We analyze numerical-relativity (NR) waveforms that cover nine orbits (18 gravitational-wave cycles) before merger of an equal-mass system with low eccentricity, with numerical uncertainties of 0.25 radians in the phase and 2% in the amplitude; such accuracy allows a direct comparison with post-Newtonian (PN) waveforms. We focus on waveforms predicted by one of the PN approximants that has been proposed for use in gravitational-wave data analysis, restricted 3.5PN TaylorT1, and compare these with a section of the numerical waveform from the second to the eighth orbit, which is about one and a half orbits before merger. This corresponds to a gravitational-wave frequency range of $M\omega =0.0455$ to 0.1 Depending on the method of matching PN and NR waveforms, the accumulated phase disagreement over this frequency range can be within numerical uncertainty. Similar results are found in comparisons with an alternative PN approximant, 3PN TaylorT3. The amplitude disagreement, on the other hand, is around 6%, but roughly constant for all 13 cycles that are compared, suggesting that for the purpose of producing “hybrid waveforms,” only 4.5 orbits need be simulated to match PN and NR waves with the same accuracy as is possible with nine orbits. If, however, we model the amplitude up to 2.5PN order, numerical and post-Newtonian amplitude disagreement is close to the numerical error of 2%.

Four-dimensional Einstein’s general relativity is shown to arise from a gauge theory for the conformal group, $SO(4,2)$. The theory is constructed from a topological dimensional reduction of the six-dimensional Euler density integrated over a manifold with a four-dimensional topological defect. The resulting action is a four-dimensional theory defined by a gauged Wess-Zumino-Witten term. An ansatz is found which reduces the full set of field equations to those of Einstein’s general relativity. When the same ansatz is replaced in the action, the gauged WZW term reduces to the Einstein-Hilbert action. Furthermore, the unique coupling constant in the action can be shown to take integer values if the fields are allowed to be analytically continued to complex values.

Most parametrizations for dark energy involve the equation of state $w$ of the dark energy. In this work, we choose the pressure of the dark energy to parametrize. As $p=\mathrm{\text{constant}}$ essentially gives a cosmological constant, we use the Taylor expansion around this behavior $p=-p_0+(1-a)p_1+\dots$ to study the small deviations from the cosmological constant. In our model, the departure from the cosmological constant behavior has been modeled by the presence of extra K-essence fields while keeping the cosmological constant term untouched. The model is similar to an assisted inflation scenario in a sense that for any higher order deviation in terms of Taylor series expansion, one needs multiple K-essence fields. We have also tested our model with the recent observational data coming from Supernova type Ia measurements, the baryon oscillations peak (BAO), and the gas mass fraction of the galaxy clusters inferred from x-ray observations and obtain constraints for our model parameters.

Lattice studies indicate existence of magnetic strings in QCD vacuum. We argue that recently found non-Abelian strings with rich world-sheet dynamics provide a pattern which fits the strings observed on the lattice. In particular, within this pattern we explain the localization of the monopole-antimonopole pairs on the magnetic string world sheet and the negative contribution of the magnetic strings into the vacuum energy and gluon condensate. We suggest the D2 brane realization of the magnetic string which explains the temperature dependence of its tension.

The moving puncture method is analyzed for a single, nonspinning black hole. It is shown that the puncture region is not resolved by current numerical codes. As a result, the geometry near the puncture appears to evolve to an infinitely long cylinder of finite areal radius. The puncture itself actually remains at spacelike infinity throughout the evolution. In the limit of infinite resolution the data never become stationary. However, at any reasonable finite resolution the grid points closest to the puncture are rapidly drawn into the black hole interior by the $\Gamma$-driver shift condition. The data can then evolve to a stationary state. These results suggest that the moving puncture technique should be viewed as a type of “natural excision.”

We present several different classes of self-dual Yang-Mills instantons in all even $d$-dimensional backgrounds with Euclidean signature. In $d=4p+2$ the only solutions we found are on constant curvature dS (de Sitter) and AdS (anti–de Sitter) backgrounds and are evaluated in closed form. In $d=4p$ an interesting class of instantons are given on black hole backgrounds. One class of solutions are (Euclidean) time-independent and spherically symmetric in $d-1$ dimensions, and the other class are spherically symmetric in all $d$ dimensions. Some of the solutions in the former class are evaluated numerically, all the rest being given in closed form. Analytic proofs of existence covering all numerically evaluated solutions are given. All instantons studied have finite action and vanishing energy momentum tensor and do not disturb the geometry.

The increasing sophistication and accuracy of numerical simulations of compact binaries (especially binary black holes) presents the opportunity to test the regime in which post-Newtonian (PN) predictions for the emitted gravitational waves are accurate. In order to confront numerical results with those of post-Newtonian theory, it is convenient to compare multipolar decompositions of the two waveforms. It is pointed out here that the individual modes can be computed to higher post-Newtonian order by examining the radiative multipole moments of the system, rather than by decomposing the 2.5PN polarization waveforms. In particular, the dominant ($l=2$, $m=\pm 2$) mode can be computed to 3PN order. Individual modes are computed to as high a post-Newtonian order as possible given previous post-Newtonian results.

No Kerr-like exact solution has yet been found in Chern-Simons modified gravity. Intrigued by this absence, we study stationary and axisymmetric metrics that could represent the exterior field of spinning black holes. For the standard choice of the background scalar, the modified field equations decouple into the Einstein equations and additional constraints. These constraints eliminate essentially all solutions except for Schwarzschild. For noncanonical choices of the background scalar, we find several exact solutions of the modified field equations, including mathematical black holes and $pp$-waves. We show that the ultrarelativistically boosted Kerr metric can satisfy the modified field equations, and we argue that physical spinning black holes may exist in Chern-Simons modified gravity only if the metric breaks stationarity, axisymmetry, or energy-momentum conservation.

Observations by the Wilkinson Microwave Anisotropy Probe (WMAP) experiment have identified an excess of microwave emission from the center of the Milky Way. It has previously been shown that this “WMAP haze” could be synchrotron emission from relativistic electrons and positrons produced in the annihilations of dark matter particles. In particular, the intensity, spectrum, and angular distribution of the WMAP haze is consistent with an electroweak scale dark matter particle (such as a supersymmetric neutralino or Kaluza-Klein dark matter in models with universal extra dimensions) annihilating with a cross section on the order of $\sigma v\sim 3\times {10}^{-26}{\mathrm{cm}}^3/\mathrm{s}$ and distributed with a cusped halo profile. No further exotic astrophysical or annihilation boost factors are required. If dark matter annihilations are in fact responsible for the observed haze, then other annihilation products will also be produced, including gamma rays. In this article, we study the prospects for the GLAST satellite to detect gamma rays from dark matter annihilations in the Galactic Center region in this scenario. We find that by studying only the inner 0.1° around the Galactic Center, GLAST will be able to detect dark matter annihilating to heavy quarks, gauge bosons, or tau leptons over astrophysical backgrounds with $5\sigma$ ($3\sigma$) significance if they are lighter than approximately 320–500 GeV (500–750 GeV). If the angular window is broadened to study the dark matter halo profile’s angular extension (while simultaneously reducing the astrophysical backgrounds), weakly interacting, massive particles (WIMPs) as heavy as several TeV can be identified by GLAST with high significance. Only if the dark matter particles annihilate mostly to electrons or muons will GLAST be unable to identify the gamma ray spectrum associated with the WMAP haze.

We consider leptogenesis in scenarios with many neutrino singlets. We find that the lower bound for the reheating temperature can be significantly relaxed with respect to the hierarchical three neutrino case. We further argue that the upper bound for the neutrino mass scale from leptogenesis gets significantly lifted in these scenarios. As a specific realization, we then discuss an extradimensional model, where the large number of neutrinos is provided by Kaluza-Klein excitations.

By analyzing the apparent horizon (AH) formation in the collision of two pp waves with rectangular sources in four dimensions, we study to what extent the AH can be distorted without violating the energy conditions. It is shown that the highly distorted AH can form in this system although it cannot be arbitrarily long. The hoop conjecture is examined for the formation of such highly distorted AHs, and our result gives a strong support to the hoop conjecture. We also point out the possible relation between the AH topology theorem and the hoop conjecture.

We present a renormalization procedure for Polyakov loops which explicitly implements the fact that the renormalization constant depends only on the ultraviolet cutoff. Using this we study the renormalized Polyakov loops in all representations up to the $\mathbf{27}$ of the gauge group SU(3). We find good evidence for Casimir scaling of the Polyakov loops and for approximate large-$N$ factorization. By studying many loops together, we are able to show that there is a matrix model with a single coupling which can describe the high temperature phase of QCD, although it is hard to construct explicitly. We present the first results for the nonvanishing renormalized octet loop in the thermodynamic limit below the SU(3) phase transition, and estimate the associated string breaking distance and the gluelump binding energy. By studying the connection of the direct renormalization procedure with a generalization of an earlier suggestion which goes by the name of the $Q\overline{Q}$ renormalization procedure, we find that they are functionally equivalent.

We construct the phase diagrams of the quark-antiquark and diquark condensates at finite temperature and density in the 3-dimensional (3D) 2-flavor Gross-Neveu model. We found that, in contrast to the case of the 4D Nambu–Jona-Lasinio model, there is no region where the quark-antiquark and diquark condensates coexist. The phase diagrams obtained for some parameter region show similar structure with the 4D QCD phase diagram.

We consider the thermodynamics of a charged black hole enclosed in a cavity. The charge in the cavity and the temperature at the walls are fixed, yielding a canonical ensemble. We derive the phase structure and stability of black hole equilibrium states. We compare our results to that of other work which uses asymptotically anti-de Sitter (AdS) boundary conditions to define the thermodynamics. The thermodynamic properties have extensive similarities which suggest that the idea of AdS holography is more dependent on the existence of the boundary than on the exact details of asymptotically AdS metrics.

We perform a Monte Carlo Markov chains (MCMC) analysis of the available cosmic microwave background (CMB) and large scale structure (LSS) data (including the three years WMAP data) with single field slow-roll new inflation and chaotic inflation models. We do this within our approach to inflation as an effective field theory in the Ginsburg-Landau spirit with fourth degree trinomial potentials in the inflaton field $\varphi$. We derive explicit formulae and study in detail the spectral index $n_s$ of the adiabatic fluctuations, the ratio $r$ of tensor to scalar fluctuations, and the running index $d{n}_s/d\ln k$. We use these analytic formulas as hard constraints on $n_s$ and $r$ in the MCMC analysis. Our analysis differs in this crucial aspect from previous MCMC studies in the literature involving the WMAP3 data. Our results are as follows: (i) The data strongly indicate the breaking (whether spontaneous or explicit) of the $\varphi \to -\varphi$ symmetry of the inflaton potentials both for new and for chaotic inflation. (ii) Trinomial new inflation naturally satisfies this requirement and provides an excellent fit to the data. (iii) Trinomial chaotic inflation produces the best fit in a very narrow corner of the parameter space. (iv) The chaotic symmetric trinomial potential is almost certainly ruled out (at 95% C.L.). In trinomial chaotic inflation the MCMC runs go towards a potential in the boundary of the parameter space and which resembles a spontaneously symmetry broken potential of new inflation. (v) The above results and further physical analysis here lead us to conclude that new inflation gives the best description of the data. (vi) We find a lower bound for $r$ within trinomial new inflation potentials: $r>0.016(95\%\mathrm{CL})$ and $r>0.049(68\%\mathrm{CL})$. (vii) The preferred new inflation trinomial potential is a double well, even function of the field with a moderate quartic coupling yielding as most probable values: $n_s\simeq 0.958$, $r\simeq 0.055$. This value for $r$ is within reach of forthcoming CMB observations.

We study the single production of excited spin-$3/2$ and spin-$1/2$ leptons in future high energy $e^{+}{e}^{-}$ collisions. We calculate the production cross section and decay widths of excited spin-$3/2$ and spin-$1/2$ leptons according to their effective currents. We show that these possible new excited states can be probed up to the mass $m^{*}\sim \sqrt{s}$ depending on their couplings to leptons and gauge bosons. We present the angular distributions of final state particles as a measure to discriminate between an excited spin-$3/2$ and spin-$1/2$ lepton signal. The signals and the corresponding backgrounds are studied in detail to obtain attainable limits on masses and couplings of excited leptons at future linear colliders.

We present a set of inner boundary conditions for the numerical construction of dynamical black hole spacetimes, when employing a $3+1$ constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically motivated by the dynamical trapping horizon framework and are enforced in an elliptic subsystem of the full Einstein equation. In the stationary limit they reduce to existing isolated horizon boundary conditions. A characteristic analysis completes the discussion of inner boundary conditions for the radiative modes.

We present a method to integrate the equations of motion that govern bound, accelerated orbits in Schwarzschild spacetime. At each instant the true worldline is assumed to lie tangent to a reference geodesic, called an osculating orbit, such that the worldline evolves smoothly from one such geodesic to the next. Because a geodesic is uniquely identified by a set of constant orbital elements, the transition between osculating orbits corresponds to an evolution of the elements. In this paper we derive the evolution equations for a convenient set of orbital elements, assuming that the force acts only within the orbital plane; this is the only restriction that we impose on the formalism, and we do not assume that the force must be small. As an application of our method, we analyze the relative motion of two massive bodies, assuming that one body is much smaller than the other. Using the hybrid Schwarzschild/post-Newtonian equations of motion formulated by Kidder, Will, and Wiseman, we treat the unperturbed motion as geodesic in a Schwarzschild spacetime with a mass parameter equal to the system’s total mass. The force then consists of terms that depend on the system’s reduced mass. We highlight the importance of conservative terms in this force, which cause significant long-term changes in the time dependence and phase of the relative orbit. From our results we infer some general limitations of the radiative approximation to the gravitational self-force, which uses only the dissipative terms in the force.

We examine the motion of a charged particle in a weak gravitational field. In addition to the Newtonian gravity exerted by a large central body, the particle is subjected to an electromagnetic self-force that contains both a conservative piece and a radiation-reaction piece. This toy problem shares many of the features of the strong-field gravitational self-force problem, and it is sufficiently simple that it can be solved exactly with numerical methods, and approximately with analytical methods. We submit the equations of motion to a multiscale analysis, and we examine the roles of the conservative and radiation-reaction pieces of the self-force. We show that the radiation-reaction force drives secular changes in the orbit’s semilatus rectum and eccentricity, while the conservative force drives a secular regression of the periapsis and affects the orbital time function; neglect of the conservative term can hence give rise to an important phasing error. We next examine what might be required in the formulation of a reliable secular approximation for the orbital evolution; this would capture all secular changes in the orbit and discard all irrelevant oscillations. We conclude that such an approximation would be very difficult to formulate without prior knowledge of the exact solution.