We study primordial nucleosynthesis abundance yields for assumed ranges of cosmological lepton numbers, sterile neutrino mass-squared differences and active-sterile vacuum mixing angles. We fix the baryon-to-photon ratio at the value derived from the cosmic microwave background (CMB) data and then calculate the deviation of the ${}^2\mathrm{H}$, ${}^4\mathrm{He}$, and ${}^7\mathrm{Li}$ abundance yields from those expected in the zero-lepton number(s), no-new-neutrino-physics case. We conclude that high precision ($<5\%$ error) measurements of the primordial ${}^2\mathrm{H}$ abundance from, e.g., QSO absorption line observations coupled with high precision ($<1\%$ error) baryon density measurements from the CMB could have the power to either: (i) reveal or rule out the existence of a light sterile neutrino if the sign of the cosmological lepton number is known; or (ii) place strong constraints on lepton numbers, sterile neutrino mixing properties and resonance sweep physics. Similar conclusions would hold if the primordial ${}^4\mathrm{He}$ abundance could be determined to better than 10%.

Gauge theories embedded into higher-dimensional spaces with certain topologies acquire inductance terms, which reflect the energy cost of topological charges accumulated in the extra dimensions. We compute topological susceptibility in the strongly-coupled two-flavor massive Schwinger model with such an inductance term and find that it vanishes, due to the contribution of a global low-energy mode (a “global axion”). This is in accord with the general argument on the absence of $\theta$ dependence in such topologies. Because the mode is a single oscillator, there is no corresponding particle, and the solution to the $U(1)$ problem is unaffected.

We show that if the visible universe is a membrane embedded in a higher-dimensional space, particles in uniform motion radiate gravitational waves because of spacetime lumpiness. This phenomenon is analogous to the electromagnetic diffraction radiation of a charge moving near to a metallic grating. In the gravitational case, the role of the metallic grating is played by the inhomogeneities of the extra-dimensional space, such as a hidden brane. We derive a general formula for gravitational diffraction radiation and apply it to a higher-dimensional scenario with flat compact extra dimensions. Gravitational diffraction radiation may carry away a significant portion of the particle’s initial energy. This allows to set stringent limits on the scale of brane perturbations. Physical effects of gravitational diffraction radiation are briefly discussed.

It is shown that the internal stationary state of the Schwarzschild black hole can be represented by a maximally entangled two-mode squeezed state of collapsing matter and infalling Hawking radiation. The final boundary condition at the singularity is then described by the random unitary transformation acting on the collapsing matter field. The outgoing Hawking radiation is obtained by the final-state projection on the total wave function, which looks like a quantum teleportation process without the classical information transmitted. The black hole evaporation process as seen by the observer outside the black hole is now a unitary process but nonlocal physics is required to transmit the information outside the black hole. It is also shown that the final-state projection by the evaporation process is strongly affected by the quantum state outside the event horizon, which clearly violates the locality principle.

We compare two strategies of multidetector detection of compact binary inspiral signals, namely, the coincidence and the coherent. For simplicity we consider here two identical detectors having the same power spectral density of noise, that of initial LIGO, located in the same place and having the same orientation. We consider the cases of independent noise as well as that of correlated noise. The coincident strategy involves separately making two candidate event lists, one for each detector, and from these choosing those pairs of events from the two lists which lie within a suitable parameter window, which then are called coincidence detections. The coherent strategy on the other hand involves combining the data phase coherently, so as to obtain a single network statistic which is then compared with a single threshold. Here we attempt to shed light on the question as to which strategy is better. We compare the performances of the two methods by plotting the receiver operating characteristics (ROC) for the two strategies. Several of the results are obtained analytically in order to gain insight. Further we perform numerical simulations in order to determine certain parameters in the analytic formulae and thus obtain the final complete results. We consider here several cases from the relatively simple to the astrophysically more relevant in order to establish our results. The bottom line is that the coherent strategy although more computationally expensive in general than the coincidence strategy, is superior to the coincidence strategy—considerably less false dismissal probability for the same false alarm probability in the viable false alarm regime.

Advanced LIGO’s present baseline design uses arm cavities with Gaussian light beams supported by spherical mirrors. Because Gaussian beams have large intensity gradients in regions of high intensity, they average somewhat poorly over fluctuating bumps and valleys on the mirror surfaces (thermal noise). Flat-topped light beams (mesa beams) are being considered as an alternative because they average over thermal noise more effectively. However, the proposed mesa beams are supported by nearly-flat mirrors, which experience a very serious tilt instability. In this paper we propose an alternative configuration in which mesa-shaped beams are supported by nearly-concentric spheres, which experience only a weak tilt instability. The tilt instability is analyzed for these mirrors in a companion paper by Savov and Vyatchanin. We also propose a one-parameter family of light beams and mirrors in which, as the parameter $\alpha$ varies continuously from 0 to $\pi$, the beams and supporting mirrors get deformed continuously from the nearly-flat-mirrored mesa configuration (FM) at $\alpha =0$, to the nearly-concentric-mirrored mesa configuration (CM) at $\alpha =\pi$. The FM and CM configurations at the endpoints are close to optically unstable, and as $\alpha$ moves away from 0 or $\pi$, the optical stability improves.

Sidles and Sigg have shown that advanced LIGO interferometers will encounter a serious tilt instability, in which symmetric tilts of the mirrors of an arm cavity cause the cavity’s light beam to slide sideways, so its radiation pressure exerts a torque that increases the tilt. Sidles and Sigg showed that the strength $T$ of this torque is 26.2 times greater for advanced LIGO’s baseline cavities—nearly flat spherical mirrors which support Gaussian beams (FG cavities), than for nearly concentric spherical mirrors which support Gaussian beams (CG cavities) with the same diffraction losses as the baseline case: $T^{\mathrm{FG}}/T^{\mathrm{CG}}=26.2$. This has motivated a proposal to change the baseline design to nearly concentric, spherical mirrors. In order to reduce thermal noises in advanced LIGO, O’Shaughnessy and Thorne have proposed replacing the spherical mirrors and their Gaussian beams by “Mexican-Hat” (MH) shaped mirrors which support flat-topped, mesa shaped beams. In this paper, we compute the tilt-instability torque for advanced-LIGO cavities with nearly flat MH mirrors and mesa beams (FM cavities) and nearly concentric MH mirrors and mesa beams (CM cavities), with the same diffraction losses as in the baseline FG case. We find that the relative sizes of the restoring torques are $T^{\mathrm{CM}}/T^{\mathrm{CG}}=0.91$, $T^{\mathrm{FM}}/T^{\mathrm{CG}}=96$, $T^{\mathrm{FM}}/T^{\mathrm{FG}}=3.67$. Thus, the nearly concentric MH mirrors have a weaker tilt instability than any other configuration. Their thermoelastic noise is the same as for nearly flat MH mirrors, and is much lower than for spherical mirrors.

A static string in an AdS Schwarzschild space is dual to a heavy quark-antiquark pair in a gauge theory at high temperature. This space is nonconfining in the sense that the energy is finite for infinite quark-antiquark separation. We introduce an infrared cutoff in this space and calculate the corresponding string energy. We find a deconfining phase transition at a critical temperature $T_C$. Above $T_C$, the string tension vanishes representing the deconfined phase. Below $T_C$, we find a linear confining behavior for large quark-antiquark separation. This simple phenomenological model leads to the appropriate zero temperature limit, corresponding to the Cornell potential and also describes a thermal deconfining phase transition. However, the temperature corrections to the string tension do not recover the expected results for low temperatures.

In the context of scalar field theories, both real and complex, we derive the cutting description at finite temperature (with zero/finite chemical potential) from the cutting rules at zero temperature through the action of a simple thermal operator. We give an alternative algebraic proof of the largest time equation which brings out the underlying physics of such a relation. As an application of the cutting description, we calculate the imaginary part of the one-loop retarded self-energy at zero/finite temperature and finite chemical potential and show how this description can be used to calculate the dispersion relation as well as the full physical self-energy of thermal particles.

We employ the method of comparison equations to study the propagation of a massless minimally coupled scalar field on the Schwarzschild background. In particular, we show that this method allows us to obtain explicit approximate expressions for the radial modes with energy below the peak of the effective potential which are fairly accurate over the whole region outside the horizon. This case can be of particular interest, for example, for the problem of black hole evaporation.

We reformulate the Bekenstein bound as the requirement of positivity of the Helmholtz free energy at the minimum value of the function $L=E-S/(2\pi R)$, where $R$ is some measure of the size of the system. The minimum of $L$ occurs at the temperature $T=1/(2\pi R)$. In the case of $n$-dimensional anti-de Sitter spacetime, the rather poorly defined size $R$ acquires a precise definition in terms of the AdS radius $l$, with $R=l/(n-2)$. We previously found that the Bekenstein bound holds for all known black holes in AdS. However, in this paper we show that the Bekenstein bound is not generally valid for free quantum fields in AdS, even if one includes the Casimir energy. Some other aspects of thermodynamics in anti-de Sitter spacetime are briefly touched upon.

We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four-dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.

The properties of string networks at scales well below the horizon are poorly understood, but they enter critically into many observables. We argue that in some regimes, stretching will be the only relevant process governing the evolution. In this case, the string two-point function is determined up to normalization: the fractal dimension approaches one at short distance, but the rate of approach is characterized by an exponent that plays an essential role in network properties. The smoothness at short distance implies, for example, that cosmic string lensing images are almost undistorted. We then add in loop production as a perturbation and find that it diverges at small scales. This need not invalidate the stretching model, since the loop production occurs in localized regions, but it implies a complicated fragmentation process. Our ability to model this process is limited, but we argue that loop production peaks a few orders of magnitude below the horizon scale, without the inclusion of gravitational radiation. We find agreement with some features of simulations, and interesting discrepancies that must be resolved by future work.

We carry out a state-of-the-art assessment of long baseline neutrino oscillation experiments with wide band beams. We describe the feasibility of an experimental program using existing high-energy accelerator facilities, a new intense wide band neutrino beam (0–6 GeV) and a proposed large detector in a deep underground laboratory. We find that a decade-long program with 1 MW operation in the neutrino mode and 2 MW operation in the antineutrino mode, a baseline as long as the distance between Fermilab and the Homestake mine (1300 km) or the Henderson mine (1500 km), and a water Cherenkov detector with fiducial mass $\sim 300\mathrm{kT}$ has optimum sensitivity to a nonzero ${\theta }_{13}$, the mass hierarchy and to neutrino $CP$ violation at the $3\sigma$ C. L. for ${sin}^{2}2{\theta }_{13}>0.008$. This program is capable of breaking the eight-fold degeneracy down to the octant degeneracy without additional external input.

We discuss the optimization of a neutrino factory experiment for neutrino oscillation physics in terms of muon energy, baselines, and oscillation channels (gold, silver, platinum). In addition, we study the impact and requirements for detector technology improvements, and we compare the results to beta beams. We find that the optimized neutrino factory has two baselines, one at about 3000 to 5000 km, the other at about 7500 km (“magic” baseline). The threshold and energy resolution of the golden channel detector have the most promising optimization potential. This, in turn, could be used to lower the muon energy from about 50 GeV to about 20 GeV. Furthermore, the inclusion of electron neutrino appearance with charge identification (platinum channel) could help for large values of ${sin}^{2}2{\theta }_{13}$. Though tau neutrino appearance with charge identification (silver channel) helps, in principle, to resolve degeneracies for intermediate ${sin}^{2}2{\theta }_{13}$, we find that alternative strategies may be more feasible in this parameter range. As far as matter density uncertainties are concerned, we demonstrate that their impact can be reduced by the combination of different baselines and channels. Finally, in comparison to beta beams and other alternative technologies, we clearly can establish a superior performance for a neutrino factory in the case ${sin}^{2}2{\theta }_{13}\lesssim 0.01$.

We consider global topological defects in symmetry-breaking models with a noncanonical kinetic term. Apart from a mass parameter entering the potential, one additional dimensional parameter arises in such models—a kinetic mass. The properties of defects in these models are quite different from standard global domain walls, vortices, and monopoles, if their kinetic mass scale is smaller than their symmetry-breaking scale. In particular, depending on the concrete form of the kinetic term, the typical size of such a defect can be either much larger or much smaller than the size of a standard defect with the same potential term. The characteristic mass of a nonstandard defect, which might have been formed during a phase transition in the early universe, depends on both the temperature of a phase transition and the kinetic mass.

Theories in which gravity is weaker on cosmological scales have been proposed to explain the observed acceleration of the universe. The nonlinear regime in such theories is not well studied, though it is likely that observational tests of structure formation will lie in this regime. A class of alternative gravity theories may be approximated by modifying Poisson’s equation. We have run $N$-body simulations of a set of such models to study the nonlinear clustering of matter on 1–100 Mpc scales. We find that nonlinear gravity enhances the deviations of the power spectrum of these models from standard gravity. This occurs due to mode coupling, so that models with an excess or deficit of large-scale power (at $k<0.2{\mathrm{Mpc}}^{-1}$) lead to deviations in the power spectrum at smaller scales as well (up to $k\sim 1{\mathrm{Mpc}}^{-1}$), even though the linear spectra match very closely on the smaller scales. This makes it easier to distinguish such models from general relativity using the three-dimensional power spectrum probed by galaxy surveys and the weak lensing power spectrum. If the potential for light deflection is modified in the same way as the potential that affects the dark matter, then weak lensing constrains deviations from gravity even more strongly. Our simulations show that, even with a modified potential, gravitational evolution is approximately universal. Based on this, the Peacock-Dodds approach can be adapted to get an analytical fit for the nonlinear power spectra of alternative gravity models, though the recent Smith et al. formula is less successful. Our conclusions extend to models with modifications of gravity on scales of 1–20 Mpc. We also use a way of measuring projected power spectra from simulations that lowers the sample variance, so that fewer realizations are needed to reach a desired level of accuracy.

We investigate the viscosity driven instability in rotating relativistic stars by means of an iterative approach. We focus on polytropic rotating equilibrium stars and impose a $m=2$ perturbation in the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study those effects on the value of the threshold. For a uniformly rotating star, the criterion $T/W$, where $T$ is the rotational kinetic energy and $W$ is the gravitational binding energy, mainly depends on the compactness of the star and takes values around $0.13–0.16$, which differ slightly from that of Newtonian incompressible stars ($\sim 0.14$). For differentially rotating stars, the critical value of $T/W$ is found to span the range $0.17-0.25$. This is significantly larger than the uniformly rotating case with the same compactness of the star. Finally we discuss a possibility of detecting gravitational waves from viscosity driven instability with ground-based interferometers.

We include the standard model (SM) leptons in a recently proposed framework for the generation of quark mass ratios and Cabibbo-Kobayashi-Maskawa (CKM) mixing angles from a $SU(3)$ family gauge interaction. The set of SM singlet scalar fields describing the spontaneous breaking is the same as employed for the quark sector. The imposition at tree level of the experimentally correct Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix, in the form of a tri-bi maximal structure, fixes several of the otherwise free parameters and renders the model predictive. The normal hierarchy among the neutrino masses emerges from this scheme.

We consider the possibility of neutrino mass generation in a supersymmetric model where lepton number can be violated by odd units. The different patterns of mixing in the quark and lepton sectors are attributed to the presence of right-chiral neutrino superfields which (a) enter into Yukawa couplings via nonrenormalizable interaction with hidden sector fields, and (b) can violate lepton number by odd units. Both of these features are shown to be the result of some global quantum number which is violated when SUSY is broken in the hidden sector. It is shown how such a scenario, together with all known $R$-parity violating effects, can lead to neutrino masses and bilarge mixing via seesaw as well as radiative mechanisms. Some sample values of the various parameters involved, consistent with electroweak symmetry breaking constraints, are presented as illustrations.