We compute bounce solutions describing false vacuum decay in a ${\Phi }^4$ model in four dimensions with quantum backreaction. The backreaction of the quantum fluctuations on the bounce profiles is computed in the one-loop and Hartree approximations. This is to be compared with the usual semiclassical approach where one computes the profile from the classical action and determines the one-loop correction from this profile. The computation of the fluctuation determinant is performed using a theorem on functional determinants, in addition we here need the Green’s function of the fluctuation operator in oder to compute the quantum backreaction. As we are able to separate from the determinant and from the Gree n’s function the leading perturbative orders, we can regularize and renormalize analytically, in analogy of standard perturbation theory. The iteration towards self-consistent solutions is found to converge for some range of the parameters. Within this range the corrections to the semiclassical action are at most a few percent, the corrections to the transition rate can amount to several orders of magnitude. The strongest deviations happen for large couplings, as to be expected. The transition rates are reduced for the one-loop backreaction, for the Hartree backreaction they are reduced for $\alpha \lesssim 0.5$ and enhanced for larger values of $\alpha$. Beyond some limit, there are no self-consistent bounce solutions.

We examine the production and evolution of microscopic black holes in the early universe in the large extra dimensions scenario. We demonstrate that, unlike in the standard four-dimensional cosmology, in large extra dimensions absorption of matter from the primordial plasma by the black holes is significant and can lead to rapid growth of the black hole mass density. This effect can be used to constrain the conditions present in the very early universe. We demonstrate that this constraint is applicable in regions of parameter space not excluded by existing bounds.

We investigate here the causal structure of spacetime in the vicinity of a spacetime singularity. The particle and energy emission from such ultradense regions forming in gravitational collapse of a massive matter cloud is governed by the nature of nonspacelike paths near the same. These trajectories are examined to show that if a null geodesic comes out from the singularity, then there exist families of future-directed nonspacelike curves which also necessarily escape from the same. The existence of such families is crucial to the physical visibility of the singularity. We do not assume any underlying symmetries for the spacetime, and earlier considerations on the nature of causal trajectories emerging from a naked singularity are generalized and clarified.

We study brane inflation scenarios in a warped throat geometry and show that there exists a consistency condition between the non-Gaussianity of the curvature perturbation and the amplitude and scale-dependence of the primordial gravitational waves. This condition is independent of the warping of the throat and the form of the inflaton potential. We find that such a relation could be tested by a future CMB polarization experiment if the Planck satellite is able to detect both a gravitational wave background and a non-Gaussian statistic. In models where the observable stage of inflation occurs when the brane is in the tip region of the throat, we derive a further consistency condition involving the scalar spectral index, the tensor-scalar ratio and the curvature perturbation bispectrum. We show that when such a relation is combined with the WMAP3 results, it leads to a model-independent bound on the gravitational wave amplitude given by ${10}^{-3}<r<{10}^{-2}$. This corresponds to the range of sensitivity of the next generation of CMB polarization experiments.

Soliton type solutions of an axionlike scalar model with self-interaction are analyzed further as a toy model of dark matter halos. For a “nonlinear superposition” of round and flattened configurations we found ringlike substructures in the density profile similarly as has been inferred for our Galaxy from the observed excess of the diffuse component of cosmic gamma rays.

Exotic dark matter together with the vacuum energy (associated with the cosmological constant) seem to dominate the Universe. Thus its direct detection is central to particle physics and cosmology. Supersymmetry provides a natural dark matter candidate, the lightest supersymmetric particle (LSP). One essential ingredient in obtaining the direct detection rates is the density and the velocity distribution of the LSP in our vicinity. In the present paper we study simultaneously density profiles and velocity distributions in the context of the Eddington approach. In such an approach, unlike the commonly assumed Maxwell-Boltzmann (M-B) distribution, the upper bound of the velocity arises naturally from the potential.

We investigate the dynamics of inflation models driven by multiple, decoupled scalar fields and calculate the Hubble parameter and the amplitude of the lightest field at the end of inflation which may be responsible for interesting, or possibly dangerous cosmological consequences after inflation. The results are very simple and similar to those of the single field inflation, mainly depending on the underlying spectrum of the masses. The mass distribution is heavily constrained by the power spectrum of density perturbations $\mathcal{P}$ and the spectral index $n_{\mathrm{s}}$. The overall mass scale gives the amplitude of $\mathcal{P}$, and $n_{\mathrm{s}}$ is affected by the number of fields and the spacing between masses in the distribution. The dropout effect of the massive fields makes the perturbation spectrum typically redder than the single field inflation spectrum. We illustrate this using two different mass distributions.

We investigate in detail the low-energy spectrum of the R-parity violating minimal supergravity model using the computer program softsusy. We impose the experimental constraints from the measurement of the anomalous magnetic moment of the muon, $(g-2{)}_{\mu }$, the decay $b\to s\gamma$ as well as the mass bounds from direct searches at colliders, in particular on the Higgs boson and the lightest chargino. We also include a new calculation for the R-parity violating contribution to $\mathrm{Br}(B_s\to {\mu }^{+}{\mu }^{-})$. We then focus on cases where the lightest neutralino is not the lightest supersymmetric particle (LSP). In this region of parameter space either the lightest scalar tau (stau) or the scalar tau neutrino (tau sneutrino) is the LSP. We suggest four benchmark points with typical spectra and novel collider signatures for detailed phenomenological analysis and simulation by the LHC collaborations.

We calculate the kaon $B$-parameter, $B_K$, in chiral perturbation theory for a partially quenched, mixed-action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At 1-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an $\mathcal{O}(a^2)$ shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of $B_K$ by an amount of $\mathcal{O}(a^2)$. This term, however, is not strictly due to taste breaking, and is therefore also present in the expression for $B_K$ for pure Ginsparg-Wilson lattice fermions. We also present a numerical study of the mixed $B_K$ expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.

The determination of the ordering of the neutrino masses (the hierarchy) is probably a crucial prerequisite to understand the origin of lepton masses and mixings and to establish their relationship to the analogous properties in the quark sector. Here, we follow an alternative strategy to the usual neutrino-antineutrino comparison in long-baseline neutrino oscillation experiments: we exploit the combination of the neutrino-only data from the $\mathrm{NO}\nu \mathrm{A}$ and the T2K experiments by performing these two off-axis experiments at different distances but at the same $⟨E⟩/L$, where $⟨E⟩$ is the mean neutrino energy and $L$ is the baseline. This would require a minor adjustment to the proposed off-axis angle for one or both of the proposed experiments.

Using a sample of $3\times {10}^6$ $\psi (2S)$ decays recorded by the CLEO detector, we study three-body decays of the ${\chi }_{c0}$, ${\chi }_{c1}$, and ${\chi }_{c2}$ produced in radiative decays of the $\psi (2S)$. We consider the final states ${\pi }^{+}{\pi }^{-}\eta$, $K^{+}{K}^{-}\eta$, $p\overline{p}\eta$, ${\pi }^{+}{\pi }^{-}{\eta }^{\prime }$, $K^{+}{K}^{-}{\pi }^0$, $p\overline{p}{\pi }^0$, ${\pi }^{+}{K}^{-}{K}_{\mathrm{S}}^0$, and $K^{+}\overline{p}\Lambda$, measuring branching fractions or placing upper limits. For ${\chi }_{c1}\to {\pi }^{+}{\pi }^{-}\eta$, $K^{+}{K}^{-}{\pi }^0$, and ${\pi }^{+}{K}^{-}{K}_{\mathrm{S}}^0$ our observed samples are large enough to indicate the largest contributions to the substructure.

We present a measurement of the fraction $f_{+}$ of right-handed $W$ bosons produced in top quark decays, based on a candidate sample of $t\overline{t}$ events in the $\ell +\mathrm{\text{jets}}$ and dilepton decay channels corresponding to an integrated luminosity of $370{\mathrm{pb}}^{-1}$ collected by the D0 detector at the Fermilab Tevatron $p\overline{p}$ Collider at $\sqrt{s}=1.96\mathrm{TeV}$. We reconstruct the decay angle ${\theta }^{*}$ for each lepton. By comparing the $\cos {\theta }^{*}$ distribution from the data with that for the expected background and signal for various values of $f_{+}$ (where we assume that the fraction of longitudinally-polarized $W$ bosons has the standard model value of 0.70), we find $f_{+}=0.056\pm 0.080(\mathrm{stat})\pm 0.057(\mathrm{syst})$ ($f_{+}<0.23$ at 95% C.L.), consistent with the standard model prediction of $f_{+}=3.6\times {10}^{-4}$.

We study the evolution of linear cosmological perturbations in $f(R)$ models of accelerated expansion in the physical frame where the gravitational dynamics are fourth order and the matter is minimally coupled. These models predict a rich and testable set of linear phenomena. For each expansion history, fixed empirically by cosmological distance measures, there exists two branches of $f(R)$ solutions that are parametrized by $B\propto d^{2}f/d{R}^2$. For $B<0$, which include most of the models previously considered, there is a short-timescale instability at high curvature that spoils agreement with high redshift cosmological observables. For the stable $B>0$ branch, $f(R)$ models can reduce the large-angle CMB anisotropy, alter the shape of the linear matter power spectrum, and qualitatively change the correlations between the CMB and galaxy surveys. All of these phenomena are accessible with current and future data and provide stringent tests of general relativity on cosmological scales.

Motivated by our attempt to understand the question of angular momentum of a relativistic rotating source carried away by gravitational waves, in the asymptotic regime near future null infinity of the Kerr metric, a family of null hypersurfaces intersecting null infinity in shearfree (good) cuts are constructed by means of asymptotic expansion of the eikonal equation. The geometry of the null hypersurfaces as well as the asymptotic structure of the Kerr metric near null infinity are studied. To the lowest order in angular momentum, the Bondi-Sachs form of the Kerr metric is worked out. The Newman-Unti formalism is then further developed, with which the Newman-Penrose constants of the Kerr metric are computed and shown to be zero. Possible physical implications of the vanishing of the Newman-Penrose constants of the Kerr metric are also briefly discussed.

The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A new formulation of constraint-preserving boundary conditions of the Sommerfeld-type for such systems has recently been proposed. We implement these boundary conditions in a nonlinear 3D evolution code and test their accuracy.

In coalescing neutron star binaries, $r$-modes in one of the stars can be resonantly excited by the gravitomagnetic tidal field of its companion. This post-Newtonian gravitomagnetic driving of these modes dominates over the Newtonian tidal driving previously computed by Ho and Lai. To leading order in the tidal expansion parameter $R/r$ (where $R$ is the radius of the neutron star and $r$ is the orbital separation), only the $l=2$, $|m|=1$, and $|m|=2$ $r$-modes are excited. The tidal work done on the star through this driving has an effect on the evolution of the inspiral and on the phasing of the emitted gravitational wave signal. For a neutron star of mass $M$, radius $R$, spin frequency $f_{\mathrm{spin}}$, modeled as a $\Gamma =2$ polytrope, with a companion also of mass $M$, the gravitational wave phase shift for the $m=2$ mode is $\sim 0.1\mathrm{radians}(R/10\mathrm{km}{)}^4(M/1.4M_{\odot }{)}^{-10/3}(f_{\mathrm{spin}}/100\mathrm{Hz}{)}^{2/3}$ for optimal spin orientation. For canonical neutron star parameters this phase shift will likely not be detectable by gravitational wave detectors such as LIGO, but if the neutron star radius is larger it may be detectable if the signal-to-noise ratio is moderately large. The energy transfer is large enough to drive the mode into the nonlinear regime if $f_{\mathrm{spin}}\gtrsim 100\mathrm{Hz}$. For neutron star—black hole binaries, the effect is smaller; the phase shift scales as companion mass to the $-4/3$ power for large companion masses. The net energy transfer from the orbit into the star is negative corresponding to a slowing down of the inspiral. This occurs because the interaction reduces the spin of the star, and occurs only for modes which satisfy the Chandrasekhar-Friedman-Schutz instability criterion. A large portion of the paper is devoted to developing a general formalism to treat mode driving in rotating stars to post-Newtonian order, which may be useful for other applications. We also correct some conceptual errors in the literature on the use of energy conservation to deduce the effect of the mode driving on the gravitational wave signal.

We present a detailed numerical study of the evolutions of cosmological linear perturbations through a simple bouncing world model based on two scalar fields. We properly identify the relatively growing and decaying solutions in expanding and collapsing phases. Using a decomposition based on the large-scale limit exact solution of curvature (adiabatic) perturbations with two independent modes, we assign the relatively growing/decaying one in an expanding phase as the $C/d$-mode. In the collapsing phase, the roles are reversed, and the $C/d$-mode is relatively decaying/growing. The analytic solution shows that, as long as the large-scale and the adiabatic conditions are met, the $C$- and $d$-modes preserve their nature throughout the bounce. Here, by using a concrete nonsingular bouncing world model based on two scalar fields, we numerically follow the evolutions of the correctly identified $C$- and $d$-modes which preserve their nature through the bounce, thus confirming our previous anticipation based on the analytic solution. Since we are currently in an expanding phase the observationally relevant one in the expanding phase is the relatively growing $C$-mode whose nature is preserved throughout the bounce. The spectrum of $C$-mode generated from quantum fluctuations in the collapsing phase has a quite blue spectrum compared with the near Harrison-Zel’dovich scale-invariant one. Thus, while the large-scale condition is satisfied and the adiabatic condition is met during the bounce, we conclude that it is not possible to obtain the near Harrison-Zel’dovich scale-invariant density spectrum through a bouncing world model as long as the seed fluctuations were generated from quantum fluctuations of the curvature perturbation in the collapsing phase. We also study the tensor-type perturbation. For the tensor-type perturbation, however, both $C$- and $d$-modes (of the tensor-type perturbations) in the collapsing phase survive as the relatively growing $C$-mode in the expanding phase. Because of its growing nature in the collapsing phase, the initial $d$-mode dominates the surviving $C$-mode spectrum after the bounce.

We review the contribution of extra galactic inspiralling double neutron stars, to the LISA astrophysical gravitational wave foreground. Using recent fits of the star formation rate, we show that sources beyond $z_{*}=0.005$ contribute to a truly continuous background, which may dominate the LISA instrumental noise in the range $3\simeq {10}^{-4}–1\times {10}^{-2}\mathrm{Hz}$ and overwhelm the galactic WD-WD confusion noise at frequencies larger than ${\nu }_o\simeq 2\times {10}^{-3}$.

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As is well known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (noncontinuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore advisable to explore other alternatives as well. In this paper, a generalized Wiener process is proposed that is continuous, avoids superluminal propagation, and reduces to the standard Wiener process in the nonrelativistic limit. The corresponding relativistic diffusion propagator is obtained directly from the nonrelativistic Wiener propagator, by rewriting the latter in terms of an integral over actions. The resulting relativistic process is non-Markovian, in accordance with the known fact that nontrivial continuous, relativistic Markov processes in position space cannot exist. Hence, the proposed process defines a consistent relativistic diffusion model for massive particles and provides a viable alternative to the solutions of the telegraph equation.

We argue that screening of higher-representation color charges by gluons implies a domain structure in the vacuum state of non-Abelian gauge theories, with the color magnetic flux in each domain quantized in units corresponding to the gauge group center. Casimir scaling of string tensions at intermediate distances results from random spatial variations in the color magnetic flux within each domain. The exceptional G(2) gauge group is an example rather than an exception to this picture, although for G(2) there is only one type of vacuum domain, corresponding to the single element of the gauge group center. We present some numerical results for G(2) intermediate string tensions and Polyakov lines, as well as results for certain gauge-dependent projected quantities. In this context, we discuss critically the idea of projecting link variables to a subgroup of the gauge group. It is argued that such projections are useful only when the representation-dependence of the string tension, at some distance scale, is given by the representation of the subgroup.