We study the generation of large scale primordial magnetic fields by a cosmological phase transition during the radiation dominated era. The setting is a theory of N charged scalar fields coupled to an Abelian gauge field, that undergoes a phase transition at a critical temperature much larger than the electroweak scale. The dynamics after the transition features two distinct stages: a spinodal regime dominated by linear long-wavelength instabilities, and a scaling stage in which the nonlinearities and back reaction of the scalar fields are dominant. This second stage describes the growth of horizon sized domains. We implement a recently introduced formulation to obtain the spectrum of magnetic fields that includes the dissipative effects of the plasma. We find that large scale magnetogenesis is very efficient during the scaling regime. The ratio between the energy density on scales larger than L and that in the background radiation $r(L,T)={\rho }_B\mathrm{}(L,T)/{\rho }_{\mathrm{cmb}}\mathrm{}\left(T\right)\mathrm{}$ is $r(L,T)\mathrm{}\sim {10}^{-34}$ at the electroweak scale and $r(L,T)\mathrm{}\sim {10}^{-14}$ at the QCD scale for $L\sim 1\mathrm{Mpc}.$ The resulting spectrum is insensitive to the magnetic diffusion length. We conjecture that a similar mechanism could be operative after the QCD chiral phase transition.

We show that the field equations for cosmological perturbations in the Newtonian gauge always have an adiabatic solution, for which a quantity $\mathcal{R}$ is nonzero and constant in all eras in the limit of large wavelength, so that it can be used to connect observed cosmological fluctuations in this mode with those at very early times. There is also a second adiabatic mode, for which $\mathcal{R}$ vanishes for a large wavelength, and in general there may be nonadiabatic modes as well. These conclusions apply in all eras and whatever the constituents of the universe, under only a mild technical assumption about the wavelength dependence of the field equations for a large wavelength. In the absence of anisotropic inertia, the perturbations in the adiabatic modes are given for a large wavelength by universal formulas in terms of the Robertson-Walker scale factor. We discuss an apparent discrepancy between these results and what appears to be a conservation law in all modes found for a large wavelength in the synchronous gauge: it turns out that, although equivalent, the synchronous and Newtonian gauges suggest inequivalent assumptions about the behavior of the perturbations for a large wavelength.

In a previous paper (paper I), we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by truncating or clipping sample values which lie in those non-Gaussian tails. The methods were derived, in the frequentist framework, by minimizing false alarm probabilities at fixed false detection probability in the limit of weak signals. For stochastic signals, the resulting statistic consisted of a sum of an autocorrelation term and a cross-correlation term; it was necessary to discard “by hand” the autocorrelation term in order to arrive at the correct, generalized cross-correlation statistic. In the present paper, we present an alternative derivation of the same signal detection techniques from within the Bayesian framework. We compute, for both deterministic and stochastic signals, the probability that a signal is present in the data, in the limit where the signal-to-noise ratio squared per frequency bin is small, where the signal is nevertheless strong enough to be detected (integrated signal-to-noise ratio large compared to 1), and where the total probability in the non-Gaussian tail part of the noise distribution is small. We show that, for each model considered, the resulting probability is to a good approximation a monotonic function of the detection statistic derived in paper I. Moreover, for stochastic signals, the new Bayesian derivation automatically eliminates the problematic autocorrelation term.

We discuss nonanomalous R symmetry in supersymmetric grand unified theories (GUTs). In particular, we explore anomaly-free solutions predicting the gravitino mass in the range of ${10}^{-3}\mathrm{eV}\lesssim m_{3/2}\lesssim 1\mathrm{TeV}$ when the $\mu$ parameter is fixed to be $\mu \simeq 1\mathrm{TeV}.$ In the minimal SU(5) GUT, we show that $\mu \simeq 1\mathrm{TeV}$ is obtained only if the gravitino is ultralight with a mass $m_{3/2}\sim {10}^{-3}\mathrm{eV}.$ If extra fields $5\oplus 5^{*}$ or $10\oplus {10}^{*}$ are introduced, many solutions predicting $m_{3/2}\gtrsim {10}^{-3}\mathrm{eV}$ are found. R parity is violated due to the vacuum expectation value of the superpotential, but it is controlled by the discrete R symmetry. We find that the R-parity violating couplings are naturally suppressed much below the experimental bounds for some charge assignments. These charge assignments predict light gravitinos with masses of order ${O(10\mathrm{}}^{-3}\mathrm{eV})–O(1\mathrm{}\mathrm{MeV}).\mathrm{}$ These discrete R symmetries can be considered as solutions to the $\mu$ problem in low energy supersymmetry breaking models such as gauge mediation.

We calculate three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with the first order electron and muon polarization loop insertions in graphs with two exchanged photons. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm squared contribution was obtained a long time ago. Here we calculate the single-logarithmic and nonlogarithmic contributions. We previously calculated the three-loop radiative-recoil corrections generated by two-loop polarization insertions in the exchanged photons. The current paper therefore concludes calculation of all three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by diagrams with closed fermion loop insertions in the exchanged photons. The new results obtained here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from experimental data on the muonium hyperfine splitting.

A recent paper by Alves, Das, and Perez contains a calculation of the one-loop self-energy in ${\phi }^3$ field theory at $T\ne 0$ using light-front quantization and concludes that the self-energy is different than the conventional answer and is not rotationally invariant. The changes of variable displayed below show that despite the complicated appearance of the thermal self-energy in light-front variables, it is exactly the same as the conventional result.

It is shown that, for systems in which the entropy is an extensive function of the energy and volume, the Bekenstein and the holographic entropy bounds predict new results. More explicitly, the Bekenstein entropy bound leads to the entropy of thermal radiation (the Unruh-Wald bound) and the spherical entropy bound implies the “causal entropy bound.” Surprisingly, the first bound shows a close relationship between black hole physics and the Stephan-Boltzmann law (for the energy and entropy flux densities of the radiation emitted by a hot blackbody). Furthermore, we find that the number of different species of massless fields is bounded by $\sim {10}^4.$

The timelike boundary Liouville (TBL) conformal field theory consisting of a negative norm boson with an exponential boundary interaction is considered. TBL theory and its close cousin, a positive norm boson with a non-Hermitian boundary interaction, arise in the description of the $c=1\mathrm{}$ accumulation point of $c<\mathrm{}1\mathrm{}$ minimal models, as the worldsheet description of open string tachyon condensation in string theory and in scaling limits of superconductors with line defects. Bulk correlators are shown to be exactly soluble. In contrast, due to OPE singularities near the boundary interaction, the computation of boundary correlators is a challenging problem which we address but do not fully solve. Analytic continuation from the known correlators of spatial boundary Liouville to TBL theory encounters an infinite accumulation of poles and zeros. A particular contour prescription is proposed which cancels the poles against the zeros in the boundary correlator $d\left(\omega \right)$ of two operators of weight ${\omega }^2$ and yields a finite result. A general relation is proposed between two-point CFT correlators and stringy Bogolubov coefficients, according to which the magnitude of $d\left(\omega \right)$ determines the rate of open string pair creation during tachyon condensation. The rate so obtained agrees at large ω with a minisuperspace analysis of previous work. It is suggested that the mathematical ambiguity arising in the prescription for analytic continuation of the correlators corresponds to the physical ambiguity in the choice of open string modes and vacua in a time dependent background.

We study the behavior of spiky features in Gowdy spacetimes. Spikes with a velocity initially high are, generally, driven to a low velocity. Let n be any integer greater than or equal to 1. If the initial velocity of an upward pointing spike is between $4n-3$ and $4n-1$ the spike persists with a final velocity between 1 and 2, while if the initial velocity is between $4n-1$ and $4n+1,$ the spiky feature eventually disappears. For downward pointing spikes the analogous rule is that spikes with an initial velocity between $4n-4$ and $4n-2$ persist with a final velocity between 0 and 1, while spikes with an initial velocity between $4n-2$ and $4n$ eventually disappear.

We study both global as well as local (Nielsen-Olesen) strings in de Sitter space. While these types of topological defects have been studied in the background of a de Sitter metric previously, we study here the full set of coupled equations. We find only “closed” solutions. The behavior of the metric tensor of these solutions resembles that of “supermassive” strings with a curvature singularity at the cosmological horizon. For global strings (and the composite defect) we are able to construct solutions which are regular on the interval from the origin to the cosmological horizon if the global string core lies completely inside the horizon.

Nonlinear covariant parity-violating deformations of free spin-two gauge theory are studied in $n>~3$ spacetime dimensions, using a linearized frame and spin-connection formalism, for a set of massless spin-two fields. It is shown that the only such deformations yielding field equations with a second order quasilinear form are the novel algebra-valued types in $n=3\mathrm{}$ and $n=5\mathrm{}$ dimensions already found in some recent related work concentrating on lowest order deformations. The complete form of the deformation to all orders in $n=5\mathrm{}$ dimensions is worked out here and some features of the resulting new algebra-valued spin-two gauge theory are discussed. In particular, the internal algebra underlying this theory on five-dimensional Minkowski space is shown to cause the energy for the spin-two fields to be of indefinite sign. Finally, a Kaluza-Klein reduction to $n=4\mathrm{}$ dimensions is derived, giving a parity-violating nonlinear gauge theory of a coupled set of spin-two, spin-one, and spin-zero massless fields.

Homodyne detection is one of the ways to circumvent the standard quantum limit by changing the readout phase of a gravitational wave detector. In this paper it is shown that the readout phase can also be changed by the radio-frequency heterodyne detection scheme that is generally used in present detectors.

We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the five helicity amplitudes is reduced to the usual angular condition relating the four helicity amplitudes due to the light-front time-reversal condition. We make some comments on the consequences of the angular condition for the analysis of the high-$Q^2$ deuteron electromagnetic form factors, and we further apply the general angular condition to the electromagnetic transition between spin-1/2 and spin-3/2 systems and find a relation useful for the analysis of the $N-\Delta$ transition form factors. We also discuss the scaling law and the subleading power corrections in the Breit and light-front frames.

In the leading order of the heavy quark expansion, we propose a method within the operator product expansion and the trace formalism that allows us to obtain, in a systematic way, Bjorken-like sum rules for the derivatives of the elastic Isgur-Wise (IW) function $\xi \mathrm{}\left(w\right)\mathrm{}$ in terms of corresponding Isgur-Wise functions of transitions to excited states. A key element is the consideration of the nonforward amplitude, as introduced by Uraltsev. A simplifying feature of our method is to consider currents aligned along the initial and final four-velocities. As an illustration, we give a very simple derivation of Bjorken and Uraltsev sum rules. On the other hand, we obtain a new class of sum rules that involve the products of IW functions at zero recoil and IW functions at any w. Special care is given to the needed derivation of the projector on the polarization tensors of particles of arbitrary integer spin. The new sum rules give further information on the slope ${\rho }^2=-{\xi }^{\prime }\mathrm{}\left(1\right)\mathrm{}$ and also on the curvature ${\sigma }^2={\xi }^{″}\mathrm{}\left(1\right)\mathrm{}$ and imply, modulo a very natural assumption, the inequality ${\sigma }^2>~\mathrm{}(5/4)\mathrm{}{\rho }^2,$ and therefore the absolute bound ${\sigma }^2>~15/16.$

In the light of the recent WMAP results we update the constraints on a class of nonstandard big bang nucleosynthesis (BBN) models with a simultaneous combination of nonstandard neutrino distributions and an extra effective number of neutrinos in the expansion rate. These models can be described in terms of the two parameters $\Delta N_{\nu }^{\mathrm{tot}},$ constrained by the primordial helium abundance $Y_p$ measurement, and $\Delta N_{\nu }^{\rho },$ constrained by a combination of cosmic microwave background and primordial deuterium data. Small deviations from standard big bang nucleosynthesis are suggested. Different nonstandard scenarios can be distinguished by a measurement of the difference $\Delta N_{\nu }^{f_{\nu }}=\Delta N_{\nu }^{\mathrm{tot}}-\Delta N_{\nu }^{\rho }.$ From the current data we estimate $\Delta N_{\nu }^{f_{\nu }}\simeq -{1.4}_{-1.4}^{+0.9\mathrm{}},$ mildly disfavoring solutions with a low expansion rate, characterized by $\Delta N_{\nu }^{f_{\nu }}=0\mathrm{}$ and negative $\Delta N_{\nu }^{\rho }.$ Active-sterile neutrino mixing could be a viable explanation only for high values of $Y_p\gtrsim \mathrm{0.24.}$ The existence of large positive neutrino chemical potentials ${\xi }_i\sim 0.05,$ implying $\Delta N_{\nu }^{\rho }\simeq 0,$ would be a possible explanation of the data within the analyzed class of nonstandard BBN models. Interestingly, it would also provide a way to evade the cosmological bounds for “class A 3+1” four neutrino mixing models. A scenario with a decaying sterile neutrino is also considered.

We study several issues related to the different choices of time available for the classical and quantum treatment of linearly polarized cylindrical gravitational waves. We pay special attention to the time evolution of creation and annihilation operators and the definition of Fock spaces for the different choices of time involved. We also discuss the issue of microcausality and the use of field commutators to extract information about the causal properties of quantum spacetime.

The Einstein evolution equations have previously been written in a number of symmetric hyperbolic forms when the gauge fields—the densitized lapse and the shift—are taken to be fixed functions of the coordinates. Extended systems of evolution equations are constructed here by adding the gauge degrees of freedom to the set of dynamical fields, thus forming symmetric hyperbolic systems for the combined evolution of the gravitational and the gauge fields. The associated characteristic speeds can be made causal (i.e., less than or equal to the speed of light) by adjusting 14 free parameters in these new systems, and 21 additional free parameters are available, for example, to optimize the stability of numerical evolutions. The gauge evolution equations in these systems are generalizations of the $“K$-driver” and “Γ-driver” conditions that have been used with some success in numerical black hole evolutions.

We construct explicit models of multifield inflation in which the primordial metric fluctuations do not necessarily obey Gaussian statistics. These models are realizations of mechanisms in which non-Gaussianity is first generated by a light scalar field and then transferred into curvature fluctuations. The probability distribution functions of the metric perturbation at the end of inflation are computed. This provides a guideline for designing strategies to search for non-Gaussian signals in future CMB and large scale structure surveys.

A new hybrid approach to air shower simulations is described. At highest energies, each particle is followed individually using the traditional Monte Carlo method; this initializes a system of cascade equations which are applicable for energies such that the shower is one dimensional. The cascade equations are solved numerically down to energies at which lateral spreading becomes significant; then, their output serves as a source function for a three-dimensional Monte Carlo simulation of the final stage of the shower. This simulation procedure reproduces the natural fluctuations in the initial stages of the shower, gives accurate lateral distribution functions, and provides detailed information about all low energy particles on an event-by-event basis. It is quite efficient in computation time.