We take advantage of the fact that, in $\lambda {\phi }^4$ problems, a large field cutoff ${\phi }_{\max }$ makes a perturbative series converge toward values exponentially close to the exact values to make optimal choices of ${\phi }_{\max }.$ For a perturbative series terminated at even order, it is in principle possible to adjust ${\phi }_{\max }$ in order to obtain the exact result. For a perturbative series terminated at odd order, the error can only be minimized. It is, however, possible to introduce a mass shift $m^2\to m^2(1+\eta )$ in order to obtain the exact result. We discuss weak and strong coupling methods to determine ${\phi }_{\max }$ and $\eta .$ The numerical calculations in this article are performed with a simple integral with one variable. We give arguments indicating that the qualitative features observed should extend to quantum mechanics and quantum field theory. We find that optimization at even order is more efficient than optimization at odd order. We compare our methods with the linear $\delta$ expansion (LDE) (combined with the principle of minimal sensitivity), which provides an upper envelope for the accuracy curves of various Padé and Padé-Borel approximants. Our optimization method performs better than the LDE at strong and intermediate coupling, but not at weak coupling, where it appears less robust and subject to further improvements. We also show that it is possible to fix the arbitrary parameter appearing in the LDE using the strong coupling expansion, in order to get accuracies comparable to ours.

The evidence for the accelerated expansion of the Universe and the time dependence of the fine-structure constant suggests the existence of at least one scalar field with a mass of order $H_0.$ If such a field exists, then it is generally assumed that its coupling to matter must be tuned to unnaturally small values in order to satisfy the tests of the equivalence principle (EP). In this paper, we present an alternative explanation which allows scalar fields to evolve cosmologically while having couplings to matter of order unity. In our scenario, the mass of the fields depends on the local matter density: the interaction range is typically of order 1 mm on Earth (where the density is high) and of order $10–{10}^4\mathrm{AU}$ in the solar system (where the density is low). All current bounds from tests of general relativity are satisfied. Nevertheless, we predict that near-future experiments that will test gravity in space will measure an effective Newton’s constant different by order unity from that on Earth, as well as EP violations stronger than currently allowed by laboratory experiments. Such outcomes would constitute a smoking gun for our scenario.

We numerically solve the inhomogeneous Zerilli-Moncrief and Regge-Wheeler equations in the time domain. We obtain the gravitational waveforms produced by a point particle of mass $\mu$ traveling around a Schwarzschild black hole of mass M on arbitrary bound and unbound orbits. Fluxes of energy and angular momentum at infinity and the event horizon are also calculated. Results for circular orbits, selected cases of eccentric orbits, and parabolic orbits are presented. The numerical results from the time-domain code indicate that, for all three types of orbital motion, black hole absorption contributes less than 1% of the total flux, so long as the orbital radius $r_p\mathrm{}\left(t\right)\mathrm{}$ satisfies $r_p\mathrm{}\left(t\right)>5M$ at all times.

We introduce two classes of rotating solutions of Einstein-Maxwell gravity in $n+1\mathrm{}$ dimensions which are asymptotically anti–de Sitter type. They have no curvature singularity and no horizons. The first class of solutions, which has a conic singularity, yields a spacetime with a longitudinal magnetic field and k rotation parameters. We show that when one or more of the rotation parameters are nonzero, the spinning brane has a net electric charge that is proportional to the magnitude of the rotation parameters. The second class of solutions yields a spacetime with an angular magnetic field and $\kappa$ boost parameters. We find that the net electric charge of these traveling branes with one or more nonzero boost parameters is proportional to the magnitude of the velocity of the brane. We also use the counterterm method inspired by AdS conformal field theory correspondence and calculate the conserved quantities of the solutions. We show that the logarithmic divergencies associated with the Weyl anomalies and matter field are zero, and the r divergence of the action can be removed by the counterterm method.

We calculate the vacuum expectation value of the stress-energy tensor for a quantized bulk scalar field in the Randall-Sundrum model and discuss the consequences of its local behavior for the self-consistency of the model. We find that, in general, the stress-energy tensor diverges in the vicinity of the branes. Our main conclusion is that the stress-energy tensor is sufficiently complicated that it has implications for the effective potential, or radion stabilization, methods that have so far been used.

We examine analytically a cosmological black hole domain wall system. Using the C-metric construction we derive the metric for the spacetime describing an infinitely thin wall intersecting a cosmological black hole. We study the behavior of the scalar field describing a self-interacting cosmological domain wall and find an approximated solution valid for large distances. The thin wall approximation and the back reaction problem are elaborated by finding that the topological kink solution smoothed out singular behavior of the zero thickness wall using a core topological and hence thick domain wall. We also analyze the nucleation of cosmological black holes on and in the presence of a domain walls and conclude that the domain wall will nucleate small black holes on it rather than large ones inside.

We investigate scalar perturbations from inflation in braneworld cosmologies with extra dimensions. For this we calculate scalar metric fluctuations around five dimensional warped geometry with four dimensional de Sitter slices. The background metric is determined self-consistently by the (arbitrary) bulk scalar field potential, supplemented by the boundary conditions at both orbifold branes. Assuming that the inflating branes are stabilized (by the brane scalar field potentials), we estimate the lowest eigenvalue of the scalar fluctuations—the radion mass. In the limit of flat branes, we reproduce well known estimates of the positive radion mass for stabilized branes. Surprisingly, however, we found that for de Sitter (inflating) branes the square of the radion mass is typically negative, which leads to a strong tachyonic instability. Thus, parameters of stabilized inflating braneworlds must be constrained to avoid this tachyonic instability. Instability of “stabilized” de Sitter branes is confirmed by the BRANECODE numerical calculations of Martin, Felder, Frolov, Peloso, and Kofman. If the model’s parameters are such that the radion mass is smaller than the Hubble parameter, we encounter a new mechanism of generation of primordial scalar fluctuations, which have a scale free spectrum and acceptable amplitude.

It is expected that the realization of a convergent and long-term stable numerical code for the simulation of a black hole inspiral collision will depend greatly upon the construction of stable algorithms capable of handling smooth and, most likely, time dependent boundaries. After deriving single grid, energy conserving discretizations for axisymmetric systems containing the axis of symmetry, we present a new excision method for moving black holes using multiple overlapping coordinate patches, such that each boundary is fixed with respect to at least one coordinate system. This multiple coordinate structure eliminates all need for extrapolation, a commonly used procedure for moving boundaries in numerical relativity. We demonstrate this excision method by evolving a massless Klein-Gordon scalar field around a boosted Schwarzschild black hole in axisymmetry. The excision boundary is defined by a spherical coordinate system comoving with the black hole. Our numerical experiments indicate that arbitrarily high boost velocities can be used without observing any sign of instability.

The Newman-Penrose formalism is used to derive the Teukolsky master equations controlling massless scalar, neutrino, electromagnetic, gravitino, and gravitational field perturbations of the Kerr–de Sitter spacetime. Then the quantum entropy of a nonextreme Kerr–de Sitter black hole due to arbitrary spin fields is calculated by the improved thin-layer brick wall model. It is shown that the subleading order contribution to the entropy is dependent on the square of the spins of particles and that of the specific angular momentum of black holes as well as the cosmological constant. The logarithmic correction of the spins of particles to the entropy relies on the rotation of the black hole and the effect of the cosmological constant.

We study the formation of domain walls in a phase transition in which an $S_5\times Z_2$ symmetry is spontaneously broken to $S_3\times S_2.$ In one compact spatial dimension we observe the formation of a stable domain wall lattice. In two spatial dimensions we find that the walls form a network with junctions, there being six walls to every junction. The network of domain walls evolves so that junctions annihilate antijunctions. The final state of the evolution depends on the relative dimensions of the simulation domain. In particular we never observe the formation of a stable lattice of domain walls for the case of a square domain but we do observe a lattice if one dimension is somewhat smaller than the other. During the evolution, the total wall length in the network decays with time as $t^{-0.71},$ as opposed to the usual $t^{-1}$ scaling typical of regular $Z_2$ networks.

Under the hypothesis of a dark matter composed by supersymmetric particles such as neutralinos, we investigate the possibility that their annihilation in the halos of nearby galaxies could produce detectable fluxes of $\gamma$ photons. Expected fluxes depend on several, poorly known quantities such as the density profiles of dark matter halos, the existence and prominence of central density cusps and the presence of a population of subhalos. We find that, for all reasonable choices of dark matter halo models, the intensity of the γ-ray flux from some of the nearest extragalactic objects, such as M31, is comparable to or higher than the diffuse galactic foreground. We show that next generation ground-based experiments could have the sensitivity to reveal such fluxes which could help us to unveil the nature of dark matter particles.

We investigate braneworld cosmology based on the D-brane initiated in our previous paper. The brane is described by a Born-Infeld action and the gauge field is contained. The higher order corrections of an inverse string tension will be addressed. The results obtained by the truncated argument are altered by the higher order corrections. The equation of state of the gauge field on the brane is radiationlike in low energy scales and almost dustlike fluid in high energy scales. Our model is, however, limited below a critical finite value of the energy density. For the description of the full history of our Universe the presence of an S-brane might be essential.

Gravity waves (GWs) in the early Universe generate B-type polarization in the cosmic microwave background (CMB), which can be used as a direct way to measure the energy scale of inflation. Gravitational lensing contaminates the GW signal by converting the dominant E polarization into B polarization. By reconstructing the lensing potential from the CMB itself one can decontaminate the B mode induced by lensing. We present results of numerical simulations of B mode delensing using quadratic and iterative maximum-likelihood lensing reconstruction methods as a function of detector noise and beam. In our simulations we find that the quadratic method can reduce the lensing B noise power by up to a factor of 7, close to the no noise limit. In contrast, the iterative method shows significant improvements even at the lowest noise levels we tested. We demonstrate explicitly that with this method at least a factor of 40 noise power reduction in lensing induced B power is possible, suggesting that ${r=P}_h{/P}_R\sim {10}^{-6}$ may be achievable in the absence of sky cuts, foregrounds, and instrumental systematics. While we do not find any fundamental lower limit due to lensing, we find that for high-sensitivity detectors residual lensing noise dominates over the detector noise.

We study the physical limitations placed on cosmic microwave background (CMB) temperature and polarization measurements of the initial power spectrum. These limitations include geometric projection, acoustic physics, gravitational lensing and degeneracies with cosmological parameters. Detailed information on the spectrum is greatly assisted by polarization information and localized to the acoustic regime $k=0.02\mathrm{}-0.2{\mathrm{Mpc}}^{-1}$ with a fundamental resolution of $\Delta k/k>\mathrm{}\mathrm{0.05.}\mathrm{}$ From this study we construct principal component based statistics, which are orthogonal to cosmological parameters including the initial amplitude and tilt of the spectrum, that best probe deviations from scale-free initial conditions. These statistics resemble Fourier modes confined to the acoustic regime and ultimately can yield $\sim 50$ independent measurements of the power spectrum features to percent level precision. They are straightforwardly related to more traditional parametrizations, such as the running of the tilt, and in the future can provide many statistically independent measurements of it for consistency checks. Though we mainly consider physical limitations on the measurements, these techniques can be readily adapted to include instrumental limitations or other sources of power spectrum information.

This article describes the cosmic microwave background anisotropies expected in a closed universe with the topology of a lens space $L(p,q)\mathrm{}$ and with a density parameter ${\Omega }_0$ close to 1. It provides the first simulated maps for such spaces along with their corresponding power spectra. In spite of our initial expectations that increasing p (and thus decreasing the size of the fundamental domain) should suppress the quadrupole, we find just the opposite: increasing p elevates the relative power of the low multipoles, for reasons that have since become clear. For ${\Omega }_0=1.02,$ an informal “by eye” examination of the simulated power spectra suggests that p must be less than 15 for consistency with WMAP’s data, while geometric considerations imply that matching circles will exist (potentially revealing the multiconnected topology) only if $p>\mathrm{}7.\mathrm{}$ These bounds become less stringent for values of ${\Omega }_0$ closer to 1.

Gauge-mediated supersymmetry breaking is known to greatly suppress flavor changing neutral current effects. However, we show that gauge mediation in the context of leptogenesis implies potentially large lepton flavor violating signals. If the heavy right-handed neutrinos that participate in leptogenesis are lighter than the messenger scale of gauge mediation, they will induce flavor off-diagonal masses to the sleptons which in turn can induce large effects in $\overrightarrow{\mu }e\gamma ,\overrightarrow{\tau }\mu \gamma ,$ and $\mu -e$ conversion in nuclei. We demonstrate this result and compute numerically the lepton-flavor violating decay and conversion rates in scenarios of direct gauge mediation.

The low energy effective action including gauge field degrees of freedom on a non-Bogomol’nyi-Prasad-Sommerfield $p=2\mathrm{}$ brane embedded in an $N=1,$ $D=4\mathrm{}$ target superspace is obtained through the method of nonlinear realizations of the associated super-Poincaré symmetries. The invariant interactions of the gauge fields and the brane excitation modes corresponding to the Nambu-Goldstone degrees of freedom resulting from the broken space translational symmetry and the target space supersymmetries are determined. Brane localized matter field interactions with the gauge fields are obtained through the construction of the combined gauge and super-Poincaré covariant derivatives for the matter fields.

Motivated by the recent discussions of the Penrose limit of ${\mathrm{AdS}}_5\times {\mathrm{S}}^5,$ we examine a more general class of supersymmetric pp-wave solutions of the type IIB theory, with a larger number of nonvanishing structures in the self-dual 5-form. One of the pp-wave solutions can be obtained as a Penrose limit of a D3-D3 intersection. In addition to 16 standard supersymmetries these backgrounds always allow for supernumerary supersymmetries. The latter are in one-to-one correspondence with the linearly realized world-sheet supersymmetries of the corresponding exactly solvable type IIB string action. The pp-waves provide new examples where supersymmetries will survive in a T-duality transformation on the $x^{+}$ coordinate. The T-dual solutions can be lifted to give supersymmetric deformed M2-branes in $D=11.\mathrm{}$ The deformed M2-brane is dual to a three-dimensional field theory whose renormalization group flow runs from the conformal fixed point in the infrared regime to a nonconformal theory as the energy increases. At a certain intermediate energy scale there is a phase transition associated with a naked singularity of the M2-brane. In the ultraviolet limit the theory is related by T duality to an exactly solvable massive type IIB string theory.

We show how to reconstruct a field theory from the spectrum of bound states on a topological defect. We apply our recipe to the case of kinks in 1+1 dimensions with one or two bound states. Our recipe successfully yields the sine-Gordon and $\lambda {\phi }^4$ field theories when suitable bound state spectra are assumed. The recipe can also be used to globally reconstruct the inflaton potential of inflationary cosmology if the inflaton produces a topological defect. We discuss how defects can provide “smoking gun” evidence for inflationary models with flat potentials.

We explore the different possibilities for branons as dark matter candidates. We consider a general brane-world model, parametrized by the number of extra dimensions, N, the fundamental scale of gravity $M_D,$ the brane tension scale f, and the branon mass M. We analyze the parameter region in which branons behave as collisionless thermal relics, either cold or hot (warm), together with less standard scenarios in which they are strongly self-interacting or produced non-thermally.