point of the maximal violation of adiabaticity in the nonadiabatic case, nor the point where the flavor conversion occurs at the maximal rate in the adiabatic case. The corresponding correct conditions, valid for all values of theta including theta>pi/4, are presented. An adiabaticity condition valid for all values of theta is also described. The results of accurate numerical computations of the level jumping probability in the Sun are presented. These calculations cover a wide range of Delta m^2, from the vacuum oscillation region to the region where the standard exponential approximation is good. A convenient empirical parametrization of these results in terms of elementary functions is given. The matter effects in the so-called "quasi-vacuum oscillation regime" are discussed. Finally, it is shown how the known analytical results for the exponential, 1/x, and linear matter distributions can be simply obtained from the formula for the hyperbolic tangent profile. An explicit formula for the jumping probability for the distribution N_e ~ (coth(x/l) +- 1) is obtained.Comment: 34 pages, 8 figure

High-energy neutrino conversion and the lepton asymmetry in the universe

We study matter effects on oscillations of high-energy neutrinos in the Universe. Substantial effect can be produced by scattering of the neutrinos from cosmological sources (z\gta 1) on the relic neutrino background, provided that the latter has large CP-asymmetry: \eta\equiv (n_\nu-n_{\bar{\nu}})/n_\gamma\gta 1, where $n_\nu$, $n_{\bar{\nu}}$ and $n_\gamma$ are the concentrations of neutrinos, antineutrinos and photons. We consider in details the dynamics of conversion in the expanding neutrino background. Applications are given to the diffuse fluxes of neutrinos from GRBs, AGN, and the decay of super-heavy relics. We find that the vacuum oscillation probability can be modified by $\sim (10-20)$ and in extreme cases allowed by present bounds on $\eta$ the effect can reach $\sim 100$. Signatures of matter effects would consist (i) for both active-active and active-sterile conversion, in a deviation of the numbers of events produced in a detector by neutrinos of different flavours, $N_{\alpha}~(\alpha=e,\mu,\tau)$, and of their ratios from the values given by vacuum oscillations; such deviations can reach $\sim 5-15$, (ii) for active-sterile conversion, in a characteristic energy dependence of the ratios $N_{e}/N_{\mu},N_{e}/N_{\tau},N_{\mu}/N_{\tau}$. Searches for these matter effects will probe large CP and lepton asymmetries in the universe.Comment: 32 pages, RevTeX, 16 figures. Substantial changes in the treatment of conversion effects in the relic neutrino background and of active-active oscillations of high-energy neutrinos. Figures and references added; conclusions partially modifie