We connect the translation modes of the instanton in the two-dimensional Abelian Higgs model with local translations of the vortex of the related model in ($3+1$) dimensions, the Nielsen-Olesen vortex. In this context these modes describe collective oscillations of the string. We construct the wave function of this mode and we derive, via a virial theorem, an effective action for these oscillations, which is consistent with the action constructed by Nielsen and Olesen using general arguments. We discuss some aspects of renormalization, based on a recent computation of one-loop corrections to string tension of the vortex.

$(p,q)$-strings are bound states of $p$ F-strings and $q$ D-strings and are predicted to form at the end of brane inflation. As such, these cosmic superstrings should be detectable in the Universe. In this paper we argue that they can be detected by the way that massive and massless test particles move in the space-time of these cosmic superstrings. In particular, we study solutions to the geodesic equation in the space-time of field theoretical $(p,q)$-strings. The geodesics can be classified according to the test particles’ energy, angular momentum and momentum in the direction of the string axis. We discuss how the change of the magnetic fluxes, the ratio between the symmetry-breaking scale and the Planck mass, the Higgs-to-gauge-boson mass ratios and the binding between the F- and D-strings, respectively, influence the motion of the test particles. While massless test particles can move only on escape orbits, a new feature as compared to the infinitely thin string limit is the existence of bound orbits for massive test particles. In particular, we observe that—in contrast to the space-time of a single Abelian-Higgs string—bound orbits for massive test particles in $(p,q)$-string space-times are possible if the Higgs boson mass is larger than the gauge boson mass. We also compute the effect of the binding between the $p$- and the $q$-string on observables such as the light deflection and the perihelion shift. While light deflection can also be caused by other matter distributions, the possibility of a negative perihelion shift seems to be a feature of finite width cosmic strings that could lead to the unmistakable identification of such objects. In Melvin space-times, which are asymptotically nonconical, massive test particles have to move on bound orbits, while massless test particles can escape to infinity only if their angular momentum vanishes.

It has been known for several decades that Einstein’s field equations, when projected onto a null surface, exhibit a structure very similar to the nonrelativistic Navier-Stokes equation. I show that this result arises quite naturally when gravitational dynamics is viewed as an emergent phenomenon. Extremizing the spacetime entropy density associated with the null surfaces leads to a set of equations which, when viewed in the local inertial frame, becomes identical to the Navier-Stokes equation. This is in contrast to the usual description of the Damour-Navier-Stokes equation in a general coordinate system, in which there appears a Lie derivative rather than a convective derivative. I discuss this difference, its importance, and why it is more appropriate to view the equation in a local inertial frame. The viscous force on fluid, arising from the gradient of the viscous stress-tensor, involves the second derivatives of the metric and does not vanish in the local inertial frame, while the viscous stress-tensor itself vanishes so that inertial observers detect no dissipation. We thus provide an entropy extremization principle that leads to the Damour-Navier-Stokes equation, which makes the hydrodynamical analogy with gravity completely natural and obvious. Several implications of these results are discussed.

To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.

Observational evidence for black hole spin down has been found in the normalized light curves of long gamma-ray bursts in the BATSE catalog. Over the duration $T_{90}$ of the burst, matter swept up by the central black hole is susceptible to nonaxisymmetries, producing gravitational radiation with a negative chirp. A time-sliced matched filtering method is introduced to capture phase coherence on intermediate time scales, $\tau$, here tested by the injection of templates into experimental strain noise, $h_n(t)$. For TAMA 300, $h_n(f)\simeq {10}^{-21}{\mathrm{Hz}}^{-1/2}$ at $f=1\mathrm{kHz}$ gives a sensitivity distance for a reasonably accurate extraction of the trajectory in the time-frequency domain of about $D\simeq 0.07–0.10\mathrm{Mpc}$ for the spin down of black holes of mass $M=10–12M_{\odot }$ with $\tau =1\mathrm{s}$. Extrapolation to advanced detectors implies $D\simeq 35–50\mathrm{Mpc}$ for $h_n(f)\simeq 2\times {10}^{-24}{\mathrm{Hz}}^{-1/2}$ around 1 kHz, which will open a new window to rigorous calorimetry on Kerr black holes.

We construct effective-one-body waveform models suitable for data analysis with the Laser Interferometer Space Antenna for extreme mass-ratio inspirals in quasicircular, equatorial orbits about a spinning supermassive black hole. The accuracy of our model is established through comparisons against frequency-domain, Teukolsky-based waveforms in the radiative approximation. The calibration of eight high-order post-Newtonian parameters in the energy flux suffices to obtain a phase and fractional amplitude agreement of better than 1 rad and 1%, respectively, over a period between 2 and 6 months depending on the system considered. This agreement translates into matches higher than 97% over a period between 4 and 9 months, depending on the system. Better agreements can be obtained if a larger number of calibration parameters are included. Higher-order mass-ratio terms in the effective-one-body Hamiltonian and radiation reaction introduce phase corrections of at most 30 rad in a 1 yr evolution. These corrections are usually 1 order of magnitude larger than those introduced by the spin of the small object in a 1 yr evolution. These results suggest that the effective-one-body approach for extreme mass-ratio inspirals is a good compromise between accuracy and computational price for Laser Interferometer Space Antenna data-analysis purposes.

Misner space is a two-dimensional (2D) locally flat spacetime which elegantly demonstrates the emergence of closed timelike curves from causally well-behaved initial conditions. Here we explore the motion of rigid extended objects in this time-machine spacetime. This kind of 2D time-travel is found to be risky due to inevitable self-collisions (i.e. collisions of the object with itself). However, in a straightforward four-dimensional generalization of Misner space (a physically more relevant spacetime obviously), we find a wide range of safe time-travel orbits free of any self-collisions.

The 4-dimensional effective theory arising from an induced gravity action for a codimension greater than one brane consists of multiple Galileon fields ${\pi }^I$, $I=1,\dots ,N$, invariant under separate Galilean transformations for each scalar, and under an internal $SO(N)$ symmetry. We study the viability of such models by examining spherically symmetric solutions. We find that for general, nonderivative couplings to matter invariant under the internal symmetry, such solutions exist and exhibit a Vainshtein screening effect. By studying perturbations about such solutions, we find both an inevitable gradient instability and fluctuations propagating at superluminal speeds. These findings suggest that more general, derivative couplings to matter are required for the viability of $SO(N)$ Galileon theories.

We analyze the impact of the leading quantum gravity effects on the properties of black holes with nonzero angular momentum by performing a suitable renormalization group improvement of the classical Kerr metric within quantum Einstein gravity. In particular, we explore the structure of the horizons, the ergosphere, and the static limit surfaces as well as the phase space available for the Penrose process. The positivity properties of the effective vacuum energy-momentum tensor are also discussed and the “dressing” of the black hole’s mass and angular momentum are investigated by computing the corresponding Komar integrals. The pertinent Smarr formula turns out to retain its classical form. As for their thermodynamical properties, a modified first law of black-hole thermodynamics is found to be satisfied by the improved black holes (to second order in the angular momentum); the corresponding Bekenstein-Hawking temperature is not proportional to the surface gravity.

We present a detailed analysis of results from a new study of the quantum evaporation of Callan-Giddings-Harvey-Strominger black holes within the mean-field approximation. This semiclassical theory incorporates backreaction. Our analytical and numerical calculations show that, while some of the assumptions underlying the standard evaporation paradigm are borne out, several are not. One of the anticipated properties we confirm is that the semiclassical space-time is asymptotically flat at right future null infinity ${\mathcal{I}}_{\mathrm{R}}^{+}$ yet incomplete in the sense that null observers reach a future Cauchy horizon in finite affine time. Unexpected behavior includes that the Bondi mass traditionally used in the literature can become negative even when the area of the horizon is macroscopic; an improved Bondi mass remains positive until the end of semiclassical evaporation, yet the final value can be arbitrarily large relative to the Planck mass; and the flux of the quantum radiation at ${\mathcal{I}}_{\mathrm{R}}^{+}$ is nonthermal even when the horizon area is large compared to the Planck scale. Furthermore, if the black hole is initially macroscopic, the evaporation process exhibits remarkable universal properties. Although the literature on Callan-Giddings-Harvey-Strominger black holes is quite rich, these features had escaped previous analyses, in part because of the lack of required numerical precision and in part due to misinterpretation of certain properties and symmetries of the model. Finally, our results provide support for the full quantum scenario recently developed by Ashtekar, Taveras, and Varadarajan and also offer a number of interesting problems to the mathematical relativity and geometric analysis communities.

We study the redshift drift, i.e., the time derivative of the cosmological redshift in the Lemaître-Tolman-Bondi (LTB) solution in which the observer is assumed to be located at the symmetry center. This solution has often been studied as an anti-Copernican universe model to explain the acceleration of cosmic volume expansion without introducing the concept of dark energy. One of the decisive differences between LTB universe models and Copernican universe models with dark energy is believed to be the redshift drift. The redshift drift is negative in all known LTB universe models, whereas it is positive in the redshift domain $z\lesssim 2$ in Copernican models with dark energy. However, there have been no detailed studies on this subject. In the present paper, we prove that the redshift drift of an off-center source is always negative in the case of LTB void models. We also show that the redshift drift can be positive with an extremely large hump-type inhomogeneity. Our results suggest that we can determine whether we live near the center of a large void without dark energy by observing the redshift drift.

We develop the halo model of large-scale structure as an accurate tool for probing primordial non-Gaussianity. In this study we focus on understanding the matter clustering at several redshifts in the context of primordial non-Gaussianity that is a quadratic correction to the local Gaussian potential, characterized by the parameter $f_{\mathrm{NL}}$. In our formulation of the halo model we pay special attention to the effect of halo exclusion and show that this can potentially solve the long-standing problem of excess power on large scales in this model. The halo model depends on the mass function, clustering of halo centers, and the density profiles. We test these ingredients using a large ensemble of high-resolution Gaussian and non-Gaussian numerical simulations, covering $f_{\mathrm{NL}}=\{0,+100,-100\}$. In particular, we provide a first exploration of how halo density profiles change in the presence of primordial non-Gaussianity. We find that for $f_{\mathrm{NL}}$ positive (negative) high-mass haloes have an increased (decreased) core density, so being more (less) concentrated than in the Gaussian case. We also examine the halo bias and show that, if the halo model is correct, then there is a small asymmetry in the scale dependence of the bias on very large scales, which arises because the Gaussian bias must be renormalized. We show that the matter power spectrum is modified by $\sim 2.5\%$ and $\sim 3.5\%$ on scales $k\sim 1.0h{\mathrm{Mpc}}^{-1}$ at $z=0$ and $z=1$, respectively. Our halo model calculation reproduces the absolute amplitude to within $\lesssim 10\%$ and the ratio of non-Gaussian to Gaussian spectra to within $\lesssim 1\%$. We also measure the matter correlation function and find similarly good levels of agreement between the halo model and the data. We anticipate that this modeling will be useful for constraining $f_{\mathrm{NL}}$ from measurements of the shear correlation function in future weak lensing surveys such as Euclid.

We provide a semianalytic derivation of approximate evolution equations for density perturbations of warm dark matter candidates that decoupled while relativistic with arbitrary distribution functions, their solutions at small scales, and a simple numerical implementation that yields their transfer functions and power spectra. Density perturbations evolve through three stages: radiation domination when the particle is relativistic and nonrelativistic and matter domination. An early integrated Sachs-Wolfe effect during the first stage leads to an enhancement of density perturbations and a plateau in the transfer function for $k\lesssim k_{\mathrm{fs}}$, the free-streaming wave vector. An effective fluid description emerges at small scales which includes the effects of free streaming in initial conditions and inhomogeneities. The transfer function features warm dark matter acoustic oscillations at scales $k\gtrsim 2k_{\mathrm{fs}}$. A simple analytic interpolation of the power spectra between large and small scales and a numerical implementation valid for arbitrary distribution functions is provided. As an application we study the power spectra for two models of sterile neutrinos with $m\sim \mathrm{keV}$ produced nonresonantly and compare our results to those obtained from Boltzmann codes.

We present a new estimation method for mapping the gravitational lensing potential from observed CMB intensity and polarization fields. Our method uses Bayesian techniques to estimate the average curvature of the potential over small local regions. These local curvatures are then used to construct an estimate of a low pass filter of the gravitational potential. By utilizing Bayesian/likelihood methods one can easily overcome problems with missing and/or nonuniform pixels and problems with partial sky observations (E- and B-mode mixing, for example). Moreover, our methods are local in nature, which allow us to easily model spatially varying beams, and are highly parallelizable. We note that our estimates do not rely on the typical Taylor approximation which is used to construct estimates of the gravitational potential by Fourier coupling. We present our methodology with a flat sky simulation under nearly ideal experimental conditions with a noise level of $1\mu \mathrm{K}\mathrm{\text{−}}\mathrm{arcmin}$ for the temperature field, $\sqrt{2}\mu \mathrm{K}\mathrm{\text{−}}\mathrm{arcmin}$ for the polarization fields, with an instrumental beam full width at half maximum (FWHM) of 0.25 arcmin.

Exact analytic solutions for a class of scalar-tensor gravity theories with a hyperbolic scalar potential are presented. Using an exact solution we have successfully constructed a model of inflation that produces the spectral index, the running of the spectral index, and the amplitude of scalar perturbations within the constraints given by the WMAP 7 years data. The model simultaneously describes the big bang and inflation connected by a specific time delay between them so that these two events are regarded as dependent on each other. In solving the Friedmann equations, we have utilized an essential Weyl symmetry of our theory in $3+1$ dimensions which is a predicted remaining symmetry of 2T-physics field theory in $4+2$ dimensions. This led to a new method of obtaining analytic solutions in the 1T field theory which could in principle be used to solve more complicated theories with more scalar fields. Some additional distinguishing properties of the solution includes the fact that there are early periods of time when the slow-roll approximation is not valid. Furthermore, the inflaton does not decrease monotonically with time; rather, it oscillates around the potential minimum while settling down, unlike the slow-roll approximation. While the model we used for illustration purposes is realistic in most respects, it lacks a mechanism for stopping inflation. The technique of obtaining analytic solutions opens a new window for studying inflation, and other applications, more precisely than using approximations.

We consider the massive scalar-tensor theory in the Jordan frame $F(\Phi )=K^2{\Phi }^2$ and $U(\Phi )=(1/2)m^2{\Phi }^2$, where $F(\Phi )$ corresponds to a constant Brans-Dicke parameter ${\omega }_{\mathrm{BD}}=1/4K^2$. The constraint of the Solar System experiments is $K^2<(1/400{)}^2$. For dustlike matter in a spatially flat, homogeneous isotropic universe, we reduce the equations of motion to a system of two differential equations of first order which can be exactly solved. We obtain simple and explicit expressions for $\frac{\Phi (z)}{\Phi (0)}$ and $\frac{H(z)}{H_0}$ that depend only on two parameters, $K^2$ and ${\Omega }_{m,0}$. For $K\le 1/400$, the expansion rate $H(z)$ can be practically superposed on the $\Lambda \mathrm{CDM}$ solution $H_{\Lambda }(z)$, up to high redshift $z$, but the equation of state $w_{\mathrm{DE}}(z)$ of the dark energy is not constant: it presents a very slight crossing of the phantom divide line $w=-1$ in the neighborhood of $z=0$ and becomes very slightly positive at high redshifts.

Using $f(R)$ gravity in the Palatini formularism, the metric for a charged spherically symmetric black hole is derived, taking the Ricci scalar curvature to be constant. The generalized uncertainty principle is then used to calculate the temperature of the resulting black hole; through this the entropy is found correcting the Bekenstein-Hawking entropy in this case. Using the entropy the tunneling probability and heat capacity are calculated up to the order of the Planck length, which produces an extra factor that becomes important as black holes become small, such as in the case of mini-black holes.

I investigate the phenomenology of supersymmetric models with extra vectorlike supermultiplets that couple to the standard model gauge fields and transform as the fundamental representation of a new confining non-Abelian gauge interaction. If perturbative gauge coupling unification is to be maintained, the new group can be $SU(2)$, $SU(3)$, or $SO(3)$. The impact on the sparticle mass spectrum is explored, with particular attention to the gaugino mass dominated limit in which the supersymmetric flavor problem is naturally solved. The new confinement length scale is astronomical for $SO(3)$, so the new particles are essentially free. For the $SU(2)$ and $SU(3)$ cases, the new vectorlike fermions are quirks; pair production at colliders yields quirk-antiquirk states bound by stable flux tubes that are microscopic but long compared to the new confinement scale. I study the reach of the Tevatron and LHC for the optimistic case that in a significant fraction of events the quirk-antiquirk bound state will lose most of its energy before annihilating as quirkonium.

We present a random matrix theory for the staggered lattice QCD Dirac operator. The staggered random matrix theory is equivalent to the zero-momentum limit of the staggered chiral Lagrangian and includes all taste breaking terms at their leading order. This is an extension of previous work which only included some of the taste breaking terms. We will also present some results for the taste breaking contributions to the partition function and the Dirac eigenvalues.

The hadronic parameters of pseudoscalar (${\eta }_c$) and scalar (${\chi }_c$) charmonium are determined at finite temperature from Hilbert moment QCD sum rules. These parameters are the hadron mass, leptonic decay constant, total width, and continuum threshold ($s_0$). Results for $s_0(T)$ in both channels indicate that $s_0(T)$ starts approximately constant, and then it decreases monotonically with increasing $T$ until it reaches the QCD threshold, $s_{th}=4m_Q^2$, at a critical temperature $T=T_c\simeq 180\mathrm{MeV}$ interpreted as the deconfinement temperature. The other hadronic parameters behave qualitatively similarly to those of the $J/\psi$, as determined in this same framework. The hadron mass is essentially constant, the total width is initially independent of $T$, and after $T/T_c\simeq 0.80$ it begins to increase with increasing $T$ up to $T/T_c\simeq 0.90(0.95)$ for ${\chi }_c$ (${\eta }_c$), and subsequently it decreases sharply up to $T\simeq 0.94(0.99)T_c$, for ${\chi }_c$ (${\eta }_c$), beyond which the sum rules are no longer valid. The decay constant of ${\chi }_c$ at first remains basically flat up to $T\simeq 0.80T_c$, then it starts to decrease up to $T\simeq 0.90T_c$, and finally it increases sharply with increasing $T$. In the case of ${\eta }_c$ the decay constant does not change up to $T\simeq 0.80T_c$ where it begins a gentle increase up to $T\simeq 0.95T_c$ beyond which it increases dramatically with increasing $T$. This behavior contrasts with that of light-light and heavy-light quark systems, and it suggests the survival of the ${\eta }_c$ and the ${\chi }_c$ states beyond the critical temperature, as already found for the $J/\psi$ from similar QCD sum rules. These conclusions are very stable against changes in the critical temperature in the wide range $T_c=180–260\mathrm{MeV}$.