We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new four-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this model has an infrared stable fixed point (at the one-loop level). We check that the NC QED (which is one-loop renormalizable with a usual NC parameter) remains renormalizable when the NC parameter is bifermionic, at least to the extent of one-loop diagrams with external photon legs. Our general conclusion is that bifermionic noncommutativity improves renormalizability properties of NC theories.

Quasibreathers (QB) are time-periodic solutions with weak spatial localization introduced in G. Fodor et al. in [Phys. Rev. D 74, 124003 (2006)]. QB’s provide a simple description of oscillons (very long-living spatially localized time dependent solutions). The small amplitude limit of QB’s is worked out in a large class of scalar theories with a general self-interaction potential, in $D$ spatial dimensions. It is shown that the problem of small amplitude QB’s is reduced to a universal elliptic partial differential equation. It is also found that there is the critical dimension, $D_{\mathrm{crit}}=4$, above which no small amplitude QB’s exist. The QB’s obtained this way are shown to provide very good initial data for oscillons. Thus these QB’s provide the solution of the complicated, nonlinear time dependent problem of small amplitude oscillons in scalar theories.

This paper studies two perfectly conducting parallel plates in the weak gravitational field on the surface of the Earth. Since the appropriate line element, to first order in the constant gravity acceleration $g$, is precisely of the Rindler type, we can exploit the formalism for studying Feynman Green functions in Rindler spacetime. Our analysis does not reduce the electromagnetic potential to the transverse part before quantization. It is instead fully covariant and well suited for obtaining all components of the regularized and renormalized energy-momentum tensor to arbitrary order in the gravity acceleration $g$. The general structure of the calculation is therefore elucidated, and the components of the Maxwell energy-momentum tensor are evaluated up to second order in $g$, improving a previous analysis by the authors and correcting their old first-order formula for the Casimir energy.

Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the effective one body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the “effective” Hamiltonian and the “real” one; (ii) a generalized effective Hamilton-Jacobi equation involving higher powers of the momenta; (iii) a Kerr-type effective metric (with Padé-resummed coefficients) which depends on the choice of some basic “effective spin vector” ${\mathbf{S}}_{\mathrm{eff}}$, and which is deformed by comparable-mass effects; and (iv) an additional effective spin-orbit interaction term involving another spin vector $\mathit{\sigma }$. As a first application of the new, NLO spin-dependent EOB Hamiltonian, we compute the binding energy of circular orbits (for parallel spins) as a function of the orbital frequency, and of the spin parameters. We also study the characteristics of the last stable circular orbit: binding energy, orbital frequency, and the corresponding dimensionless spin parameter ${\widehat{a}}_{\mathrm{LSO}}\equiv c{J}_{\mathrm{LSO}}/(G(H_{\mathrm{LSO}}/c^2{)}^2)$. We find that the inclusion of NLO spin-orbit terms has a significant “moderating” effect on the dynamical characteristics of the circular orbits for large and parallel spins.

According to Babichev et al., the accretion of a phantom test fluid onto a Schwarzschild black hole will induce the mass of the black hole to decrease, however the backreaction was ignored in their calculation. Using new exact solutions describing black holes in a background Friedmann-Robertson-Walker universe, we find that the physical black hole mass may instead increase due to the accretion of phantom energy. If this is the case, and the future universe is dominated by phantom dark energy, the black hole apparent horizon and the cosmic apparent horizon will eventually coincide and, after that, the black hole singularity will become naked in finite comoving time before the big rip occurs, violating the cosmic censorship conjecture.

We study the massless scalar, Dirac, and electromagnetic fields propagating on a $4D$-brane, which is embedded in higher-dimensional Gauss-Bonnet space-time. We calculate, in the time domain, the fundamental quasinormal modes of a spherically symmetric black hole for such fields. Using WKB approximation we study quasinormal modes in the large multipole limit. We observe also a universal behavior, independent on a field and value of the Gauss-Bonnet parameter, at an asymptotically late time.

We show that the factor ordering ambiguities associated with the loop quantization of the gravitational part of the cosmological Hamiltonian constraint disappear at the level of the Wheeler-DeWitt equation only for a particular choice of lattice refinement model, which coincides with constraints imposed from phenomenological and consistency arguments.

Properties of $n(\ge 5)$-dimensional static wormhole solutions are investigated in Einstein-Gauss-Bonnet gravity with or without a cosmological constant $\Lambda$. We assume that the spacetime has symmetries corresponding to the isometries of an $(n-2)$-dimensional maximally symmetric space with the sectional curvature $k=\pm 1$, 0. It is also assumed that the metric is at least $C^2$ and the $(n-2)$-dimensional maximally symmetric subspace is compact. Depending on the existence or absence of the general relativistic limit $\alpha \to 0$, solutions are classified into general relativistic (GR) and non-GR branches, respectively, where $\alpha$ is the Gauss-Bonnet coupling constant. We show that a wormhole throat respecting the dominant energy condition coincides with a branch surface in the GR branch, otherwise the null energy condition is violated there. In the non-GR branch, it is shown that there is no wormhole solution for $k\alpha \ge 0$. For the matter field with zero tangential pressure, it is also shown in the non-GR branch with $k\alpha <0$ and $\Lambda \le 0$ that the dominant energy condition holds at the wormhole throat if the radius of the throat satisfies some inequality. In the vacuum case, a fine-tuning of the coupling constants is shown to be necessary and the radius of a wormhole throat is fixed. Explicit wormhole solutions respecting the energy conditions in the whole spacetime are obtained in the vacuum and dust cases with $k=-1$ and $\alpha >0$.

The Blandford-Znajek mechanism, by which the rotational energy of a black hole is extracted through electromagnetic fields, is one of the promising candidates as an essential process of the central engine of active compact objects such as gamma-ray bursts. The only known analytical solution of this mechanism is the perturbative monopole solution for Kerr parameter $a$ up to the second order terms. In order to apply the Blandford-Znajek mechanism to rapidly rotating black holes, we try to obtain the perturbation solution up to the fourth order. As a result, we find that the fourth order terms of the vector potential diverge at infinity, and this implies that the perturbation approach breaks down at a large distance from the black hole. Although there are some uncertainties about the solution due to the unknown boundary condition at infinity for the fourth order terms, we can derive the evaluation of the total energy flux extracted from the black hole up to fourth order of $a$ without any ambiguity. Furthermore, from the comparison between the numerical solution, which is valid for $0<a<1$, and the fourth order solution, we find that the fourth order solution reproduces the numerical result better than the second order solution. At the same time, since the fourth order solution does not match well with the numerical result at large $a$, we conclude that more higher order terms are required to reproduce the numerical result.

The brick wall model is a semiclassical approach to understand the microscopic origin of black hole entropy. In this approach, the black hole geometry is assumed to be a fixed classical background on which matter fields propagate, and the entropy of black holes supposedly arises due to the canonical entropy of matter fields outside the black hole event horizon, evaluated at the Hawking temperature. Apart from certain lower dimensional cases, the density of states of the matter fields around black holes cannot be evaluated exactly. As a result, often, in the brick wall model, the density of states and the resulting canonical entropy of the matter fields are evaluated at the leading order (in terms of $\hslash$) in the WKB approximation. The success of the approach is reflected by the fact that the Bekenstein-Hawking area law—viz. that the entropy of black holes is equal to one-quarter the area of their event horizon, say, ${\mathcal{A}}_{\mathrm{H}}$—has been recovered using this model in a variety of black hole spacetimes. In this work, we compute the canonical entropy of a quantum scalar field around static and spherically symmetric black holes through the brick wall approach at the higher orders (in fact, up to the sixth order in $\hslash$) in the WKB approximation. We explicitly show that the brick wall model generally predicts corrections to the Bekenstein-Hawking entropy in all spacetime dimensions. In four dimensions, we find that the corrections to the Bekenstein-Hawking entropy are of the form $[{\mathcal{A}}_{\mathrm{H}}^n\log {\mathcal{A}}_{\mathrm{H}}]$, while, in six dimensions, the corrections behave as $[{\mathcal{A}}_{\mathrm{H}}^m+{\mathcal{A}}_{\mathrm{H}}^n\log {\mathcal{A}}_{\mathrm{H}}]$, where $(m,n)<1$. We compare our results with the corrections to the Bekenstein-Hawking entropy that have been obtained through the other approaches in the literature, and discuss the implications.

Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt-Deser-Misner formulation and is derived by the addition of combinations of the constraints and their derivatives to the right-hand side of the Arnowitt-Deser-Misner evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic—second-order parabolic. The second formulation is a parabolization of the Kidder-Scheel-Teukolsky formulation and is a manifestly mixed strongly hyperbolic—second-order-parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint-violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.

It has been pointed out by several groups that ekpyrotic and cyclic models generate significant non-Gaussianity. In this paper, we present a physically intuitive, semianalytic estimate of the bispectrum. We show that, in all such models, there is an intrinsic contribution to the non-Gaussianity parameter $f_{NL}$ that is determined by the geometric mean of the equation of state $w_{ek}$ during the ekpyrotic phase and $w_c$ during the phase that curvature perturbations are generated, and whose value is $\mathcal{O}(100)$ or more times the intrinsic value predicted by simple slow-roll inflationary models, $f_{NL}^{\mathrm{intrinsic}}=\mathcal{O}(0.1)$. Other contributions to $f_{NL}$, which we also estimate, can increase $|f_{NL}|$ but are unlikely to decrease it significantly, making non-Gaussianity a useful test of these models. Furthermore, we discuss a predicted correlation between the non-Gaussianity and scalar spectral index that sharpens the test.

Dark energy and dark matter are the dominant sources in the evolution of the late universe. They are currently only indirectly detected via their gravitational effects, and there could be a coupling between them without violating observational constraints. We investigate the background dynamics when dark energy is modeled as exponential quintessence and is coupled to dark matter via simple models of energy exchange. We introduce a new form of dark sector coupling, which leads to a more complicated dynamical phase space and has a better physical motivation than previous mathematically similar couplings.

In this work, a flat Friedmann-Robertson-Walker universe with dust and a cosmological constant is quantized. By means of a canonical transformation, the classical Hamiltonian is reduced to that of either a harmonic oscillator or anti-oscillator, depending on whether $\Lambda <0$ or $\Lambda >0$, respectively. In this way, exact solutions to the Wheeler-DeWitt equation can easily be obtained. It turns out that a positive cosmological constant alone may account for an early inflationary regime and a later accelerated expansion phase, with a period of decelerated expansion in between. This suggests that quantum-gravitational effects can influence most of the history or even the entire history of the Universe.

In recent years the goal of estimating different cosmological parameters precisely has set new challenges in the effort to accurately measure the angular power spectrum of the CMB. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel, model-independent method for the estimation of the CMB angular power spectrum solely from multifrequency observations has been proposed and implemented on the first year WMAP data by Saha et al. 2006. All previous estimates of the power spectrum of the CMB are based upon foreground templates using data sets from different experiments. However, our methodology demonstrates that the CMB angular spectrum can be reliably estimated with precision from a self-contained analysis of the WMAP data. In this work we provide a detailed description of this method. We also study and identify the biases present in our power spectrum estimate. We apply our methodology to extract the power spectrum from the WMAP data.

Ground-based gravitational wave laser interferometers (LIGO, GEO-600, Virgo, and Tama-300) have now reached high sensitivity and duty cycle. We present a Bayesian evidence-based approach to the search for gravitational waves, in particular aimed at the follow-up of candidate events generated by the analysis pipeline. We introduce and demonstrate an efficient method to compute the evidence and odds ratio between different models, and illustrate this approach using the specific case of the gravitational wave signal generated during the inspiral phase of binary systems, modeled at the leading quadrupole Newtonian order, in synthetic noise. We show that the method is effective in detecting signals at the detection threshold and it is robust against (some types of) instrumental artifacts. The computational efficiency of this method makes it scalable to the analysis of all the triggers generated by the analysis pipelines to search for coalescing binaries in surveys with ground-based interferometers, and to a whole variety of signal waveforms, characterized by a larger number of parameters.

We study the spectral index of curvature perturbations for inflationary models where the driving scalar field is coupled to a relativistic fluid through a friction term $\Gamma$. In the regime in which $\Gamma$ can be at most as large as $H$, the Hubble parameter during inflation, we find that only $\Gamma \ll H$ is allowed by observations; otherwise curvature fluctuations are generated with a spectral index $n_s$ unacceptably red. These results are obtained starting from vacuum initial conditions and are generic with respect to the inflationary potential and known dependence of the friction term on the scalar field and the energy density of the relativistic fluid. We compare our findings with previous investigations.

We study the effects of two-body Higgs boson scattering by exchanging unparticles. The unparticle contribution can change the standard model prediction for two-body Higgs boson scattering partial wave amplitude significantly leading to modification of the unitarity constraint on the standard model Higgs boson mass. For unparticle dimension $d_{\mathcal{U}}$ between 1 and 2, the unitarity constraint on the Higgs boson mass can be larger than that in the standard model. Information on unparticle interaction can also be obtained.

We carry out a detailed analysis of the general two Higgs doublet model with $CP$ violation. We describe two different parametrizations of this model, and then study the Higgs boson masses and the trilinear Higgs couplings for these two parametrizations. Within a rather general model, we find that the trilinear Higgs couplings have a significant dependence on the details of the model, even when the lightest Higgs boson mass is taken to be a fixed parameter. We include radiative corrections in the one-loop effective potential approximation in our analysis of the Higgs boson masses and the Higgs trilinear couplings. The one-loop corrections to the trilinear couplings of the two Higgs doublet model also depend significantly on the details of the model, and can be rather large. We study quantitatively the trilinear Higgs couplings, and show that these couplings are typically several times larger than the corresponding standard model trilinear Higgs coupling in some regions of the parameter space. We also briefly discuss the decoupling limit of the two Higgs doublet model.

Generic SO(10) grand unified theory models suffer from the problem that Planck scale induced nonrenormalizable proton-decay operators require extreme suppression of their couplings to be compatible with present experimental upper limits. One way to resolve this problem is to supplement SO(10) by simple gauged discrete symmetries which can also simultaneously suppress the renormalizable R-parity violating ones when they occur and make the theory “more natural.” Here we discuss the phenomenological viability of such models. We first show that for both classes of models, e.g the ones that use or to break B-L (baryon minus lepton number) symmetry, the minimal Higgs content which is sufficient for proton-decay suppression is inadequate for explaining fermion masses despite the presence of all apparently needed couplings. We then present an extended model, with three and three Higgs field, where is free of this problem. We propose this as a realistic and natural model for fermion unification and discuss the phenomenology of this model e.g. its predictions for neutrino mixings and lepton flavor violation.