There is increasing evidence that causality provides useful bounds in determining the domain structure after a continuous transition. In devising their scaling laws for domain size after such a transition, Zurek and Kibble presented arguments in which causality is important both before and after the time at which the transition begins to be implemented. Using numerical simulations of kinks in $1+1$ dimensions, we explain how the domain structure is determined exclusively by what happens after the transition, even though the correlation length freezes in before the transition.

Boltzmann equations are often used to study the thermal evolution of particle reaction networks. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after relativistic heavy ion collisions. However, Boltzmann equations are only a classical approximation of the quantum thermalization process which is described by the so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the full Kadanoff-Baym equations. Therefore, we present in this paper a detailed comparison between the Kadanoff-Baym and Boltzmann equations in the framework of a scalar ${\Phi }^4$ quantum field theory in $3+1$ space-time dimensions. The obtained numerical solutions reveal significant discrepancies in the results predicted by both types of equations. Apart from quantitative discrepancies, on a qualitative level the universality respected by the Kadanoff-Baym equations is severely restricted in the case of Boltzmann equations. Furthermore, the Kadanoff-Baym equations strongly separate the time scales between kinetic and chemical equilibration. This separation of time scales is absent for the Boltzmann equation.

Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion operators presented in an earlier work, form a framework for studying gravitational collapse in quantum gravity. We describe a setting for its numerical implementation, and discuss some conceptual issues associated with quantum dynamics in a partial gauge fixing.

During the coalescence of binary black holes, gravitational waves carry linear momentum away from the source, which results in the recoil of the center of mass. Using the effective one body approach, which includes nonperturbative resummed estimates for the damping and conservative parts of the compact binary dynamics, we compute the recoil during the late inspiral and the subsequent plunge of nonspinning black holes of comparable masses moving in quasicircular orbits. Further, using a prescription that smoothly connects the plunge phase to a perturbed single black hole, we obtain an estimate for the total recoil associated with the binary black hole coalescence. We show that the crucial physical feature which determines the magnitude of the terminal recoil is the presence of a burst of linear-momentum flux emitted slightly before coalescence. When using the most natural expression for the linear-momentum flux during the plunge, together with a Taylor-expanded $(v/c{)}^4$ correction factor, we find that the maximum value of the terminal recoil is $\sim 74\mathrm{km}/\mathrm{s}$ and occurs for $\eta =(m_1{m}_2)/(m_1+m_2{)}^2\simeq 0.2$, i.e., for a mass ratio $m_2/m_1\simeq 0.38$. Away from this optimal mass ratio, the recoil velocity decreases approximately proportionally to the scaling function $\tilde{f}(\eta )={\eta }^2(1-4\eta {)}^{1/2}(1.0912-1.04\eta +2.92{\eta }^2)$. We comment, however, on the fact that the above “best-bet estimate” is subject to strong uncertainties because the location and amplitude of the crucial peak of linear-momentum flux happens at a moment during the plunge where most of the simplifying analytical assumptions underlying the effective one body approach are no longer justified. Changing the analytical way of estimating the linear-momentum flux, we find maximum recoils that range between 49 and $172\mathrm{km}/\mathrm{s}$.

A previous paper constructed a kinematic basis for spin networks with planar or cylindrical symmetry and arbitrary polarization. This paper imposes a constraint which limits the gravitational wave to a single polarization. The spectrum of the constraint contains a physically reasonable number of zero eigenvalues, and the zero eigenvectors can be constructed explicitly. Commutation of the constraint with the Hamiltonian is expected to lead to a further constraint. This new constraint is not investigated in this paper, but I argue it will be nonlocal, relating states at two or more neighboring vertices.

This paper constructs a kinematic basis for spin networks with planar or cylindrical symmetry, by exploiting the fact that the basis elements are representations of an O(3) subgroup of O(4). The action of the volume operator on this basis gives a difference equation for the eigenvalues and eigenvectors of the volume operator. For basis elements of low spin, the difference equation can be solved readily on a computer, yielding the eigenvalues and eigenvectors. For higher spins, I solve for the eigenvalues using a WKBJ method. This paper considers only the case where the gravitational wave can have both polarizations. The single polarization case is considered in a separate paper.

Structure formation in the Szekeres model is investigated. Since the Szekeres model is an inhomogeneous model with no symmetries, it is possible to examine the interaction of neighboring structures and its impact on the growth of a density contrast. It has been found that the mass flow from voids to clusters enhances the growth of the density contrast. In the model presented here, the growth of the density contrast is almost 8 times faster than in the linear approach.

Direct detection dark matter experiments, lead by the CDMS Collaboration, have placed increasingly stronger constraints on the cross sections for elastic scattering of weakly interacting massive particles (WIMPs) on nucleons. These results impact the prospects for the indirect detection of dark matter using neutrino telescopes. With this in mind, we revisit the prospects for detecting neutrinos produced by the annihilation of WIMPs in the Sun. We find that the latest bounds do not seriously limit the models most accessible to next generation kilometer-scale neutrino telescopes such as IceCube. This is largely due to the fact that models with significant spin-dependent couplings to protons are the least constrained and, at the same time, the most promising because of the efficient capture of WIMPs in the Sun. We identify models where dark matter particles are beyond the reach of any planned direct detection experiments while within reach of neutrino telescopes. In summary, we find that, even when contemplating recent direct detection results, neutrino telescopes still have the opportunity to play an important as well as complementary role in the search for particle dark matter.

In gravitational wave interferometers, the input laser beam is phase modulated to generate radio-frequency side bands that are used to lock the cavities. The mechanism is the following: the frequency of the side bands and the carrier is chosen in such a way that their response to small changes of the longitudinal degrees of freedom is different. This difference is therefore monitored and it serves as an error signal for controlling the optical cavity lengths, as they are linearly related to the set of observed phases between carrier and side bands. Among the others, one longitudinal degree of freedom is optimally sensitive to the space-time distortions propagating through the cosmos, as predicted by the general theory of relativity. The observation of the astrophysical signal relies on the measurement of that specific degree of freedom. The entire problem is more complex when the transverse degrees of freedom are taken into account, because the relative phase between the fields also depends on their overlap. In order to establish an unambiguous relation between length changes and phase measurements, there must be one circulating optical mode and the only difference between carrier and side bands must be their amplitude. We will show that the variability of the transverse degrees of freedom and their different actions on carrier and side band fields puts a severe limit on this assumption. Unless the system is made of perfect and perfectly matched optical cavities, it is never governed by one unique coherent state and any adjustment of the optical lengths results from a compromise between the lengths that are optimal for the carrier field and the side band ones. Such a compromise alters the correspondence between error signals and cavity lengths, calculated in the one-dimensional treatment. We assess the strength of this effect and relate it to the sensitivity of the instrument (which relies on the reconstruction of that correspondence) in realistic circumstances.

Three-flavor lattice QCD simulations and two-loop perturbation theory are used to make the most precise determination to date of the strange-, up-, and down-quark masses, $m_s$, $m_u$, and $m_d$, respectively. Perturbative matching is required in order to connect the lattice-regularized bare-quark masses to the masses as defined in the $\overline{\mathrm{MS}}$ scheme, and this is done here for the first time at next-to-next-to leading (or two-loop) order. The bare-quark masses required as input come from simulations by the MILC collaboration using so-called staggered quarks, with three flavors of light quarks in the Dirac sea; these simulations were previously analyzed in a joint study by the HPQCD and MILC collaborations, using degenerate $u$ and $d$ quarks, with masses as low as $m_s/8$, and two values of the lattice spacing, with chiral extrapolation/interpolation to the physical masses. With the new perturbation theory presented here, the resulting $\overline{\mathrm{MS}}$ masses are $m_s^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=87(0)(4)(4)(0)\mathrm{MeV}$, and ${\widehat{m}}^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=3.2(0)(2)(2)(0)\mathrm{MeV}$, where $\widehat{m}=\frac{1}{2}(m_u+m_d)$ is the average of the $u$ and $d$ masses. The respective uncertainties are from statistics, simulation systematics, perturbation theory, and electromagnetic/isospin effects. The perturbative errors are about a factor of 2 smaller than in an earlier study using only one-loop perturbation theory. Using a recent determination of the ratio $m_u/m_d=0.43(0)(1)(0)(8)$ due to the MILC collaboration, these results also imply $m_u^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=1.9(0)(1)(1)(2)\mathrm{MeV}$ and $m_d^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=4.4(0)(2)(2)(2)\mathrm{MeV}$. A technique for estimating the next order in the perturbative expansion is also presented, which uses input from simulations at more than one lattice spacing; this method is used here in the estimate of the systematic uncertainties.

We consider one-loop effective potentials for adjoint Higgs fields that originate from flat holonomies in toroidal compactification of gauge theories. We show that such potentials are “landscape-like” for large gauge groups and generic nonsupersymmetric matter representations. In particular, there is a large number of vacua with similar local properties, scanning a broad band of vacuum energies.

We study an inhomogeneous decay of an unstable D-brane in the context of Dirac-Born-Infeld (DBI)-type effective action. We consider tachyon and electromagnetic fields with dependence of time and one spatial coordinate, and an exact solution is found under an exponentially decreasing tachyon potential, $e^{-|T|/\sqrt{2}}$, which is valid for the description of the late time behavior of an unstable D-brane. Though the obtained solution contains both time and spatial dependence, the corresponding momentum density vanishes over the entire spacetime region. The solution is governed by two parameters. One adjusts the distribution of energy density in the inhomogeneous direction, and the other interpolates between the homogeneous rolling tachyon and static configuration. As time evolves, the energy of the unstable D-brane is converted into the electric flux and tachyon matter.

We construct a quantum field theory in noncommutative space time by twisting the algebra of quantum operators (especially, creation and annihilation operators) of the corresponding quantum field theory in commutative space time. The twisted Fock space and $S$-matrix consistent with this algebra have been constructed. The resultant $S$-matrix is consistent with that of Filk [Tomas Filk, Phys. Lett. B 376, 53 (1996).]. We find from this formulation that the spin-statistics relation is not violated in the canonical noncommutative field theories.

In the Bondi formulation of the axisymmetric vacuum Einstein equations, we argue that the “surface area” coordinate condition determining the “radial” coordinate can be considered as part of the initial data and should be chosen in a way that gives information about the physical problem whose solution is sought. For the two-body problem, we choose this coordinate by imposing a condition that allows it to be interpreted, near infinity, as the (inverse of the) Newtonian potential. In this way, two quantities that specify the problem—the separation of the two particles and their mass ratio—enter the equations from the very beginning. The asymptotic solution (near infinity) is obtained and a natural identification of the Bondi “news function” in terms of the source parameters is suggested, leading to an expression for the radiated energy that differs from the standard quadrupole formula but agrees with recent nonlinear calculations. When the free function of time describing the separation of the two particles is chosen so as to make the new expression agree with the classical result, closed-form analytic expressions are obtained, the resulting metric approaching the Schwarzschild solution with time. As all physical quantities are defined with respect to the flat metric at infinity, the physical interpretation of this solution depends strongly on how these definitions are extended to the near-zone and, in particular, how the “time” function in the near-zone is related to Bondi’s null coordinate.

Construction of astrophysically realistic initial data remains a central problem when modelling the merger and eventual coalescence of binary black holes in numerical relativity. The objective of this paper is to provide astrophysically realistic freely specifiable initial data for binary black hole systems in numerical relativity, which are in agreement with post-Newtonian results. Following the approach taken by Blanchet [L. Blanchet, Phys. Rev. D 68, 084002 (2003).], we propose a particular solution to the time-asymmetric constraint equations, which represent a system of two moving black holes, in the form of the standard conformal decomposition of the spatial metric and the extrinsic curvature. The solution for the spatial metric is given in symmetric-trace-free form, as well as in Dirac coordinates. We show that the solution differs from the usual post-Newtonian metric up to the 2PN order by a coordinate transformation. In addition, the solutions, defined at every point of space, differ at second post-Newtonian order from the exact, conformally-flat, Bowen-York solution of the constraints.

Every well-posed hyperbolic problem has an associated characteristic representation. In the case of the Einstein equations, traditionally, characteristic problems have been stated in the Bondi-Sachs form, whereas initial-value problems have been represented in the ADM form, both being looked upon as independent versions of the Einstein equations. Under the restriction of spherical symmetry, we provide an ADM version of the Einstein equations that functions as the initial-value representation of the Bondi-Sachs equations. The ADM version allows us to interpret the Bondi-Sachs variables precisely in terms of characteristic fields of the Cauchy problem. The Bondi-Sachs version thus leads us to a version of the Cauchy problem that is first order in time (with no need for reduction) and automatically well posed.

We investigate the conditions under which cosmological variations in physical “constants” and scalar fields are detectable on the surface of local gravitationally bound systems, such as planets, in nonspherically symmetric background spacetimes. The method of matched asymptotic expansions is used to deal with the large range of length scales that appear in the problem. We derive a sufficient condition for the local time variation of the scalar fields driving variations in constants to track their large-scale cosmological variation and show that this is consistent with our earlier conjecture derived from the spherically symmetric problem. We perform our analysis with spacetime backgrounds that are of Szekeres-Szafron type. They are approximately Schwarzschild in some locality and free of gravitational waves everywhere. At large distances, we assume that the spacetime matches smoothly onto a Friedmann background universe. We conclude that, independent of the details of the scalar-field theory describing the varying constant, the condition for its cosmological variations to be measured locally is almost always satisfied in physically realistic situations. The very small differences expected to be observed between different scales are quantified. This strengthens the proof given in our previous paper that local experiments see global variations by dropping the requirement of exact spherical symmetry. It provides a rigorous justification for using terrestrial experiments and solar-system observations to constrain or detect any cosmological time variations in the traditional constants of nature in the case where nonspherical inhomogeneities exist.

We apply the method of matched asymptotic expansions to analyze whether cosmological variations in physical “constants” and scalar fields are detectable, locally, on the surface of local gravitationally bound systems such as planets and stars, or inside virialized systems like galaxies and clusters. We assume spherical symmetry and derive a sufficient condition for the local time variation of the scalar fields that drive varying constants to track the cosmological one. We calculate a number of specific examples in detail by matching the Schwarzschild spacetime to spherically symmetric inhomogeneous Tolman-Bondi metrics in an intermediate region by rigorously constructing matched asymptotic expansions on cosmological and local astronomical scales which overlap in an intermediate domain. We conclude that, independent of the details of the scalar-field theory describing the varying constant, the condition for cosmological variations to be measured locally is almost always satisfied in physically realistic situations. The proof of this statement provides a rigorous justification for using terrestrial experiments and solar system observations to constrain or detect any cosmological time variations in the traditional constants of nature.

A generic prediction of general relativity is that the cosmological linear density growth factor $D$ is scale independent. But in general, modified gravities do not preserve this signature. A scale dependent $D$ can cause time variation in gravitational potential at high redshifts and provides a new cosmological test of gravity, through early time integrated Sachs-Wolfe (ISW) effect-large scale structure (LSS) cross correlation. We demonstrate the power of this test for a class of $f(R)$ gravity, with the form $f(R)=-{\lambda }_1{H}_0^2\exp (-R/{\lambda }_2{H}_0^2)$. Such $f(R)$ gravity, even with degenerate expansion history to $\Lambda \mathrm{CDM}$, can produce detectable ISW effect at $z\gtrsim 3$ and $l\gtrsim 20$. Null-detection of such effect would constrain ${\lambda }_2$ to be ${\lambda }_2>1000$ at $>95\%$ confidence level. On the other hand, robust detection of ISW-LSS cross correlation at high $z$ will severely challenge general relativity.

A detection of the primordial gravitational wave background is considered to be the “smoking-gun” evidence for inflation. While superhorizon waves are probed with cosmic microwave background (CMB) polarization, the relic background will be studied with laser interferometers. The long lever arm spanned by the two techniques improves constraints on the inflationary potential and validation of consistency relations expected under inflation. If gravitational waves with a tensor-to-scalar amplitude ratio greater than 0.01 are detected by the CMB, then a direct-detection experiment with a sensitivity consistent with current concept studies should be pursued vigorously. If no primordial tensors are detected by the CMB, a direct-detection experiment to understand the simplest form of inflation must have a sensitivity improved by two to 3 orders of magnitude over current plans.