We study the effect of resonant tidal excitation of inertial modes in neutron stars during binary inspiral. For spin frequencies less than 100 Hz, the phase shift in the gravitational waveform associated with the resonance is small and does not affect the matched filtering scheme for gravitational wave detection. For higher spin frequencies, the phase shift can become significant. Most of the resonances take place at orbital frequencies comparable to the spin frequency, and thus significant phase shift may occur only in the high-frequency band (hundreds of Hertz) of gravitational waves. The exception is a single odd-parity $m=1$ mode, which can be resonantly excited for misaligned spin-orbit inclinations, and may occur in the low-frequency band (tens of Hertz) of gravitational waves and induce significant ($\gg 1\mathrm{radian}$) phase shift.

Observations of the inspiral of massive binary black holes (BBH) in the Laser Interferometer Space Antenna (LISA) and stellar mass binary black holes in the European Gravitational Wave Observatory (EGO) offer an unique opportunity to test the nonlinear structure of general relativity. For a binary composed of two nonspinning black holes, the nonlinear general relativistic effects depend only on the masses of the constituents. In a recent paper, we explored the possibility of a test to determine all the post-Newtonian coefficients in the gravitational wave phasing. However, mutual covariances dilute the effectiveness of such a test. In this paper, we propose a more powerful test in which the various post-Newtonian coefficients in the gravitational wave phasing are systematically measured by treating three of them as independent parameters and demanding their mutual consistency. LISA (EGO) will observe BBH inspirals with a signal-to-noise ratio of more than 1000 (100) and thereby test the self-consistency of each of the nine post-Newtonian coefficients that have so-far been computed, by measuring the lower order coefficients to a relative accuracy of $\sim {10}^{-5}$ (respectively, $\sim {10}^{-4}$) and the higher order coefficients to a relative accuracy in the range ${10}^{-4}-0.1$ (respectively, ${10}^{-3}-1$).

We show how braneworld cosmology with bulk matter can explain structure formation. In this scenario, the nonlocal corrections to the Friedmann equations supply a Weyl fluid that can dominate over matter at late times due to the energy exchange between the brane and the bulk. We demonstrate that the presence of the Weyl fluid radically changes the perturbation equations, which can take care of the fluctuations required to account for the large amount of inhomogeneities observed in the local universe. Further, we show how this Weyl fluid can mimic dark matter. We also investigate the bulk geometry responsible for the scenario.

This is a sequel to a previous detailed study of quantum corrections to cosmological correlations. It was found there that except in special cases these corrections depend on the whole history of inflation, not just on the behavior of fields at horizon exit. It is shown here that at least in perturbation theory these corrections can nevertheless not be proportional to positive powers of the Robertson-Walker scale factor, but only at most to powers of its logarithm, and are therefore never large.

A model-independent method to study the possible evolution of dark energy is presented. Optimal estimates of the dark energy equation of state $w$ are obtained from current supernovae data from [A. G. Riess et al. (Supernova Search Team Collaboration), Astrophys. J. 607, 665 (2004).] following a principal components approach. We assess the impact of varying the number of piecewise constant $w$ estimates $N_{\mathrm{p}}$ using a model selection method, the Bayesian information criterion, and compare the most favored models with some parametrizations commonly used in the literature. Although data seem to prefer a cosmological constant, some models are only moderately disfavored by our selection criterion: a constant $w$, $w\propto a$, $w\propto z$, and the two-parameter models introduced here. Among these, the models we find by optimization are slightly preferred. However, current data do not allow us to draw a conclusion on the possible evolution of dark energy. Interestingly, the best fits for all varying-$w$ models exhibit a $w<-1$ at low redshifts.

There has been much debate over whether or not one could explain the observed acceleration of the Universe with inhomogeneous cosmological models, such as the spherically-symmetric Lemaître-Tolman-Bondi (LTB) models. It has been claimed that the central observer in these models can observe a local acceleration, which would contradict general theorems. We resolve the contradiction by noting that many of the models that have been explored contain a weak singularity at the location of the observer which makes them unphysical. In the absence of this singularity, we show that LTB models must have a positive central deceleration parameter $q_0$, in agreement with the general theorems. We also show that it is possible to achieve a negative apparent deceleration parameter at nonzero redshifts in LTB models that do not contain this singularity. However, we find other singularities that tend to arise in LTB models when attempting to match luminosity distance data, and these generally limit the range of redshifts for which these models can mimic observations of an accelerating Universe. Exceptional models do exist that can extend to arbitrarily large redshift without encountering these pathologies, and we show how these may be constructed. These special models exhibit regions with negative effective equation of state parameter, which may fall below negative one, but we have failed to find any singularity-free models that agree with observations. Moreover, models based on dust-filled LTB metrics probably fail to reproduce observed properties of large scale structure.

We present a model which predicts inflation without the presence of inflaton fields, based on the $ϵR^2$ and Starobinsky models. It links the above models to the reheating epoch with conformally coupled massive particles created at the end of inflation. In the original Starobinsky model, the reheating era was created by massless nonconformally coupled particles. We assume here that nonconformal coupling to gravitation does not exist. In the $ϵR^2$ model, inflation is produced by the gravitational Lagrangian to which a term $ϵR^2$ is added, where $ϵ$ is a constant and $R$ is the Ricci scalar. Inflation is created by vacuum fluctuations in the Starobinsky model. Both models have the same late-inflation time-dependence, which is described by a characteristic mass $M$. There is a free parameter $H_0$ on the order of the Planck mass $M_{\mathrm{Pl}}$ that determines the Hubble parameter near the Planck epoch and which depends upon the number and type of particles creating the vacuum fluctuations in the Starobinsky model. In our model, we assume the existence of particles with a mass $m$, on the order of $M$, conformally coupled to gravity, that have a long decay time. Taking $m\equiv FM$, we investigate values of $F=0.5$ and 0.3. These particles, produced $\sim 60e$-folds before the end of inflation, created the nearly scale-invariant scalar density fluctuations which are observed. Gravitational waves (tensor fluctuations) were also produced at this epoch. At $t_{\mathrm{end}}$, the Hubble parameter begins to oscillate rapidly, gravitationally producing the bulk of the $m$ particles, which we identify as the origin of the matter content of the Universe today. The time required for the Universe to dissipate its vacuum energy into $m$ particles is found to be $t_{\mathrm{dis}}\simeq 6M_{\mathrm{Pl}}^2/M^{3}F$. We assume that the reheating time $t_{RH}$ needed for the $m$ particles to decay into relativistic particles is very much greater than that necessary to create the $m$ particles, $t_{\mathrm{dis}}$. A particle physics theory of $m$ can, in principle, predict their decay rate ${\Gamma }_{mr}\equiv t_{RH}^{-1}$. From the ratio $f\equiv t_{\mathrm{dis}}/t_{RH}$, $F$ and $g_{*}$ (the total number of degrees of freedom of the relativistic particles) we can then evaluate the maximum temperature of the Universe $T_{\max }$ and the reheat temperature $T_{RH}$ at $t_{RH}$. From the observed scalar fluctuations at large scales, $\delta \rho /\rho \sim {10}^{-5}$, we have the prediction $M\cong 1.15\times {10}^{-6}{M}_{\mathrm{Pl}}$ and the ratio of the tensor to scalar fluctuations, $r\cong 6.8\times {10}^{-4}$. Thus our model predicts $M$, $t_{\mathrm{dis}}$, $t_{\mathrm{end}}$, $T_{\max }$, $T_{RH}$, $t_{\max }$, and $t_{RH}$ as a function of $f$, $F$, and $g_{*}$ (and to a weaker extent the particle content of the vacuum near the Planck epoch). A measured value of $r$ that is appreciably different from $r=6.8\times {10}^{-4}$ would discard our model (as well as the Starobinsky and $ϵR^2$ models).

We extract parameters relevant for distinguishing among single-field inflation models from the Wilkinson Microwave Anisotropy Probe (WMAP) three-year data set, and also from WMAP in combination with the Sloan Digital Sky Survey (SDSS) galaxy power spectrum. Our analysis leads to the following conclusions: (1) the Harrison—Zel’dovich model is consistent with both data sets at a 95% confidence level; (2) there is no strong evidence for running of the spectral index of scalar perturbations; (3) potentials of the form $V\propto {\varphi }^p$ are consistent with the data for $p=2$, and are marginally consistent with the WMAP data considered alone for $p=4$, but ruled out by WMAP combined with SDSS. We perform a “Monte Carlo reconstruction” of the inflationary potential, and find that: (1) there is no evidence to support an observational lower bound on the amplitude of gravitational waves produced during inflation; (2) models such as simple hybrid potentials which evolve toward an inflationary late-time attractor in the space of flow parameters are strongly disfavored by the data, (3) models selected with even a weak slow-roll prior strongly cluster in the region favoring a red power spectrum and no running of the spectral index, consistent with simple single-field inflation models.

Capture rates of compact objects were calculated by using a recent solution of the Fokker-Planck equation in energy space, including two-body resonant effects. The fraction of compact objects (white dwarfs, neutron stars, and stellar black holes) was estimated as a function of the luminosity of the galaxy from a new grid of evolutionary models. Stellar mass densities at the influence radius of central supermassive black holes were derived from brightness profiles obtained by Hubble Space Telescope observations. The present study indicates that the capture rates scale as $\propto M_{\mathrm{bh}}^{-1.048}$, a consequence of the fact that dwarf galaxies have denser central regions than luminous objects. If the mass distribution of supermassive black holes has a lower cutoff at $\sim 1.4\times {10}^6{M}_{\odot }$ (corresponding to the lowest observed supermassive black hole mass, located in M32), then nine inspiral events are expected to be seen by the Laser Interferometer Space Antenna (7–8 corresponding to white dwarf captures and 1–2 to neutron star and stellar black hole captures) after 1 yr of operation. However, if the mass distribution extends down to $\sim 2\times {10}^5{M}_{\odot }$, then the total number of expected events increases up to 579 (corresponding to $\sim 274$ stellar black hole captures, $\sim 194$ neutron star captures, and $\sim 111$ white dwarf captures).

We report on the optical response of a suspended-mass detuned resonant sideband extraction (RSE) interferometer with power recycling. The purpose of the detuned RSE configuration is to manipulate and optimize the optical response of the interferometer to differential displacements (induced by gravitational waves) as a function of frequency, independently of other parameters of the interferometer. The design of our interferometer results in an optical gain with two peaks: an RSE optical resonance at around 4 kHz and a radiation pressure induced optical spring at around 41 Hz. We have developed a reliable procedure for acquiring lock and establishing the desired optical configuration. In this configuration, we have measured the optical response to differential displacement and found good agreement with predictions at both resonances and all other relevant frequencies. These results build confidence in both the theory and practical implementation of the more complex optical configuration being planned for Advanced LIGO.

The near-threshold enhancement in the $p\overline{p}$ invariant mass spectrum from the $B^{+}\to K^{+}p\overline{p}$ decay reported recently by the BABAR Collaboration is studied within the Jülich $N\overline{N}$ model. We illustrate that the invariant mass dependence of the $p\overline{p}$ spectrum close to the threshold can be reproduced by the final state interactions. This explanation is in line with our previous analysis of the $p\overline{p}$ invariant mass spectrum from the $J/\Psi \to \gamma p\overline{p}$ decay measured by the BES Collaboration. We also comment on a structure found recently in the ${\pi }^{+}{\pi }^{-}{\eta }^{\prime }$ mass spectrum of the radiative $J/\Psi$ decay by the BES Collaboration. In particular we argue that one should be rather cautious in bringing this structure in connection with the enhancement found in the $p\overline{p}$ invariant mass spectrum or with the existence of $N\overline{N}$ bound states.

In a theory with linear confinement, such as QCD, the masses squared $m_{n,S}^2$ of mesons with high spin $S$ or high radial excitation number $n$ are expected, from semiclassical arguments, to grow linearly with $S$ and $n$. We show that this behavior can be reproduced within a putative 5-dimensional theory holographically dual to QCD (AdS/QCD). With the assumption that such a dual theory exists and describes highly excited mesons as well, we show that an asymptotically linear $m^2$ spectrum translates into a strong constraint on the infrared behavior of that theory. In the simplest model which obeys such a constraint we find $m_{n,S}^2\sim (n+S)$.

Green’s functions are a central element in the attempt to understand nonperturbative phenomena in Yang-Mills theory. Besides the propagators, 3-point Green’s functions play a significant role, since they permit access to the running coupling constant and are an important input in functional methods. Here we present numerical results for the two nonvanishing 3-point Green’s functions in 3d pure SU(2) Yang-Mills theory in (minimal) Landau gauge, i.e. the three-gluon vertex and the ghost-gluon vertex, considering various kinematical regimes. In this exploratory investigation the lattice volumes are limited to ${20}^3$ and ${30}^3$ at $\beta =4.2$ and $\beta =6.0$. We also present results for the gluon and the ghost propagators, as well as for the eigenvalue spectrum of the Faddeev-Popov operator. Finally, we compare two different numerical methods for the evaluation of the inverse of the Faddeev-Popov matrix, the point-source and the plane-wave-source methods.

We investigate the dependence of the Drell-Yan cross section on lepton polar and azimuthal angles, as generated by the lowest-order QCD annihilation and Compton processes. We focus, in particular, on the azimuthal-angular distributions, which are of the form $\cos \varphi$ and $\cos 2\varphi$. At small transverse momentum $q_T$ of the lepton pair, $q_T\ll Q$, with $Q$ the pair mass, these terms are known to be suppressed relative to the $\varphi$-independent part of the Drell-Yan cross section by one or two powers of the transverse momentum. Nonetheless, as we show, like the $\varphi$-independent part they are subject to large logarithmic corrections, whose precise form, however, depends on the reference frame chosen. These logarithmic contributions ultimately require resummation to all orders in the strong coupling. We discuss the potential effects of resummation on the various angular terms in the cross section and on the Lam-Tung relation.

We define a new variable flavor number scheme for use in deep inelastic scattering, motivated by the need to consistently implement high energy resummations alongside a fixed order QCD expansion. We define the $\mathrm{DIS}(\chi )$ scheme at fixed order, and show how to obtain the small $x$ coefficient functions and heavy flavor matrix elements to leading order in the high energy resummation. We then implement these results in a global fit at LO which includes leading resummations with running coupling corrections. Finally, we address the impact of the resummed results on predictions for the longitudinal structure function. We find that they stabilize the behavior of $F_L$ at small $x$. Overall, we find that resummations significantly improve the fit to scattering data in the low $x$ regime, although higher orders in the fixed order expansion are needed to describe current structure function and related data over the complete $x$ range.

We study the expectation value of higher rank Polyakov-Maldacena loops that wrap the thermal circle in strongly coupled $\mathcal{N}=4$ super Yang-Mills theory. This is achieved by considering probe $D3$ and $D5$ brane embeddings in the dual black hole geometry. Nontrivial dependence on the rank is captured through $D5$ branes. We find $N^{-2/3}$ corrections, reminiscent of the scaling behavior near a Gross-Witten transition.

We study the stepwise sine-Gordon equation, in which the system parameter is different for positive and negative values of the scalar field. By applying appropriate boundary conditions, we derive relations between the soliton velocities before and after collisions. We investigate the possibility of formation of heavy soliton pairs from light ones and vice versa. The concept of the soliton gun is introduced for the first time; a light pair is produced moving with high velocity, after the annihilation of a bound, heavy pair. A few static, quasiperiodic solutions of the stepwise sine-Gordon equation are also derived.

We construct a theory of Maxwell stresses in Rindler space, presenting both a noncovariant and a covariant formulation. The theory shows how the Maxwell stresses are modified by a nonvanishing acceleration of gravity and that the Maxwell stresses of an electromagnetic field produce a volume stress force which vanishes in an inertial frame. In the noncovariant formulation we deduce the Maxwellian force due to the bending of the field lines by the acceleration of gravity. In the covariant formulation we show that Archimedes’ law is valid for stationary electromagnetic fields in Rindler space: The Maxwellian surface forces acting from the outside field upon a closed surface produce a buoyancy equal to the weight of the electromagnetic field enclosed by the surface. Generally the mechanism is different from that in a fluid in which the buoyancy is due to a pressure which increases with depth. In a vertical electrical field the buoyancy is due to a tension that increases with height, but in a horizontal field it is due to a Maxwellian pressure which increases with the depth.

In spite of the macroscopic character of the primordial fluctuations, the standard inflationary distribution (that obtained using linear mode equations) exhibits inherently quantum properties, that is, properties which cannot be mimicked by any stochastic distribution. This is demonstrated by a Gedanken experiment for which certain Bell inequalities are violated. These violations are in principle measurable because, unlike for Hawking radiation from black holes, in inflationary cosmology we can have access to both members of correlated pairs of modes delivered in the same state. We then compute the effect of decoherence and show that the violations persist provided the decoherence level (and thus the entropy) lies below a certain nonvanishing threshold. Moreover, there exists a higher threshold above which no violation of any Bell inequality can occur. In this regime, the distributions are “separable” and can be interpreted as stochastic ensembles of fluctuations. Unfortunately, the precision which is required to have access to the quantum properties is so high that, in practice, an observational verification seems excluded.

We present a mechanism for catalyzed vacuum bubble production obtained by combining moduli stabilization with a generalized attractor phenomenon in which moduli are sourced by compact objects. This leads straightforwardly to a class of examples in which the Hawking decay process for black holes unveils a bubble of a different vacuum from the ambient one, generalizing the new end point for Hawking evaporation discovered recently by Horowitz. Catalyzed vacuum bubble production can occur for both charged and uncharged bodies, including Schwarzschild black holes for which massive particles produced in the Hawking process can trigger vacuum decay. We briefly discuss applications of this process to the population and stability of metastable vacua.