Two mechanisms for nonlinear mode saturation of the $r$ mode in neutron stars have been suggested: the parametric instability mechanism involving a small number of modes and the formation of a nearly continuous Kolmogorov-type cascade. Using a network of oscillators constructed from the eigenmodes of a perfect fluid incompressible star, we investigate the transition between the two regimes numerically. Our network includes the 4995 inertial modes up to $n\le 30$ with 146 998 direct couplings to the $r$ mode and 1 306 999 couplings with detuning $<0.002$ (out of a total of approximately ${10}^9$ possible couplings). The lowest parametric instability thresholds for a range of temperatures are calculated and it is found that the $r$ mode becomes unstable to modes with $13<n<15$. In the undriven, undamped, Hamiltonian version of the network the rate to achieve equipartition is found to be amplitude dependent, reminiscent of the Fermi-Pasta-Ulam problem. More realistic models driven unstable by gravitational radiation and damped by shear viscosity are explored next. A range of damping rates, corresponding to temperatures ${10}^6\mathrm{K}$ to ${10}^9\mathrm{K}$, is considered. Exponential growth of the $r$ mode is found to cease at small amplitudes $\approx {10}^{-4}$. For strongly damped, low temperature models, a few modes dominate the dynamics. The behavior of the $r$ mode is complicated, but its amplitude is still no larger than about ${10}^{-4}$ on average. For high temperature, weakly damped models the $r$ mode feeds energy into a sea of oscillators that achieve approximate equipartition. In this case the $r$-mode amplitude settles to a value for which the rate to achieve equipartition is approximately the linear instability growth rate.

We incorporate a massless scalar field into a three-dimensional code for the characteristic evolution of the gravitational field. The extended three-dimensional code for the Einstein-Klein-Gordon system is calibrated to be second-order convergent. It provides an accurate calculation of the gravitational and scalar radiation at infinity. As an application, we simulate the fully nonlinear evolution of an asymmetric scalar pulse of ingoing radiation propagating toward an interior Schwarzschild black hole and compute the backscattered scalar and gravitational outgoing radiation patterns. The amplitudes of the scalar and gravitational outgoing radiation modes exhibit the predicted power law scaling with respect to the amplitude of the initial data. For the scattering of an axisymmetric scalar field, the final ring down matches the complex frequency calculated perturbatively for the $\ell =2$ quasinormal mode.

The dark energy in the Universe is described in the context of modified Friedmann equations as a fluid parametrized by the density of dark matter and undergoing an adiabatic expansion. This formulation is applied to the Cardassian model. Choosing then parameters consistent with the supernova observations, it gives a background expansion in which the cosmic temperature fluctuations are calculated. The resulting spectrum is quite similar to what is obtained in the standard concordance model. If the Cardassian fluid is interpreted as a new kind of interacting dark matter, its overdensities are driven into oscillations when the interaction energy is rising in importance. This does not occur in a description of the Cardassian fluctuations motivated by theories of modified gravity. There the energy of the underlying matter is also conserved, which requires appearance of effective shear stress in the late Universe. In both approaches that allow fluctuations the thermal power spectrum at large scales is much too strongly enhanced by the late integrated Sachs-Wolfe effect. With the interacting dark matter assumption, we conclude that the Cardassian model is ruled out by observations, expect in a small neighborhood of the $\Lambda$CDM limit.

The luminosity distance-redshift relation is one of the fundamental tools of modern cosmology. We compute the luminosity distance-redshift relation in a perturbed flat matter-dominated Universe, taking into account the presence of cosmological inhomogeneities up to second order in perturbation theory. Cosmological observations implementing the luminosity distance-redshift relation tell us that the Universe is presently undergoing a phase of accelerated expansion. This seems to call for a mysterious Dark Energy component with negative pressure. Our findings suggest that the need of a Dark Energy fluid may be challenged once a realistic inhomogeneous Universe is considered and that an accelerated expansion may be consistent with a matter-dominated Universe.

We present cosmological perturbation theory based on generalized gravity theories including string theory correction terms and a tachyonic complication. The classical evolution as well as the quantum generation processes in these varieties of gravity theories are presented in unified forms. These apply both to the scalar- and tensor-type perturbations. Analyses are made based on the curvature variable in two different gauge conditions often used in the literature in Einstein’s gravity; these are the curvature variables in the comoving (or uniform-field) gauge and the zero-shear gauge. Applications to generalized slow-roll inflation and its consequent power spectra are derived in unified forms which include a wide range of inflationary scenarios based on Einstein’s gravity and others.

The thermal relic density of neutralino dark matter in the brane world cosmology is studied. Since the expansion law at a high energy regime in the brane world cosmology is modified from the one in the standard cosmology, the resultant relic density can be altered. It has been found that, if the five-dimensional Planck mass $M_5$ is lower than ${10}^4\mathrm{TeV}$, the brane world cosmological effect is significant at the decoupling time, and the resultant relic density is enhanced. We calculate the neutralino relic density in the constrained minimal supersymmetric standard model and show that the allowed region is dramatically modified from the one in the standard cosmology and eventually disappears as $M_5$ is decreasing. We also find a new lower bound on $M_5\gtrsim 600\mathrm{TeV}$ based on the neutralino dark matter hypothesis, namely, the lower bound in order for the allowed region of neutralino dark matter to exist.

The matter power spectrum at comoving scales of $(1-40)h^{-1}\mathrm{Mpc}$ is very sensitive to the presence of Warm Dark Matter (WDM) particles with large free-streaming lengths. We present constraints on the mass of WDM particles from a combined analysis of the matter power spectrum inferred from the large samples of high-resolution high signal-to-noise Lyman-$\alpha$ forest data of Kim et al. (2004) and Croft et al. (2002) and the cosmic microwave background data of WMAP. We obtain a lower limit of $m_{\mathrm{WDM}}\gtrsim 550\mathrm{eV}$ ($2\sigma$) for early decoupled thermal relics and $m_{\mathrm{WDM}}\gtrsim 2.0\mathrm{keV}$ ($2\sigma$) for sterile neutrinos. We also investigate the case where in addition to cold dark matter a light thermal gravitino with fixed effective temperature contributes significantly to the matter density. In that case the gravitino density is proportional to its mass, and we find an upper limit $m_{3/2}\lesssim 16\mathrm{eV}$ ($2\sigma$). This translates into a bound on the scale of supersymmetry breaking, ${\Lambda }_{\mathrm{susy}}\lesssim 260\mathrm{TeV}$, for models of supersymmetric gauge mediation in which the gravitino is the lightest supersymmetric particle.

We use cosmic microwave background (CMB) and large scale structure data to constrain cosmological models where the primordial perturbations have both an adiabatic and a cold dark matter (CDM) isocurvature component. We allow for a possible correlation between the adiabatic and isocurvature modes, and for different spectral indices for the power in each mode and for their correlation. We do a likelihood analysis with 11 independent parameters and discuss the effect of choosing the pivot scale for the definition of amplitude parameters. The upper limit to the isocurvature fraction is 18% around a pivot scale $k=0.01{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$. For smaller pivot wavenumbers the limit stays about the same. For larger pivot wavenumbers, very large values of the isocurvature spectral index are favored, which makes the analysis problematic, but larger isocurvature fractions seem to be allowed. For large isocurvature spectral indices $n_{\mathrm{i}\mathrm{s}\mathrm{o}}>2$ a positive correlation between the adiabatic and isocurvature mode is favored, and for $n_{\mathrm{i}\mathrm{s}\mathrm{o}}<2$ a negative correlation is favored. The upper limit to the nonadiabatic contribution to the CMB temperature variance is 7.5%. Of the standard cosmological parameters, determination of the CDM density ${\omega }_c$ and the sound horizon angle $\theta$ (or the Hubble constant $H_0$) are affected most by a possible presence of a correlated isocurvature contribution. The baryon density ${\omega }_b$ nearly retains its “adiabatic value”.

The properties of future singularities are investigated in the universe dominated by dark energy including the phantom-type fluid. We classify the finite-time singularities into four classes and explicitly present the models which give rise to these singularities by assuming the form of the equation of state of dark energy. We show the existence of a stable fixed point with an equation of state $w<-1$ and numerically confirm that this is actually a late-time attractor in the phantom-dominated universe. We also construct a phantom dark energy scenario coupled to dark matter that reproduces singular behaviors of the Big Rip type for the energy density and the curvature of the universe. The effect of quantum corrections coming from conformal anomaly can be important when the curvature grows large, which typically moderates the finite-time singularities.

Our recent theoretical analysis based on the flavor SU(3) chiral quark soliton model predicts fairly large particle-antiparticle asymmetry of the strange sea in the nucleon. We point out that the predicted magnitude of asymmetry is large enough to solely resolve the so-called NuTeV anomaly on the fundamental parameter ${sin}^2{\theta }_W$ in the standard model.

The observed flavor structure of the standard model arises naturally in “split fermion” models which localize fermions at different places in an extra dimension. It has, until now, been assumed that the bulk masses for such fermions can be chosen to be flavor diagonal simultaneously at every point in the extra dimension, with all the flavor violation coming from the Yukawa couplings to the Higgs field. We consider the more natural possibility in which the bulk masses cannot be simultaneously diagonalized, that is, that they are twisted in flavor space. We show that, in general, this does not disturb the natural generation of hierarchies in the flavor parameters. Moreover, it is conceivable that all the flavor mixing and $CP$-violation in the standard model may come only from twisting, with the five-dimensional Yukawa couplings taken to be universal.

We consider finite groups of small order for family symmetry. It is found that the binary dihedral group $Q_6$, along with the assumption that the Higgs sector is of type II, predicts mass matrix of a nearest neighbor interaction type for quarks and leptons. We present a supersymmetric model based on $Q_6$ with spontaneously induced $CP$ phases. The quark sector contains 8 real parameters with one independent phase to describe the quark masses and their mixing. Predictions in the $|V_{ub}|-\overline{\eta }$, $|V_{ub}|-\sin 2\beta ({\varphi }_1)$, and $|V_{ub}|-|V_{td}/V_{ts}|$ planes are given. The lepton sector contains also 9 parameters. A normal as well as an inverted spectrum of neutrino masses is possible, and we compute $V_{e3}$. We find that $|V_{e3}{|}^2>{10}^{-4}$ in the case of a normal spectrum, and $|V_{e3}{|}^2>8\times {10}^{-4}$ in the case of an inverted spectrum. It is also found that $Q_6$ symmetry forbids all Baryon number violating terms of $d=4$, and the contributions to EDMs from the A terms vanish in this model.

We study the action and geometry of P-vortices, discriminating between the percolating and finite clusters. We also discuss the interrelation of the monopoles and P-vortices. To define P-vortices we use both the direct maximal center projection and indirect maximal center projection. We find, in particular, that the action density of the P-vortices in short clusters is substantially higher than in the percolating cluster. The surface of the percolating cluster appears random at short distances, with action density depending on the shape.

We present one-loop results for the forward twist-two matrix elements relevant to the unpolarized, helicity and transversity baryon structure functions, in partially-quenched ($N_f=2$ and $N_f=2+1$) heavy baryon chiral perturbation theory. The full-QCD limit can be straightforwardly obtained from these results and we also consider SU$(2|2)$ quenched QCD. Our calculations are performed in finite volume as well as in infinite-volume. We discuss features of lattice simulations and investigate finite volume effects in detail. We find that volume effects are not negligible, typically around 5%–10% in current partially-quenched and full-QCD calculations, and are possibly larger in quenched QCD. Extensions to the off-forward matrix elements and potential difficulties that occur there are also discussed.

Heavy meson pairs produced in the decays of heavy quarkonium resonances at $e^{+}{e}^{-}$ machines (beauty and tau-charm factories) have the useful property that the two mesons are in the $CP$-correlated states. We show that this leads to time-independent correlations allowing the extraction of the lifetime difference $\Delta {\Gamma }_D$ and other mixing parameters. In particular, for the decay $\psi (3770)\to D^0{\overline{D}}^0$ the correlation of a flavor specific decay of one $D$ with a $CP$-specific decay of the other $D$ is linearly sensitive to the $D^0$ lifetime difference. The utility of this method is considered at CLEO-c as well as future threshold charm factories. We include the impact of possible $CP$-violating effects and present the complete results for time-integrated $CP$-entangled decay rates with $CP$ violation taken into account. We comment on the utility of using this method to extract the lifetime difference of neutral $B$ mesons at future high luminosity $B$ factories.

We consider the nonforward amplitude within the heavy quark effective theory. We show that one can obtain new information on the subleading corrections in $1/m_Q$. We illustrate the method by deriving new simple relations between the functions ${\xi }_3(w)$ and $\overline{\Lambda }\xi (w)$ and the sums $\sum _n\Delta E_j^{(n)}{\tau }_j^{(n)}(1){\tau }_j^{(n)}(w)$ $(j=\frac{1}{2},\frac{3}{2})$, that involve leading quantities, namely, the Isgur-Wise functions ${\tau }_j^{(n)}(w)$ and the level spacings $\Delta E_j^{(n)}$. Our results follow because the nonforward amplitude $B(v_i)\to D^{(n)}(v^{\prime })\to B(v_f)$ depends on three variables $(w_i,w_f,w_{if})=(v_i·v^{\prime },v_f·v^{\prime },v_i·v_f)$ independent in a certain domain, and we consider the zero recoil frontier $(w,1,w)$ where only a finite number of $j^P$ states contribute $({\frac{1}{2}}^{+},{\frac{3}{2}}^{+})$. These sum rules reduce to known results at $w=1$, for $\overline{\Lambda }$ obtained by Voloshin, and for ${\xi }_3(1)$ obtained by Le Yaouanc et al. and by Uraltsev, and generalizes them to all values of $w$. We discuss phenomenological applications of these results, in particular the check of Bakamjian-Thomas quarks models and the comparison with the QCD sum rules approach.

We present an algebraic isospin approach towards a more straightforward and model-independent determination of the weak phase $\alpha$ (or ${\varphi }_2$) and QCD penguin pollution in $B\to \pi \pi$ decays. The world averages of current experimental data allow us to impose some useful constraints on the isospin parameters of $B\to \pi \pi$ transitions. We find that the magnitude of $\alpha$ (or ${\varphi }_2$) extracted from the indirect $CP$ violation in the ${\pi }^{+}{\pi }^{-}$ mode is in agreement with the standard-model expectation from other indirect measurements, but its fourfold discrete ambiguity has to be resolved in the near future.

We report a measurement of the forward-backward charge asymmetry of electrons from $W$ boson decays in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ using a data sample of $170{\mathrm{pb}}^{-1}$ collected by the Collider Detector at Fermilab. The asymmetry is measured as a function of electron rapidity and transverse energy and provides new input on the momentum fraction dependence of the $u$ and $d$ quark parton distribution functions within the proton.

If the equation of state for “dark energy” varies periodically, the expansion of the Universe may have undergone alternating eras of acceleration and deceleration. We examine a specific form that survives existing observational tests, does not single out the present state of the Universe as exceptional, and suggests a future much like the matter-dominated past: a smooth expansion without a final inflationary epoch.

We show that the large corrections due to final-state interactions in the $D^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+},$ $D_s^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$, and $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ decays can be accounted for by invoking scattering amplitudes in agreement with those derived from phase shifts studies. In this way, broad/overlapping resonances in S-waves are properly treated and the phase motions of the transition amplitudes are driven by the scattering matrix elements determined in many other experiments. This is an important step forward in resolving the puzzle of the final-state interactions in these decays. We also discuss why the $\sigma$ and $\kappa$ resonances, hardly visible in scattering experiments, are much more prominent and clearly visible in these decays, without destroying the agreement with the experimental $\pi \pi$ and $K\pi$ low energy S-wave phase shifts.