The basic objects of the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction are reformulated in terms of elements of the ${\mathcal{A}}_{\theta }({\mathbb{R}}^4)$ algebra of the noncommutative ${\mathbb{R}}_{\theta }^4$ space. This new formulation of the ADHM construction makes possible the explicit calculus of the $U(2)$ instanton number which is shown to be the product of a trace of a finite rank projector of the Fock representation space of the algebra ${\mathcal{A}}_{\theta }({\mathbb{R}}^4)$ times a noncommutative version of the winding number.

Observing dark energy dynamics is the most important aspect of the current dark energy research. In this paper we perform a global analysis of the constraints on the property of dark energy from the current observations. We pay particular attention to the effects of dark energy perturbations. Using the data from SNIa (157 gold sample), WMAP, and SDSS we find that the best fitting dark energy model is given by the dynamical model with the equation of state crossing $-1$. Nevertheless the standard $\Lambda \mathrm{CDM}$ model is still a good fit to the current data and evidence for dynamics is currently not very strong. We also consider the constraints with the recent released SNIa data from Supernova Legacy Survey.

We present the interpretation of the muon and scintillation signals of ultrahigh-energy air showers observed by AGASA and Yakutsk extensive air shower array experiments. We consider case-by-case ten highest-energy events with known muon content and conclude that at the 95% confidence level none of them was induced by a primary photon. Taking into account statistical fluctuations and differences in the energy estimation of proton and photon primaries, we derive an upper limit of 36% at a 95% confidence level on the fraction of primary photons in the cosmic-ray flux above ${10}^{20}\mathrm{eV}$. This result disfavors the $Z$-burst and superheavy dark-matter solutions to the Greisen-Zatsepin-Kuzmin–cutoff problem.

We study a $CP$-violating triple product correlation that occurs in the decay of a neutral Higgs boson into $t\overline{t}$ pairs when the Higgs boson does not have a definite $CP$ nature. We consider the $H\to t\overline{t}$ decay channel as well as the gluon fusion process $gg\to H\to t\overline{t}$. The asymmetry in Higgs decay, normalized to the $H\to t\overline{t}$ width, can reach the 6% percent level. In the gluon fusion process the corresponding normalized asymmetry is smaller by an order of magnitude. We present a crude estimate of this observable at the LHC.

We report a study of the modes $B^{\pm }\to D{K}^{\pm }$ and $B^{\pm }\to D^{*}{K}^{\pm }$ where $D^{(*)}$ decays to $CP$ eigenstates. The data sample used contains $275\times {10}^{6}B\overline{B}$ events at the ${\rm Y}(4S)$ resonance collected by the Belle detector at the KEKB energy-asymmetric $e^{+}{e}^{-}$ collider. The $CP$ asymmetries obtained for $D_{CP}K$ are: ${\mathcal{A}}_1=0.06\pm 0.14(\mathrm{stat})\pm 0.05(\mathrm{sys})$, ${\mathcal{A}}_2=-0.12\pm 0.14(\mathrm{stat})\pm 0.05(\mathrm{sys})$ and for $D_{CP}^{*}K$: ${\mathcal{A}}_1^{*}=-0.20\pm 0.22(\mathrm{stat})\pm 0.04(\mathrm{sys})$, ${\mathcal{A}}_2^{*}=0.13\pm 0.30(\mathrm{stat})\pm 0.08(\mathrm{sys})$.

We introduce a new conservative test for quantifying the consistency of two or more datasets. The test is based on the Bayesian answer to the question, “How much more probable is it that all my data were generated from the same model system than if each dataset were generated from an independent set of model parameters?” We make explicit the connection between evidence ratios and the differences in peak chi-squared values, the latter of which are more widely used and more cheaply calculated. Calculating evidence ratios for three cosmological datasets [recent cosmic microwave background data (WMAP, ACBAR, CBI, VSA), SDSS galaxy redshift survey, and the most recent SNe type 1A data] we find that concordance is favored and the tightening of constraints on cosmological parameters is indeed justified.

By using the Dirac-Born-Infeld action we study the dynamics of $Dp$-brane propagating in the NS5-near-horizon plane wave background. We study systematically $D$-brane embedding in this $pp$-wave background, and analyze the equations of motion for various auxiliary fields. We further discuss the motion of the probe $Dq$-brane in the presence of source $Dp$-branes in this plane wave background.

Charged particles in static electric and magnetic fields have Landau levels and tunneling states from the vacuum. Using the instanton method of Phys. Rev. D 65, 105002 (2002), we obtain the formulas for the pair-production rate in spinor and scalar QED, which sum over all Landau levels and recover exactly the well-known results. The pair-production rates are calculated for an electric field of finite extent, and for the Sauter potential, both with a constant magnetic field also present, and are shown to have finite-size effects.

The problem of constructing consistent parity-violating interactions for spin-3 gauge fields is considered in Minkowski space. Under the assumptions of locality, Poincaré invariance, and parity noninvariance, we classify all the nontrivial perturbative deformations of the Abelian gauge algebra. In space-time dimensions $n=3$ and $n=5$, deformations of the free theory are obtained which make the gauge algebra non-Abelian and give rise to nontrivial cubic vertices in the Lagrangian, at first order in the deformation parameter $g$. At second order in $g$, consistency conditions are obtained which the five-dimensional vertex obeys, but which rule out the $n=3$ candidate. Moreover, in the five-dimensional first-order deformation case, the gauge transformations are modified by a new term which involves the second de Wit-Freedman connection in a simple and suggestive way.

It is shown that Eppley and Hannah’s thought experiment establishing that gravity must be quantized is fatally flawed. The device they propose, even if built, cannot establish their claims, nor is it plausible that it can be built with any materials compatible with the values of $c$, $\hslash$, $G$. Finally the device, and any reasonable modification of it, would be so massive as to be within its own Schwarzschild radius—a fatal flaw for any thought experiment.

We consider how the mass of the black hole decreases due to the Hawking radiation in the Vaidya spacetime, using the concept of the dynamical horizon equation, proposed by Ashtekar and Krishnan. Using the formula for the change of the dynamical horizon, we derive an equation for the mass incorporating the Hawking radiation. It is shown that the final state is the Minkowski spacetime in our particular model.

We present an analytic method based on the Hadamard-WKB expansion to calculate the self-force for a particle with scalar charge that undergoes radial infall in a Schwarzschild spacetime after being held at rest until a time $t=0$. Our result is valid in the case of short duration from the start. It is possible to use the Hadamard-WKB expansion in this case because the value of the integral of the retarded Green’s function over the particle’s entire past trajectory can be expressed in terms of two integrals over the time period that the particle has been falling. This analytic result is expected to be useful as a check for numerical prescriptions including those involving mode-sum regularization and for any other analytical approximations to self-force calculations.

We study the nonlinear propagator, a key ingredient in renormalized perturbation theory (RPT) that allows a well-controlled extension of perturbation theory into the nonlinear regime. We show that it can be thought as measuring the memory of density and velocity fields to their initial conditions. This provides a clean definition of the validity of linear theory, which is shown to be much more restricted than usually recognized in the literature. We calculate the nonlinear propagator in RPT and compare to measurements in numerical simulations, showing remarkable agreement well into the nonlinear regime. We also show that N-body simulations require a rather large volume to recover the correct propagator, due to the missing large-scale modes. Our results for the nonlinear propagator provide an essential element to compute the nonlinear power spectrum in RPT.

We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing nonlinearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbation theory, where different loop corrections can become of the same magnitude in the nonlinear regime. In companion papers we compare the resummation of the propagator with numerical simulations, and apply these results to the calculation of the nonlinear power spectrum. Remarkably, the expressions in renormalized perturbation theory can be written in a way that closely resembles the halo model.

The thermal relic density of $W$-ino-like neutralino dark matter in brane world cosmology is studied. The expansion law at a high energy regime in brane world cosmology is modified from the one in standard cosmology, and the resultant relic density can be enhanced if the five-dimensional Planck mass $M_5$ is low enough. We calculate the $W$-ino-like neutralino relic density in the anomaly mediated supersymmetry breaking scenario and show that the allowed region is dramatically modified from the one in standard cosmology and the $W$-ino-like neutralino with mass of order 100 GeV can be a good candidate for dark matter. Since the allowed region disappears eventually as $M_5$ decreases, we can find a lower bound on $M_5\gtrsim 100\mathrm{TeV}$ according to the neutralino dark matter hypothesis, namely, the lower bound in order for the allowed region of neutralino dark matter to exist.

We argue that cosmic strings with high winding numbers generally form in first-order gauge symmetry breaking phase transitions, and we demonstrate this using computer simulations. These strings are heavier than single-winding strings and therefore more easily observable. Their cosmological evolution may also be very different.

We investigate the possibility of testing cosmological models with interaction between dark matter and the dark energy sector. We assume the standard Friedmann-Robertson-Walker (FRW) model while the so called the energy conservation condition is interpreted locally in terms of energy transfer. We analyze two forms of the dark energy sector: the cosmological constant and the phantom field. We find a simple exact solution of the models in which energy transfer is described by a Cardassian like term in the relation of $H^2(z)$, where $H$ is Hubble’s function and $z$ is redshift. The considered models have two additional parameters $({\Omega }_{\mathrm{int}},n)$ (apart from the parameters of the $\Lambda \mathrm{CDM}$ model) which can be tested using SNIa data. In the estimation of the model parameters both Riess et al.’s and Astier et al.’s samples are used. We also confront the quality of statistical fits for both the $\Lambda \mathrm{CDM}$ model and the interacting models with the help of the Akaike and Bayesian information criteria. Our conclusion from the standard best fit method is that the interacting models explain the acceleration of the Universe better but they give rise to a universe with high matter density. However, using the tools of information criteria we find that the two new parameters play an insufficient role in improving the fit to SNIa data and the standard $\Lambda \mathrm{CDM}$ model is still preferred. We conclude that high precision detection of high redshift supernovae could supply data capable of justifying the adoption of new parameters.

A modified model of gravity with additional positive and negative powers of the scalar curvature, $R$, in the gravitational action is studied. This is done using the Palatini variational principle. It is demonstrated that using such a model might prove useful to explain both the early time inflation and the late time cosmic acceleration without the need for any form of dark energy.

We show that inflation in a false vacuum becomes viable in the presence of a spectator scalar field nonminimally coupled to gravity. The field is unstable in this background; it grows exponentially and slows down the pure de Sitter phase itself, allowing then fast tunneling to a true vacuum. We compute the constraint from graceful exit through bubble nucleation and the spectrum of cosmological perturbations.

I consider constraints from observations on a cutoff scale in clustering due to free streaming of the dark matter in a warm dark matter cosmological model with a cosmological constant. The limits are derived in the framework of a sterile neutrino warm dark matter universe, but can be applied to gravitinos and other models with small-scale suppression in the linear matter power spectrum. With freedom in all cosmological parameters including the free streaming scale of the sterile neutrino dark matter, limits are derived using observations of the fluctuations in the cosmic microwave background, the 3D clustering of galaxies and 1D clustering of gas in the Lyman-alpha ($\mathrm{Ly}\alpha$) forest in the Sloan Digital Sky Survey (SDSS), as well as the $\mathrm{Ly}\alpha$ forest in high-resolution spectroscopic observations. In the most conservative case, using only the SDSS main-galaxy 3D power-spectrum shape, the limit is $m_s>0.11\mathrm{keV}$; including the SDSS $\mathrm{Ly}\alpha$ forest, this limit improves to $m_s>1.7\mathrm{keV}$. More stringent constraints may be placed from the inferred matter power spectrum from high-resolution $\mathrm{Ly}\alpha$ forest observations, which has significant systematic uncertainties; in this case, the limit improves to $m_s>3.0\mathrm{keV}$ (all at 95% CL).