A gravitational potential in the relativistic case is introduced as an alternative to Wald’s potential used by Verlinde, which reproduces the familiar entropy/area relation $S=A/4$ (in the natural units) when Verlinde’s idea is applied to the black hole case. Upon using the equipartition rule, the correct form of the Komar mass (energy) can also be obtained, which leads to the Einstein equations. It is explicitly shown that our entropy formula agrees with Verlinde’s entropy variation formula in spherical cases. The stationary space-times, especially the Kerr-Newman black hole, are then discussed, where it is shown that the equipartition rule involves the reduced mass, instead of the Arnowitt-Deser-Misner mass, on the horizon of the black hole.

We study systems analogous to binary black holes with spin in order to gain some insight into the origin and nature of “bobbing” motion and “kicks” that occur in this system. Our basic tool is a general formalism for describing the motion of extended test bodies in an external electromagnetic field in curved spacetime and possibly subject to other forces. We first show that bobbing of exactly the type as observed in numerical simulations of the binary black hole system occurs in a simple system consisting of two spinning balls connected by an elastic band in flat spacetime. This bobbing may be understood as arising from the difference between a spinning body’s “lab frame centroid” and its true center of mass, and is purely “kinematical” in the sense that it will appear regardless of the forces holding two spinning bodies in orbit. Next, we develop precise rules for relating the motion of charged bodies in a stationary external electromagnetic field in flat spacetime with the motion of bodies in a weakly curved stationary spacetime. We then consider the system consisting of two orbiting charges with magnetic dipole moment and spin at a level of approximation corresponding to 1.5 post-Newtonian order. Here we find that considerable amounts of momentum are exchanged between the bodies and the electromagnetic field; however, the bodies store this momentum entirely as “hidden” mechanical momentum, so that the interchange does not give rise to any net bobbing. The net bobbing that does occur is due solely to the kinematical spin effect, and we therefore argue that the net bobbing of the electromagnetic binary is not associated with possible kicks. We believe that this conclusion holds in the gravitational case as well.

We consider $b$-jet hadroproduction in the quasi-multi-Regge-kinematics approach based on the hypothesis of gluon and quark Reggeization in $t$-channel exchanges at high energies. The preliminary data on inclusive $b$-jet and $b\overline{b}$-dijet production taken by the CDF Collaboration at the Fermilab Tevatron are well described without adjusting parameters. We find the main contribution to inclusive $b$-jet production to be the scattering of a Reggeized gluon and a Reggeized $b$ quark to a $b$ quark, which is described by the effective Reggeon-Reggeon-quark vertex. The main contribution to $b\overline{b}$-pair production arises from the scattering of two Reggeized gluons to a $b\overline{b}$ pair, which is described by the effective Reggeon-Reggeon-quark-quark vertex. Our analysis is based on the Kimber-Martin-Ryskin prescription for unintegrated gluon and quark distribution functions using as input the Martin-Roberts-Stirling-Thorne collinear parton distribution functions of the proton.

In this work we study the $\kappa K^{+}{\pi }^{-}$ vertex in the framework of light cone QCD sum rules. We predict the coupling constant $g_{\kappa K^{+}{\pi }^{-}}$ to be $g_{\kappa K^{+}{\pi }^{-}}=(6.0\pm 1.0)\mathrm{GeV}$ and estimate the scalar $f_0-\sigma$ mixing angle from the experimental ratio $g^2(\kappa \to K\pi )/g^2(\sigma \to \pi \pi )$.

We present a relativistic formulation of noncommutative mechanics where the object of noncommutativity ${\theta }^{\mu \nu }$ is considered as an independent quantity. Its canonical conjugate momentum is also introduced so that it permits one to obtain an explicit form for the generators of the extended Poincaré group in the noncommutative case. The theory, which is invariant under reparametrization, generalizes recent nonrelativistic results. Free noncommutative bosonic particles satisfy an extended Klein-Gordon equation depending on two parameters.

We compute one-loop corrections to the annihilation of nonrelativistic particles $\chi$ due to the exchange of a (gauge or Higgs) boson $\phi$ with mass $\mu$ in the initial state. In the limit $m_{\chi }\gg \mu$ this leads to the “Sommerfeld enhancement” of the annihilation cross section. However, here we are interested in the case $\mu \lesssim m_{\chi }$, where the one-loop corrections are well behaved, but can still be sizable. We find simple and accurate expressions for annihilation from both $S$- and $P$-wave initial states; they differ from each other if $\mu \ne 0$. In order to apply our results to the calculation of the relic density of weakly interacting massive particles (WIMPs), we describe how to compute the thermal average of the corrected cross sections. We apply this formalism to scalar and Dirac fermion singlet WIMPs, and show that the corrections are always very small in the former case, but can be very large in the latter. Moreover, in the context of the minimal supersymmetric standard model, these corrections can decrease the relic density of neutralinos by more than 1%, if the lightest neutralino is a strongly mixed state.

Recently, Verlinde discussed that gravity can be understood as an entropic force caused by changes in the information associated with the positions of material bodies. In Verlinde’s argument, the area law of the black hole entropy plays a crucial role. However, the entropy-area relation can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. In this note, by employing this modified entropy-area relation, we derive corrections to Newton’s law of gravitation as well as modified Friedmann equations by adopting the viewpoint that gravity can be emerged as an entropic force. Our study further supports the universality of the log correction and provides a strong consistency check on Verlinde’s model.

We compute the ghost anomalous dimension within the asymptotic-safety scenario for quantum gravity. For a class of covariant gauge fixings and using a functional renormalization group scheme, the anomalous dimension ${\eta }_c$ is negative, implying an improved UV behavior of ghost fluctuations. At the non-Gaussian UV fixed point, we observe a maximum value of ${\eta }_c\simeq -0.78$ for the Landau-deWitt gauge within the given scheme and truncation. Most importantly, the backreaction of the ghost flow onto the Einstein-Hilbert sector preserves the non-Gaussian fixed point with only mild modifications of the fixed-point values for the gravitational coupling and cosmological constant and the associated critical exponents; also their gauge dependence is slightly reduced. Our results provide further evidence for the asymptotic-safety scenario of quantum gravity.

Spectacular breakthroughs in numerical relativity now make it possible to compute spacetime dynamics in almost complete generality, allowing us to model the coalescence and merger of binary black holes with essentially no approximations. The primary limitation of these calculations is now computational. In particular, it is difficult to model systems with large mass ratio and large spins, since one must accurately resolve the multiple length scales that play a role in such systems. Perturbation theory can play an important role in extending the reach of computational modeling for binary systems. In this paper, we present first results of a code that allows us to model the gravitational waves generated by the inspiral, merger, and ringdown of a binary system in which one member of the binary is much more massive than the other. This allows us to accurately calibrate binary dynamics in the large mass ratio regime. We focus in this analysis on the recoil imparted to the merged remnant by these waves. We closely examine the “antikick,” an antiphase cancellation of the recoil arising from the plunge and ringdown waves, described in detail by Schnittman et al. We find that, for orbits aligned with the black hole spin, the antikick grows as a function of spin. The total recoil is smallest for prograde coalescence into a rapidly rotating black hole, and largest for retrograde coalescence. Amusingly, this completely reverses the predicted trend for kick versus spin from analyses that only include inspiral information.

The observation of massive black hole binaries with pulsar timing arrays (PTAs) is one of the goals of gravitational-wave astronomy in the coming years. Massive ($\gtrsim {10}^8{M}_{\odot }$) and low-redshift ($\lesssim 1.5$) sources are expected to be individually resolved by upcoming PTAs, and our ability to use them as astrophysical probes will depend on the accuracy with which their parameters can be measured. In this paper we estimate the precision of such measurements using the Fisher-information-matrix formalism. For this initial study we restrict ourselves to “monochromatic” sources, i.e. binaries whose frequency evolution is negligible during the expected $\approx 10\mathrm{yr}$ observation time, which represent the bulk of the observable population based on current astrophysical predictions. In this approximation, the system is described by seven parameters and we determine their expected statistical errors as a function of the number of pulsars in the array, the array sky coverage, and the signal-to-noise ratio (SNR) of the signal. At fixed SNR (regardless of the number of pulsars in the PTA), the gravitational-wave astronomy capability of a PTA is achieved with $\approx 20$ pulsars; adding more pulsars (up to 1000) to the array reduces the source error box in the sky $\Delta \Omega$ by a factor $\approx 5$ and has negligible consequences on the statistical errors on the other parameters, because the correlations among parameters are already removed to a large extent. If one folds in the increase of coherent SNR proportional to the square root of the number of pulsars, $\Delta \Omega$ improves as $1/{\mathrm{SNR}}^2$ and the other parameters as $1/\mathrm{SNR}$. For a fiducial PTA of 100 pulsars uniformly distributed in the sky and a coherent $\mathrm{SNR}=10$, we find $\Delta \Omega \approx 40{\mathrm{deg}}^2$, a fractional error on the signal amplitude of $\approx 30\%$ (which constrains only very poorly the chirp mass—luminosity distance combination ${\mathcal{M}}^{5/3}/D_L$), and the source inclination and polarization angles are recovered at the $\approx 0.3\mathrm{rad}$ level. The ongoing Parkes PTA is particularly sensitive to systems located in the southern hemisphere, where at $\mathrm{SNR}=10$ the source position can be determined with $\Delta \Omega \approx 10{\mathrm{deg}}^2$, but has poorer (by an order of magnitude) performance for sources in the northern hemisphere.

We consider Friedmann-Lemaître-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling functions, in the era when the energy density of the scalar potential dominates over the energy density of ordinary matter. We focus upon the phase space of the scalar field. To study the regime suggested by the local weak field tests (i.e. close to the so-called limit of general relativity) we propose a nonlinear approximation scheme, solve for the phase trajectories, and provide a complete classification of possible phase portraits. We argue that the topology of trajectories in the nonlinear approximation is representative of those of the full system, and thus can tell for which scalar-tensor models general relativity functions as an attractor.

We construct a multimetric gravity theory containing $N\ge 3$ copies of standard model matter and a corresponding number of metrics. In the Newtonian limit, this theory generates attractive gravitational forces within each matter sector and repulsive forces of the same strength between matter from different sectors. This result demonstrates that the recently proven no-go theorem that forbids gravity theories of this type in $N=2$ cannot be extended beyond the bimetric case. We apply our theory to cosmology and show that the repulsion between different types of matter may induce the observed accelerating expansion of the universe. In this way dark energy can be explained simply by dark copies of the well-understood standard model.

We study a class of nonlocal, purely gravitational models, which have the correct structure to reproduce the leading infrared logarithms of quantum gravitational backreaction during the inflationary regime. These models end inflation in a distinctive phase of oscillations with slight and short violations of the weak energy condition and should, when coupled to matter, lead to rapid reheating. By elaborating this class of models we exhibit one that has the same behavior during inflation, goes quiescent until the onset of matter domination, and induces a small, positive cosmological constant of about the right size thereafter.

We investigate consequences of an ultraviolet fixed point in quantum gravity for the cosmological constant. For this purpose we perform dimensional reduction of a general dilatation-symmetric effective action $\Gamma$ in dimension $d>4$ to an effective four-dimensional theory of gravity with a dilaton field. We find a stable flat phase in the space of the extrema of $\Gamma$ which results in a vanishing four-dimensional cosmological constant $\Lambda$. In order to understand the self-tuning mechanism leading to $\Lambda =0$ we discuss in detail the most general warped geometries with maximal four-dimensional symmetry and $SO(d-4)$ isometry of internal space. While the solutions of the $d$-dimensional field equations admit singular spaces with arbitrary $\Lambda$, the extremum condition for $\Gamma$ imposes additional restrictions which result in $\Lambda =0$. In cosmology, the dilatation-symmetric fixed point may only be reached for asymptotic time $t\to \infty$. At finite $t$ dilatation anomalies result in an effective potential and mass for the pseudodilaton or cosmon and in dark energy.

We discuss a possible solution to the cosmological constant problem based on the hypothesis of a fixed point for higher-dimensional quantum gravity coupled to a scalar. At the fixed point, which is reached only for an infinite value of the scalar field, dilatation symmetry becomes exact. For this limit we concentrate on the absence of a scalar potential since a polynomial potential is not consistent with dilatation symmetry in higher dimensions. We find generic solutions of the higher-dimensional field equations for which the effective four-dimensional cosmological constant vanishes independently of the parameters of the higher-dimensional effective action. Under rather general circumstances these are the only quasistatic stable extrema of the effective action which lead to a finite four-dimensional Planck mass. We discuss the associated higher-dimensional self-tuning mechanism for the cosmological constant. If cosmological runaway solutions approach the fixed point as time goes to infinity, the effective dark energy vanishes asymptotically. In the present cosmological epoch the fixed point is not yet reached completely, resulting in a tiny amount of dark energy, comparable to dark matter. We discuss explicitly higher-dimensional geometries which realize such asymptotic solutions for time going to infinity.

We investigate a possibility of reheating in a scenario of D-brane inflation in a warped deformed conifold background which includes perturbative corrections to throat geometry sourced by a chiral operator of dimension $3/2$ in the conformal field theory. The effective D-brane potential, in this case, belongs to the class of nonoscillatory models of inflation for which the conventional reheating mechanism does not work. We find that gravitational particle production is inefficient and leads to reheating temperature of the order of ${10}^8\mathrm{GeV}$. We show that instant preheating is quite suitable to the present scenario and can easily reheat the universe to a temperature which is higher by about 3 orders of magnitude than its counterpart associated with gravitational particle production. The reheating temperature is shown to be insensitive to a particular choice of inflationary parameters suitable to observations.

We solve analytically and numerically the generalized Einstein equations in scalar-tensor cosmologies to obtain the evolution of dark energy and matter linear perturbations. We compare our results with the corresponding results for minimally coupled quintessence perturbations. We find that scalar-tensor dark energy density perturbations are amplified by a factor of about ${10}^4$ compared to minimally coupled quintessence perturbations on scales less than about $1000{\mathrm{h}}^{-1}\mathrm{Mpc}$ (sub-Hubble scales). On these scales dark energy perturbations constitute a fraction of about 10% compared to matter density perturbations. Scalar-tensor dark energy density perturbations are anticorrelated with matter linear perturbations on sub-Hubble scales. This anticorrelation of matter with negative pressure perturbations induces a mild amplification of matter perturbations by about 10% on sub-Hubble scales. The evolution of scalar field perturbations on sub-Hubble scales is scale independent and therefore corresponds to a vanishing effective speed of sound ($c_{s\Phi }=0$). We briefly discuss the observational implications of our results, which may include predictions for galaxy and cluster halo profiles that are modified compared to $\Lambda \mathrm{CDM}$. The observed properties of these profiles are known to be in some tension with the predictions of $\Lambda \mathrm{CDM}$.

In the inflationary universe, there can be light fields other than the inflaton. We explore a possibility that such light fields source the primordial perturbations, while minimally affecting the inflaton dynamics. We show that during inflation, fluctuations of the light fields can be converted to adiabatic curvature perturbations, which accumulate and become significant by the end of the inflationary era. An additional goal of this work is to distinguish between light fields which can/cannot be ignored during inflation. Such criteria become useful for examining cosmological scenarios with multiple fields. As concrete examples, our results are applied to D-brane inflation models. We consider effects from KK modes (oscillation modes) of wrapped branes in monodromy-driven large-field models, and angular directions of throat geometries in warped D-brane inflation.

We present results from an all-sky search for unmodeled gravitational-wave bursts in the data collected by the LIGO, GEO 600 and Virgo detectors between November 2006 and October 2007. The search is performed by three different analysis algorithms over the frequency band 50–6000 Hz. Data are analyzed for times with at least two of the four LIGO-Virgo detectors in coincident operation, with a total live time of 266 days. No events produced by the search algorithms survive the selection cuts. We set a frequentist upper limit on the rate of gravitational-wave bursts impinging on our network of detectors. When combined with the previous LIGO search of the data collected between November 2005 and November 2006, the upper limit on the rate of detectable gravitational-wave bursts in the 64–2048 Hz band is 2.0 events per year at 90% confidence. We also present event rate versus strength exclusion plots for several types of plausible burst waveforms. The sensitivity of the combined search is expressed in terms of the root-sum-squared strain amplitude for a variety of simulated waveforms and lies in the range $6\times {10}^{-22}{\mathrm{Hz}}^{-1/2}$ to $2\times {10}^{-20}{\mathrm{Hz}}^{-1/2}$. This is the first untriggered burst search to use data from the LIGO and Virgo detectors together, and the most sensitive untriggered burst search performed so far.

We estimate the QCD effective charge ${\alpha }_s$ in the low-energy region by exploiting the conventional meson spectrum within a relativistic quantum-field model based on analytic confinement. The ladder Bethe-Salpeter equation is solved for the masses of two-quark bound states. We found a new, independent, and specific infrared-finite behavior of QCD coupling below energy scale 1 GeV. Particularly, an infrared-fixed point is extracted at ${\alpha }_s(0)\simeq 0.757$ for confinement scale $\Lambda =345\mathrm{MeV}$. As an application, we estimate masses of some intermediate and heavy mesons and obtain results in reasonable agreement with recent experimental data.