We present a general method for the analysis of the stability of static, spherically symmetric solutions to spherically symmetric perturbations in an arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves fixing the gauge and solving the linearized gravitational field equations to eliminate the metric perturbation variables in terms of the matter variables. In a wide class of cases—which include $f(R)$ gravity, the Einstein-æther theory of Jacobson and Mattingly, and Bekenstein’s TeVeS theory—the remaining perturbation equations for the matter fields are second order in time. We show how the symplectic current arising from the original Lagrangian gives rise to a symmetric bilinear form on the variables of the reduced theory. If this bilinear form is positive definite, it provides an inner product that puts the equations of motion of the reduced theory into a self-adjoint form. A variational principle can then be written down immediately, from which stability can be tested readily. We illustrate our method in the case of Einstein’s equation with perfect fluid matter, thereby rederiving, in a systematic manner, Chandrasekhar’s variational principle for radial oscillations of spherically symmetric stars. In a subsequent paper, we will apply our analysis to $f(R)$ gravity, the Einstein-æther theory, and Bekenstein’s TeVeS theory.

Little Higgs models with $T$ parity contain an attractive dark matter candidate, the heavy photon. We compute the cross section of the heavy photon annihilation into $Z$-photon pairs, which turns out to be substantially higher than the previously computed cross section for the two photon final state. Unfortunately, even with this enhancement, the monochromatic photon flux from galactic heavy photon annihilation is unlikely to be detectable by GLAST or the currently operating atmospheric Cerenkov telescopes. We also compute the flux of high-energy neutrinos from the annihilation of the heavy photons captured by the Sun and the Earth. The maximum flux of upward-going muons due to such neutrinos is about $1{\mathrm{yr}}^{-1}{\mathrm{km}}^{-2}$.

Scalar and tensorial cosmological perturbations generated in warm inflationary scenarios whose matter-radiation fluid is endowed with a viscous pressure are considered. Recent observational data from the Wilkinson Microwave Anisotropy Probe experiment are employed to restrict the parameters of the model. Although the effect of this pressure on the matter power spectrum is of the order of a few percent, it may be detected in future experiments.

Gamma-ray bursts, which are among the most violent events in the Universe, are one of the few viable candidates to produce ultra high-energy cosmic rays. Recently, observations have revealed that GRBs generally originate from metal-poor, low-luminosity galaxies and do not directly trace cosmic star formation, as might have been assumed from their association with core-collapse supernovae. Several implications follow from these findings. The redshift distribution of observed GRBs is expected to peak at higher redshift (compared to cosmic star formation), which is supported by the mean redshift of the Swift GRB sample, $⟨z⟩\sim 3$. If GRBs are, in fact, the source of the observed UHECR, then cosmic-ray production would evolve with redshift in a stronger fashion than has been previously suggested. This necessarily leads, through the GZK process, to an enhancement in the flux of cosmogenic neutrinos, providing a near-term approach for testing the gamma-ray burst-cosmic-ray connection with ongoing and proposed UHE neutrino experiments.

We modified the modal expansion, which is the traditional method used to calculate thermal noise. This advanced modal expansion provides physical insight about the discrepancy between the actual thermal noise caused by inhomogeneously distributed loss and the traditional modal expansion. This discrepancy comes from correlations between the thermal fluctuations of the resonant modes. The thermal-noise spectra estimated by the advanced modal expansion are consistent with the results of measurements of thermal fluctuations caused by inhomogeneous losses.

The twin Higgs mechanism was proposed recently to solve the little hierarchy problem. We study the implementation of the twin Higgs mechanism in left-right models. At the TeV scale, heavy quark and gauge bosons appear, with rich collider phenomenology. In addition, there are extra Higgs bosons, some of which couple to both the standard model fermion sector and the gauge sector, while others couple to the gauge bosons only. We present the particle spectrum and study the general features of the collider phenomenology of this class of model at the Large Hadron Collider.

In an extension of the Nambu–Jona-Lasinio model where the quarks interact with the temporal gluon field, represented by the Polyakov loop, we explore the relation between the deconfinement and chiral phase transitions. The effect of Polyakov loop dynamics on thermodynamic quantities, on the phase structure at finite temperature and baryon density and on various susceptibilities is presented. Particular emphasis is put on the behavior and properties of the fluctuations of the (approximate) order parameters and their dependence on temperature and net-quark number density. We also discuss how the phase structure of the model is influenced by the coupling of the quarks to the Polyakov loop.

The time series of the ${}^8\mathrm{B}$ solar neutrino measurements released by the Super- Kamiokande and SNO Collaborations have been recently investigated by several groups for possible modulation signatures through standard Fourier-based techniques. In this work we present an alternative analysis of the same data sets based on the wavelet approach, whose key advantage with respect to the traditional methodologies is the ability to capture and follow the time evolution of transient modulation features as well. Moreover, we show the results of the wavelet analysis applied to the mean solar magnetic field and flare index data recorded in the same data-taking period of the two experiments, with the goal of carrying out a direct check of the concurrent presence (if any) of evidence for corresponding time variations in the solar data and in the solar neutrino series. The main outcomes of this investigation are, on one hand, the clear identification of the expected annual modulation variation due to the eccentricity of the Earth’s orbit, and on the other, the demonstration that no further reliable time variation signals can be unraveled, within the current experimental sensitivity, in the measured solar neutrino flux.

We study transitions between ${\rm Y}$ states with the emission of charged pions using $477{\mathrm{fb}}^{-1}$ of data collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The measured product branching fraction $\mathcal{B}({\rm Y}(4S)\to {\rm Y}(1S){\pi }^{+}{\pi }^{-})\times \mathcal{B}({\rm Y}(1S)\to {\mu }^{+}{\mu }^{-})=(4.42\pm 0.81(\mathrm{stat})\pm 0.56(\mathrm{sys}))\times {10}^{-6}$. When the PDG value for $\mathcal{B}({\rm Y}(1S)\to {\mu }^{+}{\mu }^{-})$ is used, this corresponds to $\mathcal{B}({\rm Y}(4S)\to {\rm Y}(1S){\pi }^{+}{\pi }^{-})=(1.78\pm 0.33(\mathrm{stat})\pm 0.23(\mathrm{sys}))\times {10}^{-4}$ and a partial decay width $\Gamma ({\rm Y}(4S)\to {\rm Y}(1S){\pi }^{+}{\pi }^{-})=(3.65\pm 0.67(\mathrm{stat})\pm 0.65(\mathrm{sys}))\mathrm{keV}$.

A two dimensional model of chiral bosons in noncommutative field space is considered in the framework of the Batalin-Fradkin-Tyutin Hamiltonian embedding method converting the second-class constrained system into the first-class one. The symmetry structure associated with the first-class constraints is explored and the propagation speed of fields is equivalent to that of the second-class constraint system.

$\mathcal{N}=(2,2)$ theories in $1+1\mathrm{D}$ exhibit a direct correspondence between the $R$ charges of chiral operators at a conformal point and the multiplicities of Bogomol’nyi-Prasad-Sommerfield (BPS) kinks in a massive deformation, as shown by Cecotti and Vafa. We obtain an analogous relation in $3+1\mathrm{D}$ for $\mathcal{N}=2$ gauge theories that are massive perturbations of Argyres-Douglas fixed points, utilizing the geometric engineering approach to $\mathcal{N}=2$ vacua within IIB string theory. In this case the scaling dimensions of a certain subset of chiral operators at the UV fixed point are related to the multiplicities of BPS dyons. When the Argyres-Douglas superconformal field theory is realized at the root of a baryonic Higgs branch, this translation from $1+1\mathrm{D}$ to $3+1\mathrm{D}$ can be understood physically from the relation between the bulk dynamics and the $\mathcal{N}=(2,2)$ world-sheet dynamics of vortices in the baryonic Higgs phase. Under a relevant perturbation, the BPS kink multiplicity on the vortex world sheet translates to that of the bulk dyonic states. The latter viewpoint suggests the $3+1\mathrm{D}$ version of the Cecotti-Vafa relation may hold more generally, and simple tests provide evidence in favor of this for more generic choices of the baryonic root.

The one-loop effective energy density of a pure $SU(2)$ Yang-Mills theory in the Savvidy background at finite temperature and chemical potential is examined with emphasis on the unstable modes. After identifying the stable and unstable modes, the stable modes are treated in the quadratic approximation. For the unstable modes, the full expansion including the cubic and the quartic terms in the fluctuations is used. The functional integrals for the unstable modes are evaluated and added to the results for the stable modes. The resulting energy density is found to be real, coinciding with the real part of the energy density in the quadratic approximation of earlier study. There is now no imaginary part. Numerical results are presented for the variation of the energy density with temperature for various choices of the chemical potential.

We investigate an alternative compactification of extra dimensions using local cosmic string in the Brans-Dicke gravity framework. In the context of dynamical systems it is possible to show that there exist a stable field configuration for the Einstein-Brans-Dicke equations. We explore the analogies between this particular model and the Randall-Sundrum scenario.

After its reduction by a gauge-fixing procedure, the family of linearly polarized Gowdy $T^3$ cosmologies admits a scalar field description whose evolution is governed by a Klein-Gordon type equation in a flat background in $1+1$ dimensions with the spatial topology of $S^1$, though in the presence of a time-dependent potential. The model is still subject to a homogeneous constraint, which generates $S^1$-translations. Recently, a Fock quantization of this scalar field was introduced and shown to be unique under the requirements of unitarity of the dynamics and invariance under the gauge group of $S^1$-translations. In this work, we extend and complete this uniqueness result by considering other possible scalar field descriptions, resulting from reasonable field reparametrizations of the induced metric of the reduced model. In the reduced phase space, these alternate descriptions can be obtained by means of a time-dependent scaling of the field, the inverse scaling of its canonical momentum, and the possible addition of a time-dependent, linear contribution of the field to this momentum. Demanding again unitarity of the field dynamics and invariance under the gauge group, we prove that the alternate canonical pairs of fieldlike variables admit a Fock representation if and only if the scaling of the field is constant in time. In this case, there exists essentially a unique Fock representation, provided by the quantization constructed by Corichi, Cortez, and Mena Marugán. In particular, our analysis shows that the scalar field description proposed by Pierri does not admit a Fock quantization with the above unitarity and invariance properties.

Pointlike objects cause many of the divergences that afflict physical theories. For instance, the gravitational binding energy of a point particle in Newtonian mechanics is infinite. In general relativity, the analog of a point particle is a black hole and the notion of binding energy must be replaced by quasilocal energy (QLE). The QLE derived by York, and elaborated by Brown and York, is finite outside the horizon but it was not considered how to evaluate it inside the horizon. We present a prescription for finding the QLE inside a horizon, and show that it is finite at the singularity for a variety of types of black holes. The energy is typically concentrated just inside the horizon, not at the central singularity.

Cosmic microwave background (CMB) polarization observations will require superb control of systematic errors in order to achieve their full scientific potential, particularly in the case of attempts to detect the $B$ modes that may provide a window on inflation. Interferometry may be a promising way to achieve these goals. This paper presents a formalism for characterizing the effects of a variety of systematic errors on interferometric CMB polarization observations, with particular emphasis on estimates of the $B$-mode power spectrum. The most severe errors are those that couple the temperature anisotropy signal to polarization; such errors include cross talk within detectors, misalignment of polarizers, and cross polarization. In a $B$ mode experiment, the next most serious category of errors are those that mix $E$ and $B$ modes, such as gain fluctuations, pointing errors, and beam shape errors. The paper also indicates which sources of error may cause circular polarization (e.g., from foregrounds) to contaminate the cosmologically interesting linear polarization channels, and conversely whether monitoring of the circular-polarization channels may yield useful information about the errors themselves. For all the sources of error considered, estimates of the level of control that will be required for both $E$ and $B$ mode experiments are provided. Simulations of a mock experiment are presented to illustrate the results. Both experiments that interfere linear polarizations and those that interfere circular polarizations are considered. The fact that circular experiments simultaneously measure both linear polarization Stokes parameters in each baseline mitigates some sources of error.

The property of the spectrum of large-scale magnetic fields generated due to the breaking of the conformal invariance of the Maxwell theory through some mechanism in inflationary cosmology is studied. It is shown that the spectrum of the generated magnetic fields should not be perfectly scale-invariant but be slightly red so that the amplitude of large-scale magnetic fields can be stronger than $\sim {10}^{-12}\mathrm{G}$ at the present time. This analysis is performed by assuming the absence of amplification due to the late-time action of some dynamo (or similar) mechanism.

We apply the statefinder diagnostic to the modified polytropic Cardassian universe in this work. We find that the statefinder diagnostic is quite effective to distinguish Cardassian models from a series of other cosmological models. The $s-r$ plane is used to classify the modified polytropic Cardassian models into six cases. The evolutionary trajectories in the $s-r$ plane for the cases with different $n$ and $\beta$ reveal different evolutionary properties of the universe. In addition, we combine the observational $H(z)$ data, the cosmic microwave background data, and the baryonic acoustic oscillation data to make a joint analysis. We find that case 2 can be excluded at the 68.3% confidence level and any case is consistent with the observations at the 95.4% confidence level.

Up to now, dark energy evidences are based on the dynamics of the universe on very large scales, above 1 Gpc. Assuming it continues to behave like a cosmological constant $\Lambda$ on much smaller scales, I discuss its effects on the motion of nonrelativistic test particles in a weak gravitational field, and I propose a way to detect evidences of $\Lambda \ne 0$ at the scale of about 1 Mpc: the main ingredient is the measurement of galaxy cluster masses.

Dense neutrino gases exhibit collective oscillations where “self-maintained coherence” is a characteristic feature, i.e., neutrinos of different energies oscillate with the same frequency. In a nonisotropic gas, however, the flux term of the neutrino-neutrino interaction has the opposite effect of causing kinematical decoherence of neutrinos propagating in different directions, an effect that is at the origin of the “multiangle behavior” of neutrinos streaming off a supernova core. We cast the equations of motion in a form where the role of the flux term is manifest. We study in detail the symmetric case of equal neutrino and antineutrino densities where the evolution consists of collective pair conversions (“bipolar oscillations”). A gas of this sort is unstable in that an infinitesimal anisotropy is enough to trigger a runaway towards flavor equipartition. The “self-maintained coherence” of a perfectly isotropic gas gives way to “self-induced decoherence.”