Using gauge/gravity duality, we compute the energy density and angular distribution of the power radiated by a quark undergoing circular motion in strongly coupled $\mathcal{N}=4$ supersymmetric Yang-Mills theory. We compare the strong coupling results to those at weak coupling, finding them to be very similar. In both regimes, the angular distribution of the radiated power is in fact similar to that of synchrotron radiation produced by an electron in circular motion in classical electrodynamics: the quark emits radiation in a narrow beam along its velocity vector with a characteristic opening angle $\alpha \sim 1/\gamma$. To an observer far away from the quark, the emitted radiation appears as a short periodic burst, just like the light from a lighthouse does to a ship at sea. Our strong coupling results are valid for any strongly coupled conformal field theory with a dual classical gravity description.

Supersymmetric renormalization group flow equations for the effective superpotential of the three-dimensional Wess-Zumino model are derived at zero and non-zero temperature. This model with fermions and bosons interacting via a Yukawa term possesses a supersymmetric analogue of the Wilson-Fisher fixed-point. At zero temperature we determine the phase-transition line in coupling-constant space separating the supersymmetric from the nonsupersymmetric phase. At finite temperature we encounter dimensional reduction from 3 to 2 dimensions in the infrared regime. We determine the finite-temperature phase diagram for the restoration of the global ${\mathbb{Z}}_2$-symmetry and show that for temperatures above the ${\mathbb{Z}}_2$ phase transition the pressure obeys the Stefan-Boltzmann law of a gas of massless bosons in $2+1$ dimensions.

We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the $3+1$ formalism for hyperbolic partial differential equations on a given background. Our approach is based on compactification at null infinity in hyperboloidal scri fixing coordinates. We report numerical tests for the particular example of a scalar wave equation on Minkowski and Schwarzschild backgrounds. We address issues related to the implementation of the hyperboloidal approach for the Einstein equations, such as nonlinear source functions, matching, and evaluation of formally singular terms at null infinity.

Much of the progress in the gravitational self-force problem has involved the use of singular perturbation techniques. Yet the formalism underlying these techniques is not widely known. I remedy this situation by explicating the foundations and geometrical structure of singular perturbation theory in general relativity. Within that context, I sketch precise formulations of the methods used in the self-force problem: dual expansions (including matched asymptotic expansions), for which I identify precise matching conditions, one of which is a weak condition arising only when multiple coordinate systems are used; multiscale expansions, for which I provide a covariant formulation; and a self-consistent expansion with a fixed worldline, for which I provide a precise statement of the exact problem and its approximation. I then present a detailed analysis of matched asymptotic expansions as they have been utilized in calculating the self-force. Typically, the method has relied on a weak matching condition, which I show cannot determine a unique equation of motion. I formulate a refined condition that is sufficient to determine such an equation. However, I conclude that the method yields significantly weaker results than do alternative methods.

We present a unified framework for the study of late time cosmic acceleration. Using methods of effective field theory, we show that existing proposals for late time acceleration can be subsumed in a single framework, rather than many compartmentalized theories. We construct the most general action consistent with symmetry principles, derive the background and perturbation evolution equations, and demonstrate that for special choices of our parameters we can reproduce results already existing in the literature. Lastly, we lay the foundation for future work placing phenomenological constraints on the parameters of the effective theory. Although in this paper we focus on late time acceleration, our construction also generalizes the effective field theory of inflation to the scalar-tensor and multifield case for perturbatively constructed backgrounds.

We investigate static and dynamical $n(\ge 6)$-dimensional black holes in Einstein-Gauss-Bonnet gravity of which horizons have the isometries of an ($n-2$)-dimensional Einstein space with a condition on its Weyl tensor originally given by Dotti and Gleiser. Defining a generalized Misner-Sharp quasilocal mass that satisfies the unified first law, we show that most of the properties of the quasilocal mass and the trapping horizon are shared with the case with horizons of constant curvature. It is shown that the Dotti-Gleiser solution is the unique vacuum solution if the warp factor on the ($n-2$)-dimensional Einstein space is nonconstant. The quasilocal mass becomes constant for the Dotti-Gleiser black hole and satisfies the first law of the black-hole thermodynamics with its Wald entropy. In the non-negative curvature case with positive Gauss-Bonnet constant and zero cosmological constant, it is shown that the Dotti-Gleiser black hole is thermodynamically unstable. Even if it becomes locally stable for the nonzero cosmological constant, it cannot be globally stable for the positive cosmological constant.

Starting from the definition of entropy used in statistical mechanics we show that it is proportional to the gravity action. For a stationary black hole this entropy is expressed as $S=E/2T$, where $T$ is the Hawking temperature and $E$ is shown to be the Komar energy. This relation is also compatible with the generalized Smarr formula for mass.

By detecting gravitational wave signals from extreme mass ratio inspiraling sources (EMRIs) we will be given the opportunity to check our theoretical expectations regarding the nature of supermassive bodies that inhabit the central regions of galaxies. We have explored some qualitatively new features that a perturbed Kerr metric induces in its geodesic orbits. Since a generic perturbed Kerr metric does not possess all the special symmetries of a Kerr metric, the geodesic equations in the former case are described by a slightly nonintegrable Hamiltonian system. According to the Poincaré-Birkhoff theorem, this causes the appearance of the so-called Birkhoff chains of islands on the corresponding surfaces of section in between the anticipated KAM curves of the integrable Kerr case, whenever the intrinsic frequencies of the system are at resonance. The chains of islands are characterized by finite width, i.e. there is a finite range of initial conditions that correspond to a particular resonance and consequently to a constant rational ratio of intrinsic frequencies. Thus while the EMRI changes adiabatically by radiating energy and angular momentum, by monitoring the frequencies of a signal we can look for a transient pattern, in the form of a plateau, in the evolution of their ratio. We have shown that such a plateau is anticipated to be apparent in a quite large fraction of possible orbital characteristics if the central gravitating source is not a Kerr black hole. Moreover, the plateau in the ratio of frequencies is expected to be more prominent at specific rational values that correspond to the strongest resonances. This gives a possible observational detection of such non-Kerr exotic objects.

The averaged null energy condition has known violations for quantum fields in curved space, even when one considers only achronal geodesics. Many such examples involve rapid variation in the stress-energy tensor in the vicinity of the geodesic under consideration, giving rise to the possibility that averaging in additional dimensions would yield a principle universally obeyed by quantum fields. However, after discussing various procedures for additional averaging, including integrating over all dimensions of the manifold, we give here a class of examples that violate any such averaged condition.

The Wightman function and the vacuum expectation values of the field squared and of the energy-momentum tensor are obtained, for a massive scalar field with an arbitrary curvature coupling parameter, in the region between two infinite parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. For the calculation, a mode-summation method is used, supplemented with a variant of the generalized Abel-Plana formula. This allows one to explicitly extract the contributions to the expectation values, which come from each single boundary, and to expand the second-plate-induced part in terms of exponentially convergent integrals. Several limiting cases of interest are then studied. Moreover, the Casimir forces acting on the plates are evaluated, and it is shown that the curvature of the background spacetime decisively influences the behavior of these forces at separations larger than the curvature scale of de Sitter spacetime. In terms of the curvature coupling parameter and the mass of the field, two very different regimes are realized, which exhibit monotonic and oscillatory behavior of the vacuum expectation values, respectively. The decay of the Casimir force at large plate separation is shown to be power law (monotonic or oscillating), with independence of the value of the field mass.

We study a gravitational model with curvature-squared $R^2$ and curvature-quartic $R^4$ nonlinearities. The effective scalar degree of freedom $\varphi$ (the scalaron) has a multivalued potential $U(\varphi )$ consisting of a number of branches. These branches are fitted with each other in the branching and monotonic points. In the case of four-dimensional space-time, we show that the monotonic points are penetrable for the scalaron, while in the vicinity of the branching points, the scalaron has the bouncing behavior and cannot cross these points. Moreover, there are branching points where the scalaron bounces an infinite number of times with decreasing amplitude, and the Universe asymptotically approaches the de Sitter stage. Such accelerating behavior we call bouncing inflation. For this accelerating expansion, there is no need for original potential $U(\varphi )$ to have a minimum or to check the slow-roll conditions. A necessary condition for such inflation is the existence of the branching points. This is a new type of inflation. We show that bouncing inflation takes place both in the Einstein and Brans-Dicke frames.

We compute here the spin-orbit and spin-spin couplings needed for an accurate computation of the phasing of gravitational waves emitted by comparable-mass binaries on eccentric orbits at the second post-Newtonian (PN) order. We use a quasi-Keplerian parametrization of the orbit free of divergencies in the zero-eccentricity limit. We find that spin-spin couplings induce a residual eccentricity for coalescing binaries at 2PN, of the order of ${10}^{-4}–{10}^{-3}$ for supermassive black hole binaries in the LISA band. Spin-orbit precession also induces a nontrivial pattern in the evolution of the eccentricity, which could help to reduce the errors on the determination of the eccentricity and spins in a gravitational wave measurement.

Cosmic (super)string loops emit moduli as they oscillate under the effect of their tension. Abundance of such moduli is constrained by diffuse gamma ray background, dark matter, and primordial element abundances if their lifetime is of the order of the relevant cosmic time. It is shown that the constraints on string tension $G\mu$ and modulus mass $m$ are significantly relaxed for moduli coupling to matter stronger than gravitational strength which appears to be quite generic in large volume and warped compactification scenarios in string theory. It is also shown that thermal production of strongly coupled moduli is not efficient, hence free from constraints. In particular, the strongly coupled moduli in warped and large volume compactification scenarios and the radial modulus in the Randall-Sundrum model are found to be free from the constraints when their coupling constant is sufficiently large.

We analyze the dynamics of a Dirac-Born-Infeld (DBI) field in a cosmological setup which includes a perfect fluid. Introducing convenient dynamical variables, we show that the evolution equations form an autonomous system when the potential and the brane tension of the DBI field are arbitrary power law or exponential functions of the DBI field. In particular we find scaling solutions can exist when powers of the field in the potential and warp factor satisfy specific relations. A new class of fixed-point solutions are obtained corresponding to points which initially appear singular in the evolution equations, but on closer inspection are actually well defined. In all cases, we perform a phase-space analysis and obtain the late-time attractor structure of the system. Of particular note when considering cosmological perturbations in DBI inflation is a fixed-point solution where the Lorentz factor is a finite large constant and the equation of state parameter of the DBI field is $w=-1$. Since in this case the speed of sound $c_s$ becomes constant, the solution can be thought to serve as a good background to perturb about.

We perform direct numerical simulations of forced and freely decaying 3D magnetohydrodynamic turbulence in order to model magnetic field evolution during cosmological phase transitions in the early Universe. Our approach assumes the existence of a magnetic field generated either by a process during inflation or shortly thereafter, or by bubble collisions during a phase transition. We show that the final configuration of the magnetic field depends on the initial conditions, while the velocity field is nearly independent of initial conditions.

Motivated by Pierre Auger Observatory results favoring a heavy nuclear composition for ultrahigh-energy (UHE) cosmic rays, we investigate implications for the cumulative neutrino background. The requirement that nuclei not be photodisintegrated constrains their interactions in sources, therefore limiting neutrino production via photomeson interactions. Assuming a $d{N}_{\mathrm{CR}}/d{E}_{\mathrm{CR}}\propto E_{\mathrm{CR}}^{-2}$ injection spectrum and photodisintegration via the giant dipole resonance, the background flux of neutrinos is lower than $E_{\nu }^2{\Phi }_{\nu }\sim {10}^{-9}\mathrm{GeV}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$ if UHE nuclei ubiquitously survive in their sources. This is smaller than the analogous Waxman-Bahcall flux for UHE protons by about 1 order of magnitude and is below the projected IceCube sensitivity. If IceCube detects a neutrino background, it could be due to other sources, e.g., hadronuclear interactions of lower-energy cosmic rays; if it does not, this supports our strong restrictions on the properties of sources of UHE nuclei.

We obtain in closed form the probability distribution for individual measurements of the stress-energy tensor of two-dimensional conformal field theory in the vacuum state, smeared in time against a Gaussian test function. The result is a shifted gamma distribution with the shift given by the previously known optimal quantum inequality bound. For small values of the central charge it is overwhelmingly likely that individual measurements of the sampled energy density in the vacuum give negative results. For the case of a single massless scalar field, the probability of finding a negative value is 84%. We also report on computations for four-dimensional massless scalar fields showing that the probability distribution of the smeared square field is also a shifted gamma distribution, but that the distribution of the energy density is not.

We study the formation and detection at the next linear $e^{+}{e}^{-}$ collider of bound states of level-1 quark Kaluza-Klein excitations ${\mathcal{B}}_{\mathrm{KK}}$ within a scenario of universal extra dimensions. The interactions of such Kaluza-Klein excitations are modeled by an ${\alpha }_s$ driven Coulomb potential. In order to obtain the threshold cross section, we employ the Green function method which is known to properly describe the peaks below threshold and to yield a net increase in the continuum region (above threshold) relative to the naive Born cross section. We study such effect at different values of the scale ($R^{-1}$) of the extra dimensions with an explicit calculation for the mass spectrum as given by radiative corrections. The overall effect is roughly 2.7 at $R^{-1}=300\mathrm{GeV}$ and goes down to 2.2 at $R^{-1}=1000\mathrm{GeV}$ and a relatively large number of events is expected from $N_{\mathrm{events}}\approx 2.5\times {10}^4$ at $R^{-1}=300\mathrm{GeV}$ down to $N_{\mathrm{events}}\approx {10}^3$ at $R^{-1}=1000\mathrm{GeV}$ at the anticipated annual integrated luminosity of $L_0=100{\mathrm{fb}}^{-1}$. We finally discuss some potentially observable signatures such as the multilepton channels $2\mathrm{j}+2\ell +\mathrm{E̸}$ and $2\mathrm{j}+4\ell +\mathrm{E̸}$ for which we estimate statistical significance $\gtrsim 2$ for $R^{-1}$ up to $600\sim 700\mathrm{GeV}$.

The effects of “quark sea” in determining the flavor structure of the octet baryons have been investigated in the chiral constituent quark model ($\chi \mathrm{CQM}$). The $\chi \mathrm{CQM}$ is able to qualitatively generate the requisite amount of quark sea and is also known to provide a satisfactory explanation of the proton spin and related issues in the nonperturbative regime. The Bjorken scaling variable $x$ has been included phenomenologically in the sea quark distribution functions to understand its implications on the quark sea asymmetries like $\overline{d}(x)-\overline{u}(x)$, $\overline{d}(x)/\overline{u}(x)$, and Gottfried integral for the octet baryons. The results strengthen the importance of quark sea at lower values of $x$.

A chiral field theory of $0^{-+}$ glueball is presented. The Lagrangian of this theory is constructed by adding a $0^{-+}$ glueball field to a successful Lagrangian of the chiral field theory of pseudoscalar, vector, and axial-vector mesons. The couplings between the pseodoscalar glueball field and the mesons are revealed via a U(1) anomaly. Quantitative study of the physical processes of the $0^{-+}$ glueball of $m=1.405\mathrm{GeV}$ is presented. The theoretical predictions can be used to identify the $0^{-+}$ glueball.