We derive a general equation relating the gravitational-wave observables $r$ and ${\Omega }_0^{\mathrm{gw}}(f)$; or the observables ${\Omega }_0^{\mathrm{gw}}(f_1)$ and ${\Omega }_0^{\mathrm{gw}}(f_2)$. Here, $r$ is the so-called “tensor-to-scalar ratio,” which is constrained by cosmic-microwave-background experiments; and ${\Omega }_0^{\mathrm{gw}}(f)$ is the energy spectrum of primordial gravitational waves, which is constrained, e.g., by pulsar-timing measurements, laser-interferometer experiments, and the standard big bang nucleosynthesis bound. Differentiating this equation yields a new expression for the tilt $d\ln {\Omega }_0^{\mathrm{gw}}(f)/d\ln f$ of the present-day gravitational-wave spectrum. The relationship between $r$ and ${\Omega }_0^{\mathrm{gw}}(f)$ depends sensitively on the uncertain physics of the early universe, and we show that this uncertainty may be encapsulated (in a model-independent way) by two quantities: $\widehat{w}(f)$ and ${\widehat{n}}_t(f)$, where ${\widehat{n}}_t(f)$ is a certain logarithmic average over $n_t(k)$ (the primordial tensor spectral index); and $\widehat{w}(f)$ is a certain logarithmic average over $\tilde{w}(a)$ (the effective equation-of-state parameter in the early universe, after horizon re-entry). Here, the effective equation-of-state parameter $\tilde{w}(a)$ is a combination of the ordinary equation-of-state parameter $w(a)$ and the bulk viscosity $\zeta (a)$. Thus, by comparing observational constraints on $r$ and ${\Omega }_0^{\mathrm{gw}}(f)$, one obtains (remarkably tight) constraints in the $\{\widehat{w}(f),{\widehat{n}}_t(f)\}$ plane. In particular, this is the best way to constrain (or detect) the presence of a stiff energy component (with $w>1/3$) in the early universe, prior to big bang nucleosynthesis. (The discovery of such a component would be no more surprising than the discovery of a tiny cosmological constant at late times!) Finally, although most of our analysis does not assume inflation, we point out that if cosmic-microwave-background experiments detect a nonzero value for $r$, then we will immediately obtain (as a free by-product) a new upper bound $\widehat{w}\lesssim 0.55$ on the logarithmically averaged effective equation-of-state parameter during the “primordial dark age” between the end of inflation and the start of big bang nucleosynthesis.

We derive constraints on the parameter space of the unified model of dark energy and dark matter, the generalized Chaplygin gas, from the amplitudes and positions of the first few peaks and first trough of the cosmic microwave background radiation power spectrum, using the latest WMAP five-year data.

The faint radio point sources that are unresolved in cosmic microwave background (CMB) anisotropy maps are likely to be a biased tracer of the large-scale structure dark matter distribution. While the shot-noise contribution to the angular power spectrum of unresolved radio point sources is included either when optimally constructing the CMB angular power spectrum, as with WMAP data, or when extracting cosmological parameters, we suggest that clustering part of the point source power spectrum should also be included. This is especially necessary at high frequencies above 150 GHz, where the clustering of far-IR sources is expected to dominate the shot-noise level of the angular power spectrum at tens of arcminute angular scales of both radio and sub-mm sources. We make an estimate of source clustering of unresolved radio sources in both WMAP and ACBAR, and marginalize over the amplitude of source clustering in each CMB data set when model fitting for cosmological parameters. For the combination of WMAP 5-year data and ACBAR, we find that the spectral index changes from the value of $0.963\pm 0.014$ to $0.959\pm 0.014$ (at 68% C.L.) when the clustering power spectrum of point sources is included in model fits. While we find that the differences are marginal with and without source clustering in current data, it may be necessary to account for source clustering with future data sets such as Planck, especially to properly model fit anisotropies at arcminute angular scales. If clustering is not accounted and point sources are modeled with a shot noise only out to $l\sim 2000$, the spectral index will be biased by about $1.5\sigma$.

Atom interferometry is now reaching sufficient precision to motivate laboratory tests of general relativity. We begin by explaining the nonrelativistic calculation of the phase shift in an atom interferometer and deriving its range of validity. From this, we develop a method for calculating the phase shift in general relativity. Both the atoms and the light are treated relativistically and all coordinate dependencies are removed, thus revealing novel terms, cancellations, and new origins for previously calculated terms. This formalism is then used to find the relativistic effects in an atom interferometer in a weak gravitational field for application to laboratory tests of general relativity. The potentially testable relativistic effects include the nonlinear three-graviton coupling, the gravity of kinetic energy, and the falling of light. We propose specific experiments, one currently under construction, to measure each of these effects. These experiments could provide a test of the principle of equivalence to 1 part in ${10}^{15}$ (300 times better than the present limit), and general relativity at the 10% level, with many potential future improvements. We also consider applications to other metrics including the Lense-Thirring effect, the expansion of the Universe, and preferred frame and location effects.

We apply the pseudoparticle approach to SU(2) Yang-Mills theory and perform a detailed study of the potential between two static charges for various representations. Whereas for charges in the fundamental representation we find a linearly rising confining potential, we clearly observe string breaking, when considering charges in the adjoint representation. We also demonstrate Casimir scaling and compute gluelump masses for different spin and parity. Numerical results are in qualitative agreement with lattice results.

We study the double-lepton polarization asymmetries and single and double-lepton polarization forward-backward asymmetries of the rare $b\to s{\ell }^{+}{\ell }^{-}$ mode within the standard model and in the Appelquist-Cheng-Dobrescu model, which is a new physics scenario with a single universal extra dimension. In particular, we examine the sensitivity of the observables to the radius $R$ of the compactified extra dimension, which is the new parameter in this new physics model.

We analyze macroscopic effects of TeV-scale black holes, such as could possibly be produced at the LHC, in what is regarded as an extremely hypothetical scenario in which they are stable and, if trapped inside Earth, begin to accrete matter. We examine a wide variety of TeV-scale gravity scenarios, basing the resulting accretion models on first-principles, basic, and well-tested physical laws. These scenarios fall into two classes, depending on whether accretion could have any macroscopic effect on the Earth at times shorter than the Sun’s natural lifetime. We argue that cases with such an effect at shorter times than the solar lifetime are ruled out, since in these scenarios black holes produced by cosmic rays impinging on much denser white dwarfs and neutron stars would then catalyze their decay on time scales incompatible with their known lifetimes. We also comment on relevant lifetimes for astronomical objects that capture primordial black holes. In short, this study finds no basis for concerns that TeV-scale black holes from the LHC could pose a risk to Earth on time scales shorter than the Earth’s natural lifetime. Indeed, conservative arguments based on detailed calculations and the best-available scientific knowledge, including solid astronomical data, conclude, from multiple perspectives, that there is no risk of any significance whatsoever from such black holes.

The determination of the spin of the quantum states exchanged in the various nonstandard interactions is a relevant aspect in the identification of the corresponding scenarios. We discuss the identification reach at the CERN LHC on the spin-2 of the lowest-lying Randall-Sundrum (RS) resonance, predicted by gravity with one warped extra dimension, against spin-1 and spin-0 nonstandard exchanges with the same mass and producing the same number of events in the cross section. We focus on the angular distributions of leptons produced in the Drell-Yan process at the LHC; in particular, we use as a basic observable a “normalized” integrated angular asymmetry $A_{\mathrm{CE}}$. Our finding is that the 95% C.L. identification reach on the spin-2 of the RS resonance (equivalently, the exclusion reach on both the spin-1 and spin-0 hypotheses for the peak) is up to a resonance mass scale of the order of 1.0 or 1.6 TeV in the case of weak coupling between graviton excitations and SM particles ($k/{\overline{M}}_{\mathrm{Pl}}=0.01$) and 2.4 or 3.2 TeV for a larger coupling constant ($k/{\overline{M}}_{\mathrm{Pl}}=0.1$) for a time-integrated LHC luminosity of 10 or $100{\mathrm{fb}}^{-1}$, respectively. Also, some comments are given on the complementary roles of the angular analysis and the eventual discovery of the predicted second graviton excitation in the identification of the RS scenario.

Using the example of the $SU(2)$ gauge theory in $3+1$ dimensions we consider the construction of a 3-dimensional effective model in terms of Polyakov loops. We demonstrate the application of an equilibrium self-consistency condition to the systematic analysis of the contribution of various [global $Z(2)$ symmetric] terms in the effective model action. We apply this analysis to the construction of a simple effective action with the minimum necessary number of operators. Such an action is shown to be capable of reproducing relevant observables, e.g. the Polyakov loop ensemble average, within the desired accuracy.

We study trial states modelling the heavy quark-antiquark ground state in SU(2) Yang-Mills theory. A state describing the flux tube between quarks as a thin string of glue is found to be a poor description of the continuum ground state; the infinitesimal thickness of the string leads to UV artifacts which suppress the overlap with the ground state. Contrastingly, a state which surrounds the quarks with non-Abelian Coulomb fields is found to have a good overlap with the ground state for all charge separations. In fact, the overlap increases as the lattice regulator is removed. This opens up the possibility that the Coulomb state is the true ground state in the continuum limit.

We investigate the possibility of measuring the top quark mass using the collider variable $m_{T2}$ at the CERN LHC experiment. Monte Carlo studies of $m_{T2}$ are performed with the events corresponding to the dilepton decays of $t\overline{t}$ produced at the LHC with $10{\mathrm{fb}}^{-1}$ integrated luminosity. Our analysis suggests that the top quark mass can be determined by the $m_{T2}$ variable with a reasonable accuracy, though the precision will be determined by systematic errors for which a more complete analysis would need to be performed.

We calculate the vector and axial-vector form factors of $B_{u,d,s}$ decays into $P$-wave axial-vector mesons in the light-cone sum rule approach. For the sum rule results, we have included corrections of order $m_A/m_b$, where $m_A$ is the mass of the axial-vector meson $A$. The results are relevant to the light-cone distribution amplitudes of the axial-vector mesons. It is important to note that, owing to the $G$ parity, the chiral-even two-parton light-cone distribution amplitudes of the ${}^{3}P_1$ (${}^{1}P_1$) mesons are symmetric (antisymmetric) under the exchange of quark and antiquark momentum fractions in the SU(3) limit. For chiral-odd light-cone distribution amplitudes, it is the other way around. The predictions for decay rates of $B_{u,d,s}\to Ae{\nu }_e$ are also presented.

In this followup to Phys. Rev. D 75, 053001 (2007) , we report updated constraints on neutrino mass-mixing parameters, in light of recent neutrino oscillation data (KamLAND, SNO, and MINOS) and cosmological observations (WMAP 5-year and other data). We discuss their interplay with the final $0\nu 2\beta$ decay results in ${}^{76}\mathrm{Ge}$ claimed by part of the Heidelberg-Moscow Collaboration, using recent evaluations of the corresponding nuclear matrix elements, and their uncertainties. We also comment on the $0\nu 2\beta$ limits in ${}^{130}\mathrm{Te}$ recently set by Cuoricino and on prospective limits or signals from the Karlsruhe tritium neutrino experiment.

We have calculated the leading-twist next-to-leading order (NLO), i.e., $\mathcal{O}({\alpha }_s)$, correction to the light-cone sum rules prediction for the electromagnetic form factors of the nucleon. We have used the Ioffe nucleon interpolation current and worked in $M_N=0$ approximation, with $M_N$ being the mass of the nucleon. In this approximation, only the Pauli form factor $F_2$ receives a correction and the calculated correction is quite sizable (ca. 60%). The numerical results for the proton form factors show the improved agreement with the experimental data. We also discuss the problems encountered when going away from $M_N=0$ approximation at NLO, as well as gauge invariance of the perturbative results. This work presents the first step towards the NLO accuracy in the light-cone sum rules for baryon form factors.

The Collins effect connects transverse quark spin with a measurable azimuthal asymmetry in the yield of hadronic fragments around the quark’s momentum vector. Using two different reconstruction methods we measure statistically significant azimuthal asymmetries for charged pion pairs in $e^{+}{e}^{-}$ annihilation at center-of-mass energies of 10.52 GeV and 10.58 GeV, which can be attributed to the fragmentation of primordial quarks with transverse spin components. The measurement was performed using a data set of $547{\mathrm{fb}}^{-1}$ collected by the Belle detector at KEKB improving the statistics of the previously published results by nearly a factor of 20.

We evaluate the ability of future data sets to discriminate among different quintessence dark energy models. This approach gives an alternative (and complementary) measure for assessing the impact of future experiments, as compared with the large body of literature that compares experiments in abstract parameter spaces (such as the well-known $w_0-w_a$ parameters) and more recent work that evaluates the constraining power of experiments on individual parameter spaces of specific quintessence models. We use the Dark Energy Task Force (DETF) models of future data sets and compare the discriminative power of experiments designated by the DETF as stages 2, 3, and 4 (denoting increasing capabilities). Our work reveals a minimal increase in discriminating power when comparing stage 3 to stage 2, but a very striking increase in discriminating power when going to stage 4 (including the possibility of completely eliminating some quintessence models). We also see evidence that even modest improvements over DETF stage 4 (which many believe are realistic) could result in even more dramatic discriminating power among quintessence dark energy models. We develop and demonstrate the technique of using the independently measured modes of the equation of state (derived from principle component analysis) as a common parameter space in which to compare the different quintessence models, and we argue that this technique is a powerful one. We use the pseudo-Nambu-Goldstone boson, exponential, Albrecht-Skordis, and inverse tracker (or inverse power law) quintessence models for this work. One of our main results is that the goal of discriminating among these models sets a concrete measure on the capabilities of future dark energy experiments. Experiments have to be somewhat better than DETF stage 4 simulated experiments to fully meet this goal.

We have obtained nonperturbative one-loop expressions for the mean-energy-momentum tensor and current density of Dirac’s field on a constant electriclike background. One of the goals of this calculation is to give a consistent description of backreaction in such a theory. Two cases of initial states are considered: the vacuum state and the thermal equilibrium state. First, we perform calculations for the vacuum initial state. In the obtained expressions, we separate the contributions due to particle creation and vacuum polarization. The latter contributions are related to the Heisenberg-Euler Lagrangian. Then, we study the case of the thermal initial state. Here, we separate the contributions due to particle creation, vacuum polarization, and the contributions due to the work of the external field on the particles at the initial state. All these contributions are studied in detail, in different regimes of weak and strong fields and low and high temperatures. The obtained results allow us to establish restrictions on the electric field and its duration under which QED with a strong constant electric field is consistent. Under such restrictions, one can neglect the backreaction of particles created by the electric field. Some of the obtained results generalize the calculations of Heisenberg-Euler for energy density to the case of arbitrary strong electric fields.

We introduce a minimal supersymmetric extension of a Higgsless model for electroweak symmetry breaking in a warped extra dimension. In contrast to the nonsupersymmetric version, our model naturally contains a candidate for cold dark matter. No Kaluza-Klein parity is required, because its stability is guaranteed by an $R$-parity. We discuss the regions in parameter space that are compatible with the observed dark matter content of our Universe and are allowed by electroweak precision measurements as well as direct searches.

Electromagnetic wave propagation inside isotropic material media characterized by dielectric coefficients ${\epsilon }_{\mu \nu }(E,B)$ and ${\mu }_{\mu \nu }(E,B)$ is examined. The regime of the eikonal approximation is considered. The Hadamard method of field disturbances is used and the dispersion relations are obtained by solving the Fresnel equation. Some applications of the formalism are presented. Particularly, birefringence phenomena induced by applied external fields are derived and discussed. It is shown that the magnetoelectric birefringence effect can occur even without the presence of Kerr and Cotton-Mouton effects, provided the physical system satisfies certain conditions.