A new implementation for magnetohydrodynamics (MHD) simulations in full general relativity (involving dynamical spacetimes) is presented. In our implementation, Einstein’s evolution equations are evolved by a Baumgarte-Shapiro-Shibata-Nakamura formalism, MHD equations by a high-resolution central scheme, and induction equation by a constraint transport method. We perform numerical simulations for standard test problems in relativistic MHD, including special relativistic magnetized shocks, general relativistic magnetized Bondi flow in stationary spacetime, and a long-term evolution for self-gravitating system composed of a neutron star and a magnetized disk in full general relativity. In the final test, we illustrate that our implementation can follow winding-up of the magnetic field lines of magnetized and differentially rotating accretion disks around a compact object until saturation, after which magnetically driven wind and angular momentum transport inside the disk turn on.

We discuss features of the brane cosmological evolution that arise through the presence of matter in the bulk. As these deviations from the conventional evolution are not associated with some observable matter component on the brane, we characterize them as mirage effects. We review an example of expansion that can be attributed to mirage nonrelativistic matter (mirage cold dark matter) on the brane. The real source of the evolution is an anisotropic bulk fluid with negative pressure along the extra dimension. We also study the general problem of exchange of real nonrelativistic matter between the brane and the bulk, and discuss the related mirage effects. Finally, we derive the brane cosmological evolution within a bulk that contains a global monopole (hedgehog) configuration. This background induces a mirage curvature term in the effective Friedmann equation, which can cause a brane universe with positive spatial curvature to expand forever.

We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of ${\phi }_v$ order higher than the second-order terms where ${\phi }_v$ is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have $\delta \Phi \sim \frac{3}{5}{\phi }_v$ to the linear order. Therefore, the pure general relativistic effects are of ${\phi }_v$ order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropy of cosmic microwave background, we have $\frac{\delta T}{T}\sim \frac{1}{3}\delta \Phi \sim \frac{1}{5}{\phi }_v\sim {10}^{-5}$. Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon.

The dynamic world model and its linear perturbations were first studied in Einstein’s gravity. In the system without pressure, the relativistic equations coincide exactly with the later known ones in Newton’s gravity. Here we prove that, except for the gravitational wave contribution, even to the second-order perturbations, equations for the relativistic irrotational zero-pressure fluid in a flat Friedmann background coincide exactly with the previously known Newtonian equations. Thus, to the second order, we correctly identify the relativistic density and velocity perturbation variables, and we expand the range of applicability of the Newtonian medium without pressure to all cosmological scales including the superhorizon scale. In the relativistic analyses, however, we do not have a relativistic variable which corresponds to the Newtonian potential to the second order. Mixed usage of different gauge conditions is useful to make such proofs and to examine the result with perspective. We also present the gravitational wave equation to the second order. Since our correspondence includes the cosmological constant, our results are relevant to currently favored cosmology. Our result has an important practical implication that one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near horizon.

The space-based gravitational-wave observatory LISA, a NASA-ESA mission to be launched after 2012, will achieve its optimal sensitivity using time delay interferometry (TDI), a LISA-specific technique needed to cancel the otherwise overwhelming laser noise in the interspacecraft phase measurements. The TDI observables of the Michelson and Sagnac types have been interpreted physically as the virtual measurements of a synthesized interferometer. In this paper, I present Geometric TDI, a new and intuitive approach to extend this interpretation to all TDI observables. Unlike the standard algebraic formalism, Geometric TDI provides a combinatorial algorithm to explore exhaustively the space of second-generation TDI observables (i.e., those that cancel laser noise in LISA-like interferometers with time-dependent arm lengths). Using this algorithm, I survey the space of second-generation TDI observables of length (i.e., number of component phase measurements) up to 24, and I identify alternative, improved forms of the standard second-generation TDI observables. The alternative forms have improved high-frequency gravitational-wave sensitivity in realistic noise conditions (because they have fewer nulls in the gravitational-wave and noise response functions), and are less susceptible to instrumental gaps and glitches (because their component phase measurements span shorter time periods).

We have performed a search for bursts of gravitational waves associated with the very bright gamma ray burst GRB030329, using the two detectors at the LIGO Hanford Observatory. Our search covered the most sensitive frequency range of the LIGO detectors (approximately $80–-2048\mathrm{Hz}$), and we specifically targeted signals shorter than $\simeq 150\mathrm{ms}$. Our search algorithm looks for excess correlated power between the two interferometers and thus makes minimal assumptions about the gravitational waveform. We observed no candidates with gravitational-wave signal strength larger than a predetermined threshold. We report frequency-dependent upper limits on the strength of the gravitational waves associated with GRB030329. Near the most sensitive frequency region, around $\simeq 250\mathrm{Hz}$, our root-sum-square (RSS) gravitational-wave strain sensitivity for optimally polarized bursts was better than $h_{\mathrm{RSS}}\simeq 6\times {10}^{-21}{\mathrm{Hz}}^{-1/2}$. Our result is comparable to the best published results searching for association between gravitational waves and gamma ray bursts.

Using effective field theory approach, we study the constraints from electroweak data on the $SU(5)/SO(5)$, $SU(6)/SP(6)$, $SU(3)\times U(1)$ little Higgs models and their variations. We construct an effective theory valid above the electroweak symmetry breaking scale in these models that includes dimension-six operators induced by integrating out heavy fields. We calculate the constraints on the models using the results of [Z. Han and W. Skiba, Phys. Rev. D 71, 075009 (2005)], where bounds on arbitrary linear combinations of flavor and $CP$ conserving dimension-six operators are given. We present the constraints in terms of the bounds on the masses of heavy fermions and heavy gauge bosons. The constraints are often stringent, but in some regions of the parameter space the constraints are mild enough and do not imply significant fine-tuning.

Recently an effective Lagrangian for the interactions of photons, Nambu-Goldstone bosons and superfluid phonons in dense quark matter has been derived using anomaly matching arguments. In this paper we illuminate the nature of certain anomalous terms in this Lagrangian by an explicit microscopic calculation. We also generalize the corresponding construction to introduce the axion field. We derive an anomalous axion effective Lagrangian describing the interactions of axions with photons and superfluid phonons in the dense matter background. This effective Lagrangian, among other things, implies that an axion current will be induced in the presence of magnetic field. We speculate that this current may be responsible for the explanation of neutron star kicks.

We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations. Local Lorentz invariance is treated as a gauge theory with the spin connection field taken in the so(3,1) enveloping algebra. The resulting theory appears to be a noncommutative extension of the unimodular theory of gravitation. We compute the leading order noncommutative correction to the action and derive the noncommutative correction to the equations of motion of the weak gravitation field.

We perform a very detailed investigation into the possibility of Lorentz and $CPT$ violations in the photon sector, of the Chern-Simons form, being induced by radiative corrections arising from the Lorentz and $CPT$ noninvariant fermionic sector of an extended version of QED. In the discussions it is considered the role played by the scale ambiguities in the perturbative calculations. The origin of the possible contributions are clearly identified, due to the very general character of the calculational method applied, concerning the manipulations and calculations of divergent amplitudes. We show that constraints dictated by the consistency in the perturbative calculations, imposed by physical reasons, eliminate all the sources of violating contributions, leaving no room for the existence of a radiatively induced Lorentz and $CPT$ violations in the extended QED, putting the perturbative evaluations in accordance with the predictions made, by using very general arguments, stated by other authors.

We present cosmological constraints on deviations of Newton’s constant at large scales without specifying a model, analyzing latest cosmic microwave background (CMB) anisotropies and primordial abundances of light elements synthesized by big bang nucleosynthesis (BBN). BBN limits the possible deviation at typical scales of BBN epoch, say at ${10}^8–{10}^{12}\mathrm{m}$, to lie between $-5\%$ and $+1\%$ of the experimental value, and CMB restricts the deviation at larger scales ${10}^2–{10}^9\mathrm{pc}$ to be between $-26\%$ and $+66\%$ at the $2\sigma$ confidence level. The cosmological constraints are compared with the astronomical one from the evolution of isochrone of globular clusters.

Recently Gibbons et al. in [G. W. Gibbons et al. Class. Quant. Grav. 22, 1503 (2005)] defined a set of conserved quantities for Kerr-AdS black holes with the maximal number of rotation parameters in arbitrary dimension. This set of conserved quantities is defined with respect to a frame which is nonrotating at infinity. On the other hand, there is another set of conserved quantities for Kerr-AdS black holes, defined by Hawking et al. in [Hawking et al. Phys. Rev. D 59, 064005 (1999)], which is measured relative to a frame rotating at infinity. Gibbons et al. explicitly showed that the quantities defined by them satisfy the first law of black hole thermodynamics, while those quantities defined by Hawking et al. do not obey the first law. In this paper we discuss thermodynamics of dual CFTs to the Kerr-AdS black holes by mapping the bulk thermodynamic quantities to the boundary of the AdS space. We find that thermodynamic quantities of dual CFTs satisfy the first law of thermodynamics and Cardy-Verlinde formula only when these thermodynamic quantities result from the set of bulk quantities given by Hawking et al.. We discuss the implication of our results.

We present new sequences of general relativistic, quasiequilibrium black hole-neutron star binaries. We solve for the gravitational field in the conformal thin-sandwich decomposition of Einstein’s field equations, coupled to the equations of relativistic hydrostatic equilibrium for a perfect fluid. We account for the black hole by solving these equations in the background metric of a Schwarzschild black hole whose mass is much larger than that of the neutron star. The background metric is treated in Kerr-Schild as well as isotropic coordinates. For the neutron star, we assume a polytropic equation of state with adiabatic index $\Gamma =2$, and solve for both irrotational and corotational configurations. By comparing the results of irrotational and synchronized configurations with the same background metric, we conclude that the effect of the rotation on the location of tidal breakup is only on the order of a few percent. The different choices in the background also lead to differences on the order of a few percent, which may be an indication of the level to which these configurations approximate quasiequilibrium.

We have reexamined the holographic dark energy model by considering the spatial curvature. We have refined the model parameter and observed that the holographic dark energy model does not behave as phantom model. Comparing the holographic dark energy model to the supernova observation alone, we found that the closed Universe is favored. Combining with the Wilkinson microwave anisotropy probe (WMAP) data, we obtained the reasonable value of the spatial curvature of our Universe.

For exploring the physics behind the accelerating Universe a crucial question is how much we can learn about the dynamics through next generation cosmological experiments. For example, in defining the dark energy behavior through an effective equation of state, how many parameters can we realistically expect to tightly constrain? Through both general and specific examples (including new parametrizations and principal component analysis) we argue that the answer is two. Cosmological parameter analyses involving a measure of the equation of state value at some epoch (e.g. $w_0$) and a measure of the change in equation of state (e.g. $w^{\prime }$) are therefore realistic in projecting dark energy parameter constraints. More elaborate parametrizations could have some uses (e.g. testing for bias or comparison with model features), but do not lead to accurately measured dark energy parameters.

We explore several strategies of eliminating (or nulling) the small-scale information in weak lensing convergence power spectrum measurements in order to protect against undesirable effects, for example, the effects of baryonic cooling and pressure forces on the distribution of large-scale structures. We selectively throw out the small-scale information in the convergence power spectrum that is most sensitive to the unwanted bias, while trying to retain most of the sensitivity to cosmological parameters. The strategies are effective in the difficult but realistic situations when we are able to guess the form of the contaminating effect only approximately. However, we also find that the simplest scheme of simply not using information from the largest multipoles works about as well as the proposed techniques in most, although not all, realistic cases. We advocate further exploration of nulling techniques and believe that they will find important applications in the weak lensing data mining.

Wave effects can be important for the gravitational lensing of gravitational waves. In such a case, wave optics must be used instead of geometric optics. We consider a plane wave entering a lens object and solve numerically the wave equation for three lens models: the uniform density sphere, the singular isothermal sphere, and the Hernquist model. By comparing our numerical solutions with the analytical solutions under the thin lens approximation, we evaluate the error of this approximation. The results show that the relative error of the thin lens approximation is small if the geometrical thickness of the lens is much smaller than the distance between the lens and the observer.

Gauge theories of gravity provide an elegant and promising extension of general relativity. In this paper we show that the Poincaré gauge theory exhibits gravity-induced birefringence under the assumption of a specific gauge invariant nonminimal coupling between torsion and Maxwell’s field. Furthermore we give for the first time an explicit expression for the induced phase shift between two orthogonal polarization modes within the Poincaré framework. Since such a phase shift can lead to a depolarization of light emitted from an extended source this effect is, in principle, observable. We use white dwarf polarimetric data to constrain the essential coupling constant responsible for this effect.

The recent measurements of the solar neutrino mixing angle ${\theta }_{\mathrm{sol}}$ and the Cabibbo mixing angle ${\theta }_C$ reveal a surprising relation, ${\theta }_{\mathrm{sol}}+{\theta }_C\simeq \frac{\pi }{4}$, which has been interpreted as an evidence for quark-lepton unification. We show in realizations of quark-lepton unification that the PMNS mixing matrix can be decomposed into a CKM-like matrix and maximal mixing matrices. We explore a possibility to probe such implications by considering the relative sizes of branching ratios for the lepton flavor violating radiative decay processes, $l_i\to l_j\gamma$, in the context of the supersymmetric standard model with heavy right-handed Majorana neutrinos.

The recent measurements of large transverse fractions in $B\to \varphi K^{*}$ decays represent a challenge for theory. It was shown that the QCD penguin annihilation could contribute to the transverse amplitudes such that the observation could be accounted for in the standard model. However, if one resorts to new physics for resolutions, then the relevant 4-quark operators should be tensorlike or scalarlike. We show that the same annihilation effects could remarkably enhance the longitudinal rates of factorization-suppressed ${\overline{B}}^0\to h_1(1380){\overline{K}}^{*0},b_1(1235){\overline{K}}^{*0}$ modes to be $({12.0}_{-3.0}^{+4.1})\times {10}^{-6}$ and $(7.0\pm 3.5)\times {10}^{-6}$, respectively, but attend to be canceled in the transverse components. Nevertheless, the transverse fractions of $B\to h_1(1380)K^{*}$ can become sizable due to new physics contributions. The measurements of these decays can thus help us to realize the role of annihilation topologies in charmless $B$ decays and offer a theoretically clean window to search for the evidence of new physics.