We consider a relative of semidirect gauge mediation where the hidden sector exists at large ’t Hooft coupling. Such scenarios can be difficult to describe using perturbative field theory methods but may fall into the class of holographic gauge mediation scenarios, meaning that they are amenable to the techniques of gauge/gravity duality. We use a recently found gravity solution to examine one such case, where the hidden sector is a cascading gauge theory resulting in a confinement scale not much smaller than the messenger mass. In the original construction of holographic gauge mediation, as in other examples of semidirect gauge mediation at strong coupling, the primary contributions to visible sector soft terms come from weakly coupled messenger mesons. In contrast to these examples, we describe the dual of a gauge theory where there are significant contributions from scales in which the strongly coupled messenger quarks are the effective degrees of freedom. In this regime, the visible sector gaugino mass can be calculated entirely from holography.

In order to investigate the systematics of the loop expansion in high temperature gauge theories beyond the leading order hard thermal loop (HTL) approximation, we calculate the two-loop electron proper self-energy $\Sigma$ in high temperature QED. The two-loop bubble diagram of $\Sigma$ contains a linear infrared divergence. Even if regulated with a nonzero photon mass $M$ of order of the Debye mass, this infrared sensitivity implies that the two-loop self-energy contributes terms to the fermion dispersion relation that are comparable to or even larger than the next-to-leading order (NLO) contributions of the one-loop $\Sigma$. Additional evidence for the necessity of a systematic restructuring of the loop expansion comes from the explicit gauge-parameter dependence of the fermion damping rate at both one and two loops. The leading terms in the high temperature expansion of the two-loop self-energy for all topologies arise from an explicit hard-soft factorization pattern, in which one of the loop integrals is hard ($p\simeq T$), nested inside a second loop integral which is soft ($0\le p\lesssim T$ for real parts; $p\simeq eT$ for imaginary parts). There are no hard-hard contributions to the two-loop $\Sigma$ at leading order at high $T$. Provided the same factorization pattern holds for arbitrary $\ell$ loops, the NLO high temperature contributions to the electron self-energy come from $\ell -1$ hard loops factorized with one soft loop integral. This hard-soft pattern is a necessary condition for the resummation over $\ell$ to coincide with the one-loop self-energy calculated with HTL dressed propagators and vertices, and to yield the complete NLO correction to $\Sigma$ at scales $\sim eT$, which is both infrared finite and gauge invariant. We employ spectral representations and the Gaudin method for evaluating finite temperature Matsubara sums, which facilitates the analysis of multiloop diagrams at high $T$.

We study the field equations of the Plebanski action for general relativity when both the cosmological constant and an Immirzi parameter are present. We show that the Lagrange multiplier, which usually gets identified with the Weyl curvature, now acquires a trace part. Some consequences of this for a class of modified gravity theories recently proposed in the literature are briefly discussed.

We provide simple and accurate analytical expressions for the Regge poles of the Schwarzschild black hole. This is achieved by using third-order WKB approximations to solve the radial wave equations for spins 0, 1, and 2. These results permit us to obtain analytically the dispersion relation and the damping of the “surface waves” lying close to the photon sphere of the Schwarzschild black hole and which generate the weakly damped quasinormal modes of its spectrum. Our results could be helpful in order to simplify considerably the description of wave scattering from the Schwarzschild black hole as well as the analysis of the gravitational radiation created in many black hole processes. Furthermore, the existence of nonlinear dispersion relations for the photons propagating close to the photon sphere could have also important consequences in the context of gravitational lensing.

Our Universe contains a great number of extremely compact and massive objects which are generally accepted to be black holes. Precise observations of orbital motion near candidate black holes have the potential to determine if they have the spacetime structure that general relativity demands. As a means of formulating measurements to test the black hole nature of these objects, Collins and Hughes introduced “bumpy black holes”: objects that are almost, but not quite, general relativity’s black holes. The spacetimes of these objects have multipoles that deviate slightly from the black hole solution, reducing to black holes when the deviation is zero. In this paper, we extend this work in two ways. First, we show how to introduce bumps which are smoother and lead to better behaved orbits than those in the original presentation. Second, we show how to make bumpy Kerr black holes—objects which reduce to the Kerr solution when the deviation goes to zero. This greatly extends the astrophysical applicability of bumpy black holes. Using Hamilton-Jacobi techniques, we show how a spacetime’s bumps are imprinted on orbital frequencies, and thus can be determined by measurements which coherently track the orbital phase of a small orbiting body. We find that in the weak field, orbits of bumpy black holes are modified exactly as expected from a Newtonian analysis of a body with a prescribed multipolar structure, reproducing well-known results from the celestial mechanics literature. The impact of bumps on strong-field orbits is many times greater than would be predicted from a Newtonian analysis, suggesting that this framework will allow observations to set robust limits on the extent to which a spacetime’s multipoles deviate from the black hole expectation.

The metric of a nonrotating black hole deformed by a tidal interaction is calculated and expressed as an expansion in the strength of the tidal coupling. The expansion parameter is the inverse length scale ${\mathcal{R}}^{-1}$, where $\mathcal{R}$ is the radius of curvature of the external spacetime in which the black hole moves. The expansion begins at order ${\mathcal{R}}^{-2}$, and it is carried out through order ${\mathcal{R}}^{-4}$. The metric is parametrized by a number of tidal multipole moments, which specify the black hole’s tidal environment. The tidal moments are freely-specifiable functions of time that are related to the Weyl tensor of the external spacetime. At order ${\mathcal{R}}^{-2}$ the metric involves the tidal quadrupole moments ${\mathcal{E}}_{ab}$ and ${\mathcal{B}}_{ab}$. At order ${\mathcal{R}}^{-3}$ it involves the time derivative of the quadrupole moments and the tidal octupole moments ${\mathcal{E}}_{abc}$ and ${\mathcal{B}}_{abc}$. At order ${\mathcal{R}}^{-4}$ the metric involves the second time derivative of the quadrupole moments, the first time derivative of the octupole moments, the tidal hexadecapole moments ${\mathcal{E}}_{abcd}$ and ${\mathcal{B}}_{abcd}$, and bilinear combinations of the quadrupole moments. The metric is presented in a light-cone coordinate system that possesses a clear geometrical meaning: The advanced-time coordinate $v$ is constant on past light cones that converge toward the black hole; the angles $\theta$ and $\varphi$ are constant on the null generators of each light cone; and the radial coordinate $r$ is an affine parameter on each generator, which decreases as the light cones converge toward the black hole. The coordinates are well-behaved on the black-hole horizon, and they are adjusted so that the coordinate description of the horizon is the same as in the Schwarzschild geometry: $r=2M+O({\mathcal{R}}^{-5})$. At the order of accuracy maintained in this work, the horizon is a stationary null hypersurface foliated by apparent horizons; it is an isolated horizon in the sense of Ashtekar and Krishnan. As an application of our results we examine the induced geometry and dynamics of the horizon, and calculate the rate at which the black-hole surface area increases as a result of the tidal interaction.

We study the dynamical evolution of a massless scalar perturbation in the Hořava-Lifshitz black-hole spacetimes with the coupling constants $\lambda =\frac{1}{3}$, $\lambda =\frac{1}{2}$ and $\lambda =3$, respectively. Our calculation shows that, for the three cases, the scalar perturbations decay without any oscillation in which the decay rate imprints the parameter of the Hořava-Lifshitz black hole. The results are quite different from those in the Schwarzschild AdS black hole and can help us understand more about the Hořava-Lifshitz gravity.

We investigate the effect of the intrinsic spin of a fundamental spinor field on the surrounding spacetime geometry. We show that despite the lack of a rotating stress-energy source (and despite claims to the contrary) the intrinsic spin of a spin-half fermion gives rise to a frame-dragging effect analogous to that of orbital angular momentum, even in Einstein-Hilbert gravity where torsion is constrained to be zero. This resolves a paradox regarding the counter-force needed to restore Newton’s third law in the well-known spin-orbit interaction. In addition, the frame-dragging effect gives rise to a long-range gravitationally mediated spin-spin dipole interaction coupling the internal spins of two sources. We argue that despite the weakness of the interaction, the spin-spin interaction will dominate over the ordinary inverse square Newtonian interaction in any process of sufficiently high energy for quantum field theoretical effects to be non-negligible.

The concordance model of cosmology contains several unknown components such as dark matter and dark energy. Many proposals have been made to describe them by choosing an appropriate potential for a scalar field. We study four models in the realm of loop quantum cosmology: the Chaplygin gas, an inflationary and radiationlike potential, quintessence and an anti-Chaplygin gas. For the latter we show that all trajectories start and end with a type II singularity and, depending on the initial value, may go through a bounce. On the other hand the evolution under the influence of the first three scalar fields behaves classically at times far away from the big bang singularity and bounces as the energy density approaches the critical density.

The dynamics of branelike extended objects in spacetimes with torsion is derived from the conservation equations of stress-energy and spin tensors. Thus obtained world-sheet equations are applied to macroscopic test membranes made of spinning matter. Specifically, we consider membranes with maximally symmetric distribution of stress energy and spin. These are characterized by two constants only: the tension and spin magnitude. By solving the world-sheet equations, we discover a similarity between such membranes in Riemann-Cartan backgrounds, and string theory membranes in low-energy string backgrounds. In the second part of the paper, we apply this result to cylindrical membranes wrapped around the extra compact dimension of a ($D+1$)-dimensional spacetime. In the narrow membrane limit, we discover how effective macroscopic strings couple to torsion. An observed similarity with the string sigma model is noted.

A Hamiltonian description of the $N=1$ supergravity theory containing the topological Nieh-Yan term in its Lagrangian density is developed. The constraints are analyzed without choosing any gauge. In the time gauge, this theory results in a real $SU(2)$ formulation.

We construct a cosmological model of late acceleration based on the new agegraphic dark energy model in the framework of Brans-Dicke cosmology where the new agegraphic energy density ${\rho }_D=3n^2{m}_p^2/{\eta }^2$ is replaced with ${\rho }_D=3n^2{\varphi }^2/(4\omega {\eta }^2)$. We show that the combination of the Brans-Dicke field and agegraphic dark energy can accommodate a $w_D=-1$ crossing for the equation of state of noninteracting dark energy. When an interaction between dark energy and dark matter is taken into account, the transition of $w_D$ to the phantom regime can be more easily accounted for than when we resort to the Einstein field equations. In the limiting case $\alpha =0$ ($\omega \to \infty$), all previous results of the new agegraphic dark energy in Einstein gravity are restored.

We generalize the renormalized perturbation theory (RPT) formalism of Crocce and Scoccimarro [M. Crocce and R. Scoccimarro, Phys. Rev. D 73, 063519 (2006)] to deal with multiple fluids in the Universe and here we present the complete calculations up to the one-loop level in the RPT. We apply this approach to the problem of following the nonlinear evolution of baryon and cold dark matter (CDM) perturbations, evolving from the distinct sets of initial conditions, from the high redshift post-recombination Universe right through to the present day. In current theoretical and numerical models of structure formation, it is standard practice to treat baryons and CDM as an effective single matter fluid—the so-called dark matter only modeling. In this approximation, one uses a weighed sum of late-time baryon and CDM transfer functions to set initial mass fluctuations. In this paper we explore whether this approach can be employed for high precision modeling of structure formation. We show that, even if we only follow the linear evolution, there is a large-scale scale-dependent bias between baryons and CDM for the currently favored WMAP5 $\Lambda \mathrm{CDM}$ model. This time evolving bias is significant ($>1\%$) until the present day, when it is driven towards unity through gravitational relaxation processes. Using the RPT formalism we test this approximation in the nonlinear regime. We show that the nonlinear CDM power spectrum in the two-component fluid differs from that obtained from an effective mean-mass one-component fluid by $\sim 3\%$ on scales of order $k\sim 0.05h{\mathrm{Mpc}}^{-1}$ at $z=10$, and by $\sim 0.5\%$ at $z=0$. However, for the case of the nonlinear evolution of the baryons the situation is worse and we find that the power spectrum is suppressed, relative to the total matter, by $\sim 15\%$ on scales $k\sim 0.05h{\mathrm{Mpc}}^{-1}$ at $z=10$, and by $\sim 3\%–5\%$ at $z=0$. Importantly, besides the suppression of the spectrum, the baryonic acoustic oscillation (BAO) features are amplified for baryon and slightly damped for CDM spectra. If we compare the total matter power spectra in the two- and one-component fluid approaches, then we find excellent agreement, with deviations being $<0.5\%$ throughout the evolution. Consequences: high precision modeling of the large-scale distribution of baryons in the Universe cannot be achieved through an effective mean-mass one-component fluid approximation; detection significance of BAO will be amplified in probes that study baryonic matter, relative to probes that study the CDM or total mass only. The CDM distribution can be modeled accurately at late times and the total matter at all times. This is good news for probes that are sensitive to the total mass, such as gravitational weak lensing as existing modeling techniques are good enough. Lastly, we identify an analytic approximation that greatly simplifies the evaluation of the full PT expressions, and it is better than $<1\%$ over the full range of scales and times considered.

There exist consistent low energy effective field theories describing gravity in the Higgs phase that allow the coexistence of massive gravitons and the conventional $1/r$ potential of gravity. In an effort to constrain the value of the graviton mass in these theories, we study the tensor contribution to the CMB temperature anisotropy and polarization spectra in the presence of a nonvanishing graviton mass. We find that the observation of a $B$-mode signal consistent with the spectrum predicted by inflationary models would provide the strongest limit yet on the mass of an elementary particle—a graviton—at a level of $m\lesssim {10}^{-30}\mathrm{eV}\approx (10\mathrm{Mpc}{)}^{-1}$. We also find that a graviton mass in the range between $(10\mathrm{Mpc}{)}^{-1}$ and $(10\mathrm{kpc}{)}^{-1}$ leads to interesting modifications of the polarization spectrum. The characteristic signature of a graviton mass in this range would be a plateau in the $B$-mode spectrum up to angular multipoles of $\ell \sim 100$. For even larger values of the graviton mass the tensor contribution to the CMB spectra becomes strongly suppressed.

We consider the particle creation process associated with a quantum field $\chi$ in a time-dependent, homogeneous and isotropic, classical background. It is shown that the field square ${\chi }^2$, the energy density, and the pressure of the created particles have large fluctuations comparable to their vacuum expectation values. Possible effects of these fluctuations on the reheating process after inflation are discussed. After determining the correlation length of the fluctuations in two different models, corresponding to the decay in the parametric resonance regime and in the perturbation theory, it is found that these fluctuations should be taken into account in the final thermalization process, in the backreaction effects, and when the formation of primordial black holes is considered. In both models, by comparing quantum and thermal fluctuations with each other it is observed that very quick thermalization after the complete inflaton decay is not always possible even when the interaction rates are large. On the other hand, when the backreaction effects are included during the preheating stage, the coherence of the inflaton oscillations is shown to be lost because of the fluctuations in ${\chi }^2$. Finally, we note that a large fluctuation in the energy density may cause a black hole to form, and we determine the fraction of total energy density that goes into such primordial black holes in the model of preheating we consider.

The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst potential is considered. The coupling between the nonlocal curvature content of the spacetime as encoded in the Weyl tensor, and the existence of a Killing tensor is explored and a constructive, algebraic test for a fourth-order Killing tensor suggested. The approach used exploits the variables defined for the Bäcklund transformations to clarify the relationship between Weyl curvature, constants of geodesic motion, expressed as Killing tensors, and the solution-generation techniques. A new symmetric noncovariant formulation of the Killing equations is given. This formulation transforms the problem of looking for fourth-order Killing tensors in 4D into one of looking for four interlocking two-manifolds admitting fourth-order Killing tensors in 2D.

This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture of what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing tensors.

We propose a holographic description of four-dimensional single-scalar inflationary universes, and show how cosmological observables, such as the primordial power spectrum, are encoded in the correlation functions of a three-dimensional quantum field theory (QFT). The holographic description correctly reproduces standard inflationary predictions in the regime where a perturbative quantization of fluctuations is justified. In the opposite regime, wherein gravity is strongly coupled at early times, we propose a holographic description in terms of perturbative large $N$ QFT. Initiating a holographic phenomenological approach, we show that models containing only two parameters, $N$ and a dimensionful coupling constant, are capable of satisfying the current observational constraints.

Accumulation of electrical charge on the end mirrors of gravitational-wave observatories can become a source of noise limiting the sensitivity of such detectors through electronic couplings to nearby surfaces. Torsion balances provide an ideal means for testing gravitational-wave technologies due to their high sensitivity to small forces. Our torsion pendulum apparatus consists of a movable plate brought near a plate pendulum suspended from a nonconducting quartz fiber. A UV LED located near the pendulum photoejects electrons from the surface, and a UV LED driven electron gun directs photoelectrons towards the pendulum surface. We have demonstrated both charging and discharging of the pendulum with equivalent charging rates of $\sim {10}^{5}e/\mathrm{s}$, as well as spectral measurements of the pendulum charge resulting in a white noise level equivalent to $3\times {10}^{5}e/\sqrt{\mathrm{Hz}}$.

We study the radiative electroweak symmetry breaking and the relic abundance of neutralino dark matter in the supersymmetric type I seesaw model. In this model, there exist threshold corrections to Higgs bilinear terms coming from heavy singlet sneutrino loops, which make the soft supersymmetry breaking (SSB) mass for up-type Higgs shift at the seesaw scale and thus a minimization condition for the Higgs potential is affected. We show that the required fine-tuning between the Higgsino mass parameter $\mu$ and the SSB mass for up-type Higgs may be reduced at the electroweak scale, due to the threshold corrections. We also present how the parameter $\mu$ depends on the SSB $B$-parameter for heavy singlet sneutrinos. Since the property of neutralino dark matter is quite sensitive to the size of $\mu$, we discuss how the relic abundance of neutralino dark matter is affected by the SSB $B$-parameter. Taking the SSB $B$-parameter of order of a few hundreds TeV, the required relic abundance of neutralino dark matter can be correctly achieved. In this case, dark matter is a mixture of bino and Higgsino, under the condition that gaugino masses are universal at the grand unification scale.