We show that there are physically relevant situations where gravitational waves do not inherit the frequency spectrum of their source but its wavenumber spectrum.

We show that Fronsdal’s Lagrangian for a free massless spin-3 gauge field in Minkowski spacetime is contained in a general Yang-Mills–like Lagrangian of metric-affine gravity (MAG), the gauge theory of the general affine group in the presence of a metric. Because of the geometric character of MAG, this can best be seen by using Vasiliev’s frame formalism for higher-spin gauge fields in which the spin-3 frame is identified with the tracefree nonmetricity one-form associated with the shear generators of $GL(n,\mathbb{R})$. Furthermore, for specific gravitational gauge models in the framework of full nonlinear MAG, exact solutions are constructed, featuring propagating massless and massive spin-3 fields.

We use Hamiltonian methods to study curved domain walls and cosmologies. This leads naturally to first-order equations for all domain walls and cosmologies foliated by slices of maximal symmetry. For Minkowski and AdS-sliced domain walls (flat and closed FLRW cosmologies) we recover a recent result concerning their (pseudo)supersymmetry. We show how domain-wall stability is consistent with the instability of AdS vacua that violate the Breitenlohner-Freedman bound. We also explore the relationship to Hamilton-Jacobi theory and compute the wave-function of a 3-dimensional closed universe evolving towards de Sitter spacetime.

We treat the coupled Dirac-Einstein system in the framework of effective field theories in order to quantize the gravitational field at long distances in a consistent manner. In the Dirac-Einstein system we consider the leading post-Newtonian and quantum corrections to the nonrelativistic scattering amplitude of charged spin-$\frac{1}{2}$ fermions. We extract the relevant vertex rules from the action appropriate to the one-loop level calculations and find the nonrelativistic scattering matrix potential for two massive charged spin-$\frac{1}{2}$ fermions. Our focus is kept only on the nonanalytic parts contributing to the potential which are known to generate the long-range interactions.

Within the framework of a manifestly gauge invariant exact renormalization group for $SU(N)$ Yang-Mills, we derive a simple expression for the expectation value of an arbitrary gauge invariant operator. We illustrate the use of this formula by computing the $\mathrm{O}(g^2)$ correction to the rectangular, Euclidean Wilson loop with sides $T\gg L$. The standard result is trivially obtained, directly in the continuum, for the first time without fixing the gauge. We comment on possible future applications of the formalism.

We discuss in detail the uniform discretization approach to the quantization of totally constrained theories. This approach allows to construct the continuum theory of interest as a well defined, controlled, limit of well behaved discrete theories. We work out several finite dimensional examples that exhibit behaviors expected to be of importance in the quantization of gravity. We also work out the case of BF theory. At the time of quantization, one can take two points of view. The technique can be used to define, upon taking the continuum limit, the space of physical states of the continuum constrained theory of interest. In particular we show in models that it agrees with the group averaging procedure when the latter exists. The technique can also be used to compute, at the discrete level, conditional probabilities and the introduction of a relational time. Upon taking the continuum limit one can show that one reproduces results obtained by the use of evolving constants, and therefore recover all physical predictions of the continuum theory. This second point of view can also be used as a paradigm to deal with cases where the continuum limit does not exist. There one would have discrete theories that at least at certain scales reproduce the semiclassical properties of the theory of interest. In this way the approach can be viewed as a generalization of the Dirac quantization procedure that can handle situations where the latter fails.

We analyze the problem of the existing ambiguities in the conformal anomaly in theories with an external scalar field in curved backgrounds. In particular, we consider the anomaly of a self-interacting massive scalar field theory and of a Yukawa model in the massless conformal limit. In all cases the ambiguities are related to finite renormalizations of local nonminimal terms in the effective action. We point out the generic nature of this phenomenon and provide a general method to identify the theories where such an ambiguity can arise.

The coalescence of a binary black hole system is one of the main sources of gravitational waves that present and future detectors will study. Apart from the energy and angular momentum that these waves carry, for unequal-mass binaries there is also a net flux of linear momentum that implies a recoil velocity of the resulting final black hole in the opposite direction. Due to the relevance of this phenomenon in astrophysics, in particular, for galaxy merger scenarios, there have been several attempts to estimate the magnitude of this velocity. Since the main contribution to the recoil comes from the last orbit and plunge, an approximation valid at the last stage of coalescence is well motivated for this type of calculation. In this paper, we present a computation of the recoil velocity based on the close-limit approximation scheme, which gives excellent results for head-on and grazing collisions of black holes when compared to full numerical relativistic calculations. We obtain a maximum recoil velocity of $\sim 57\mathrm{km}/s$ for a symmetric mass ratio $\eta =M_1{M}_2/(M_1+M_2{)}^2\sim 0.19$ and an initial proper separation of $4M$, where $M$ is the total Arnowitt-Deser-Misner (ADM) mass of the system. This separation is the maximum at which the close-limit approximation is expected to provide accurate results. Therefore, it cannot account for the contributions due to inspiral and initial merger. If we supplement this estimate with post-Newtonian (PN) calculations up to the innermost stable circular orbit, we obtain a lower bound for the recoil velocity, with a maximum around $80\mathrm{km}/s$. This is a lower bound because it neglects the initial merger phase. We can however obtain a rough estimate by using PN methods or the close-limit approximation. Since both methods are known to overestimate the amount of radiation, we obtain in this way an upper bound for the recoil with maxima in the range of $214–240\mathrm{km}/s$. We also provide nonlinear fits to these estimated upper and lower bounds. These estimates are subject to uncertainties related to issues such as the choice of initial data and higher effects in perturbation theory. Nonetheless, our estimates are consistent with previous results in the literature and suggest a narrower range of possible recoil velocities.

The model of natural inflation is examined in light of recent 3-year data from the Wilkinson Microwave Anisotropy Probe and shown to provide a good fit. The inflaton potential is naturally flat due to shift symmetries, and in the simplest version takes the form $V(\varphi )={\Lambda }^4[1\pm \cos (N\varphi /f)]$. The model agrees with WMAP3 measurements as long as $f>0.7m_{\mathrm{Pl}}$ (where $m_{\mathrm{Pl}}=1.22\times {10}^{19}\mathrm{GeV}$) and $\Lambda \sim m_{\mathrm{GUT}}$. The running of the scalar spectral index is shown to be small—an order of magnitude below the sensitivity of WMAP3. The location of the field in the potential when perturbations on observable scales are produced is examined; for $f>5m_{\mathrm{Pl}}$, the relevant part of the potential is indistinguishable from a quadratic, yet has the advantage that the required flatness is well-motivated. Depending on the value of $f$, the model falls into the large field ($f\ge 1.5m_{\mathrm{Pl}}$) or small field ($f<1.5m_{\mathrm{Pl}}$) classification scheme that has been applied to inflation models. Natural inflation provides a good fit to WMAP3 data.

We show that the inclusion of backreaction of massive long wavelengths imposes dynamical constraints on the allowed phase space of initial conditions for inflation, which results in a superselection rule for the initial conditions. Only high energy inflation is stable against collapse due to the gravitational instability of massive perturbations. We present arguments to the effect that the initial conditions problem cannot be meaningfully addressed by thermostatistics as far as the gravitational degrees of freedom are concerned. Rather, the choice of the initial conditions for the universe in the phase space and the emergence of an arrow of time have to be treated as a dynamic selection.

In addition to density perturbations, inflationary models of the early Universe generally predict a stochastic background of gravitational waves or tensor fluctuations. By making use of the inflationary flow approach for single field models and fitting the models with Monte Carlo techniques to cosmic microwave background (CMB) data from the Wilkinson Microwave Anisotropy Probe (WMAP), we discuss the expected properties of the gravitational wave background from inflation at scales corresponding to direct detection experiments with laser interferometers in space. We complement the Monte Carlo numerical calculations by including predictions expected under several classes of analytical inflationary models. We find that an improved version of big bang observer (BBO-grand) can be used to detect a gravitational wave background at 0.1 Hz with a corresponding CMB tensor-to-scalar ratio above ${10}^{-4}$. Even if the CMB tensor-to-scalar ratio were to be above ${10}^{-2}$, we suggest that BBO-grand will be useful to study inflationary models as the standard version of BBO, with a sensitivity to a stochastic gravitational wave background ${\Omega }_{\mathrm{GW}}{h}^2>{10}^{-17}$, will only allow a marginal detection of the amplitude while leaving the tensor spectral index at 0.1 Hz unconstrained. Also, inflationary models with a large tensor-to-scalar ratio predict a substantial negative tensor spectral index such that the gravitational wave amplitude is damped at direct detection frequencies. We also discuss the extent to which CMB measurements can be used to predict the gravitational wave background amplitude in a direct detection experiment and how any measurement of the amplitude and the spectral tilt of the gravitational wave background at direct detection frequencies together with the CMB tensor-to-scalar ratio can be used to establish slow-roll inflation.

Recently, two issues concerning the three-year Wilkinson Microwave Anisotropy Probe (WMAP) likelihood code were pointed out. On large angular scales ($l\lesssim 30$), a suboptimal likelihood approximation resulted in a small power excess. On small angular scales ($l\gtrsim 300$), over-subtraction of unresolved point sources produced a small power deficit. For a minimal six-parameter cosmological model, these two effects conspired to decrease the value of $n_s$ by $\sim 0.7\sigma$. In this paper, we study the change in preferred parameter ranges for extended cosmological models, including running of $n_s$, massive neutrinos, curvature, and the equation of state for dark energy. We also include large-scale structure and supernova data in our analysis. We find that the parameter ranges for ${\alpha }_s$, ${\Omega }_k$ and $w$ are not much altered by the modified analysis. For massive neutrinos the upper limit on the sum of the neutrino masses decreases from $M_{\nu }<1.90\mathrm{eV}$ to $M_{\nu }<1.57\mathrm{eV}$ when using the modified WMAP code and WMAP data only. We also find that the shift of $n_s$ to higher values is quite robust to these extensions of the minimal cosmological model.

We present evidence that Abrikosov-Nielsen-Olesen (ANO) strings pass through each other for very high speeds of approach due to a double intercommutation. In near-perpendicular collisions numerical simulations give threshold speeds bounded above by $\sim 0.98c$ for type I, and by $\sim 0.88c$ for deep type II strings. The second intercommutation occurs because at ultrahigh collision speeds, the connecting segments formed by the first intercommutation are nearly static and almost antiparallel, which gives them time to interact and annihilate. A simple model explains the rough features of the threshold velocity dependence with the incidence angle. For deep type II strings and large incidence angles a second effect becomes dominant, the formation of a loop that catches up with the interpolating segments. The loop is related to the observed vortex-antivortex reemergence in two dimensions. In this case the critical value for double intercommutation can become much lower.

We examine the effect of the rise in the survival probability of the electron neutrinos with the decrease in the neutrino energy on the recoil electron spectrum at Super-Kamiokande.

We analyze the complementarity between lepton flavor violation (LFV) and LHC experiments in probing the supersymmetric (SUSY) grand unified theories (GUT) when neutrinos get a mass via the seesaw mechanism. Our analysis is performed in an SO(10) framework, where at least one neutrino Yukawa coupling is necessarily as large as the top Yukawa coupling. Our study thoroughly takes into account the whole renormalization group running, including the GUT and the right-handed neutrino mass scales, as well as the running of the observable neutrino spectrum. We find that the upcoming (MEG, SuperKEKB) and future (PRISM/PRIME, super flavor factory) LFV experiments will be able to test such SUSY framework for SUSY masses to be explored at the LHC and, in some cases, even beyond the LHC sensitivity reach.

We explore the prospects for indirect detection of neutralino dark matter in supersymmetric models with an extended Higgs sector (next-to-minimal supersymmetric standard model, or NMSSM). We compute, for the first time, one-loop amplitudes for NMSSM neutralino pair annihilation into two photons and two gluons, and point out that extra diagrams (with respect to the minimal supersymmetric standard model, or MSSM), featuring a potentially light $CP$-odd Higgs boson exchange, can strongly enhance these radiative modes. Expected signals in neutrino telescopes due to the annihilation of relic neutralinos in the Sun and in the Earth are evaluated, as well as the prospects of detection of a neutralino annihilation signal in space-based gamma-ray, antiproton and positron search experiments, and at low-energy antideuteron searches. We find that in the low mass regime the signals from capture in the Earth are enhanced compared to the MSSM, and that NMSSM neutralinos have a remote possibility of affecting solar dynamics. Also, antimatter experiments are an excellent probe of galactic NMSSM dark matter. We also find enhanced two-photon decay modes that make the possibility of the detection of a monochromatic gamma-ray line within the NMSSM more promising than in the MSSM, although likely below the sensitivity of next generation gamma-ray telescopes.

We report a study describing the charm quark by a domain-wall fermion (DWF) in lattice quantum chromodynamics (QCD). Our study uses a quenched gauge ensemble with the DBW2 rectangle-improved gauge action at a lattice cutoff of $a^{-1}\sim 3\mathrm{GeV}$. We calculate masses of heavy-light (charmed) and heavy-heavy (charmonium) mesons with spin-parity $J^P=0^{\mp }$ and $1^{\mp }$, leptonic decay constants of the charmed pseudoscalar mesons ($D$ and $D_s$), and the $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing parameter. The charm quark mass is found to be $m_c^{\overline{\mathrm{MS}}}(m_c)=1.24(1{)}_{\mathrm{stat}}(18{)}_{\mathrm{syst}}\mathrm{GeV}$. The mass splittings in charmed-meson parity partners ${\Delta }_{q,J=0}$ and ${\Delta }_{q,J=1}$ are degenerate within statistical errors, in accordance with experiment, and they satisfy a relation ${\Delta }_{q=ud,J}>{\Delta }_{q=s,J}$, also consistent with experiment. Using our lattice calculation of the splitting between $h_c$ and ${\chi }_{c1}$ and the experimental ${\chi }_{c1}$ mass, we obtain a parity-odd axial-vector charmonium state $m_{h_c}=3533(11{)}_{\mathrm{stat}}(336{)}_{\mathrm{syst}}\mathrm{MeV}$, with a systematic error dominated by heavy quark discretization at order $(a{m}_c{)}^2$. However, in this regard, we emphasize significant discrepancies in the calculation of hyperfine splittings on the lattice. The leptonic decay constants of $D$ and $D_s$ mesons are found to be $f_D=232(7{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+6}{-0}{)}_{\mathrm{chiral}}(17{)}_{\mathrm{syst}}\mathrm{MeV}$ and $f_{D_s}/f_D=1.05(2{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+0}{-2}{)}_{\mathrm{chiral}}(2{)}_{\mathrm{syst}}$, where the first error is statistical, the second is systematic due to chiral extrapolation, and the third error is a combination of other known systematics. The $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing bag parameter, which enters the $\Delta C=2$ transition amplitude, is found to be $B_D(2\mathrm{GeV})=0.845(24{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+24}{-6}{)}_{\mathrm{chiral}}(105{)}_{\mathrm{syst}}$. All the above systematic errors include our estimates of quenching errors.

I present a calculation of threshold soft-gluon corrections to single top-quark production in $p\overline{p}$ collisions via all partonic processes in the $t$ and $s$ channels and via associated top quark and $W$ boson production. The soft-gluon corrections are formally resummed to all orders, and finite-order expansions of the resummed cross section are calculated through next-to-next-to-next-to-leading-order (NNNLO) at next-to-leading logarithmic (NLL) accuracy. Numerical results for single top-quark production at the Tevatron are presented, including the dependence of the cross sections on the top-quark mass and on the factorization and renormalization scales. The threshold corrections in the $t$ channel are small while in the $s$ channel they are large and dominant. Associated $tW$ production remains relatively minor due to the small leading-order cross section even though the $K$ factors are large.

We calculate the effective potential of the $2\mathrm{SC}/\mathrm{g}2\mathrm{SC}$ phases including vector condensates ($⟨g{A}_z^6⟩$ and $⟨g{A}_z^8⟩$) and study the gluonic phase and the single plane-wave Larkin-Ovchinnikov-Fulde-Ferrell state at nonzero temperature. Our analysis is performed within the framework of the gauged Nambu-Jona-Lasinio model. We compute potential curvatures with respect to the vector condensates and investigate the temperature dependence of the Meissner masses squared of gluons of color 4–7 and 8 in the neutral $2\mathrm{SC}/\mathrm{g}2\mathrm{SC}$ phases. The phase diagram is presented in the plane of temperature and coupling strength. The unstable regions for gluons 4–7 and 8 are mapped out on the phase diagram. We find that, apart from the case of strong coupling, the $2\mathrm{SC}/\mathrm{g}2\mathrm{SC}$ phases at low temperatures are unstable against the vector condensation until the temperature reaches tens of MeV.

Within perturbative QCD approach based on $k_T$ factorization, we analyze the scalar mesons $f_0(980)$ and $f_0(1500)$ productions in $B$ decays. By identifying $f_0(980)$ as the composition of $\overline{s}s$ and $\overline{n}n=(\overline{u}u+\overline{d}d)/\sqrt{2}$, we calculate the exclusive decays $B\to f_0(980)K$. We find that the nonfactorization $f_0$-emission diagrams can give larger contribution to the branching ratio, than the previous PQCD calculation. Our new results can explain the current experimental data well. Under the assumption of quarkonium dominance, we study the branching ratio of decays $B\to f_0(1500)K$. The results show that in the two-quark picture of $f_0$ meson the contribution from $\overline{s}s$ component is at the similar size as that from the $\overline{n}n$ component. Comparing the data, our results show the preference of $f_0(1500)$ as a member of the ground state of scalar $\overline{q}q$ nonet. Similar results can also apply to $f_0(1370)$ and $f_0(1710)$, if these mesons are dominated by the quarkonium content. With more experimental data in the future, these studies will help us understand the intrinsic characters of these scalar mesons.