Singularities in the thermodynamics of Kerr-Newman black holes are commonly associated with phase transitions. However, such interpretations are complicated by a lack of stability and, more significantly, by a lack of conclusive insight from microscopic models. Here, I focus on the later problem. I use the thermodynamic Riemannian curvature scalar $R$ as a try to get microscopic information from the known thermodynamics. The hope is that this could facilitate matching black hole thermodynamics to known models of statistical mechanics. For the Kerr-Newman black hole, the sign of $R$ is mostly positive, in contrast to that for ordinary thermodynamic models, where $R$ is mostly negative. Cases with negative $R$ include most of the simple critical point models. An exception is the Fermi gas, which has positive $R$. I demonstrate several exact correspondences between the two-dimensional Fermi gas and the extremal Kerr-Newman black hole. Away from the extremal case, $R$ diverges to $+\infty$ along curves of diverging heat capacities $C_{J,\Phi }$ and $C_{\Omega ,Q}$, but not along the Davies curve of diverging $C_{J,Q}$. Finding statistical mechanical models with like behavior might yield additional insight into the microscopic properties of black holes. I also discuss a possible physical interpretation of $|R|$.

The acceleration of the Universe can be explained either through dark energy or through the modification of gravity on large scales. In this paper we investigate modified gravity models and compare their observable predictions with dark energy models. Modifications of general relativity are expected to be scale independent on superhorizon scales and scale dependent on subhorizon scales. For scale-independent modifications, utilizing the conservation of the curvature scalar and a parametrized post-Newtonian formulation of cosmological perturbations, we derive results for large-scale structure growth, weak gravitational lensing, and cosmic microwave background anisotropy. For scale-dependent modifications, inspired by recent $f(R)$ theories we introduce a parametrization for the gravitational coupling $G$ and the post-Newtonian parameter $\gamma$. These parametrizations provide a convenient formalism for testing general relativity. However, we find that if dark energy is generalized to include both entropy and shear stress perturbations, and the dynamics of dark energy is unknown a priori, then modified gravity cannot in general be distinguished from dark energy using cosmological linear perturbations.

We discuss the possible role of quantum horizon fluctuations on black hole radiance, especially whether they can invalidate Hawking’s analysis based upon transplanckian modes. We are particularly concerned with “enhanced” fluctuations produced by gravitons or matter fields in squeezed vacuum states sent into the black hole after the collapse process. This allows for the possibility of increasing the fluctuations well above the vacuum level. We find that these enhanced fluctuations could significantly alter stimulated emission, but have little effect upon the spontaneous emission. Thus the thermal character of the Hawking radiation is remarkably robust.

We calculate the perihelion precession $\delta$ for nearly circular orbits in a central potential $V(r)$. Differently from other approaches to this problem, we do not assume that the potential is close to the Newtonian one. The main idea in the deduction is to apply the underlying symmetries of the system to show that $\delta$ must be a function of $r·V^{\prime \prime }(r)/V^{\prime }(r)$ and to use the transformation behavior of $\delta$ in a rotating system of reference. This is equivalent to say that the effective potential can be written in a one-parameter set of possibilities as the sum of centrifugal potential and potential of the central force. We get the following universal formula valid for $V^{\prime }(r)>0$ reading $\delta (r)=2\pi ·[\frac{1}{\sqrt{3+r·V^{\prime \prime }(r)/V^{\prime }(r)}}-1]$. It has to be read as follows: a circular orbit at this value $r$ exists and is stable if and only if this $\delta$ is well-defined as real; and if this is the case, then the angular difference from one perihelion to the next one for nearly circular orbits at this $r$ is exactly $2\pi +\delta (r)$. Then we apply this result to examples of recent interest like modified Newtonian gravity and linearized fourth-order gravity. In the second part of the paper, we generalize this universal formula to static spherically symmetric space-times $d{s}^2=-e^{2\lambda (r)}d{t}^2+e^{2\mu (r)}d{r}^2+r^{2}d{\Omega }^2$; for orbits near $r$ it reads $\delta =2\pi ·[\frac{e^{\mu (r)}}{\sqrt{3-2r·{\lambda }^{\prime }(r)+r·{\lambda }^{\prime \prime }(r)/{\lambda }^{\prime }(r)}}-1]$ and can be applied to a large class of theories. For the Schwarzschild black hole with mass parameter $m>0$ it leads to $\delta =2\pi ·[\frac{1}{\sqrt{1-\frac{6m}{r}}}-1]$, a surprisingly unknown formula. It represents a strict result and is applicable for all values $r>6m$ and is in good agreement with the fact that stable circular orbits exist for $r>6m$ only. For $r\gg m$, one can develop in powers of $m$ and get the well-known approximation $\delta \approx \frac{6\pi m}{r}$.

We consider theories in which there exists a nontrivial coupling between the dark matter sector and the sector responsible for the acceleration of the Universe. Such theories can possess an adiabatic regime in which the quintessence field always sits at the minimum of its effective potential, which is set by the local dark matter density. We show that if the coupling strength is much larger than gravitational, then the adiabatic regime is always subject to an instability. The instability, which can also be thought of as a type of Jeans instability, is characterized by a negative sound speed squared of an effective coupled dark matter/dark energy fluid, and results in the exponential growth of small scale modes. We discuss the role of the instability in specific coupled cold dark matter and mass varying neutrino models of dark energy and clarify for these theories the regimes in which the instability can be evaded due to nonadiabaticity or weak coupling.

Several recent theories suggest that light moduli or particles in “large” extra dimensions could mediate macroscopic forces exceeding gravitational strength at length scales below a millimeter. Such new forces can be parameterized as a Yukawa-type correction to the Newtonian potential of strength $\alpha$ relative to gravity and range $\lambda$. To extend the search for such new physics we have improved our apparatus utilizing cryogenic micro-cantilevers capable of measuring attonewton forces, which now includes a switchable magnetic force for calibration. Our most recent experimental constraints on Yukawa-type deviations from Newtonian gravity are more than 3 times as stringent as our previously published results and represent the best bound in the range of $5–15\mu \mathrm{m}$, with a 95% confidence exclusion of forces with $|\alpha |>14,000$ at $\lambda =10\mu \mathrm{m}$.

We use effective magnetic $SU(N)$ pure gauge theory with cutoff $M$ and fixed gauge coupling $g_m$ to calculate the nonperturbative magnetic response in the deconfined phase of $SU(N)$ Yang-Mills theory. We obtain the response to an external closed loop of electric current by reinterpreting and regulating the calculation of the one loop effective potential in Yang-Mills theory. This effective potential gives rise to a color magnetic charge density, the counterpart in the deconfined phase of color magnetic currents introduced in effective dual superconductor theories of the confined phase via magnetically charged Higgs fields. The resulting spatial Wilson loop has area law behavior. Using values of $M$ and $g_m$ determined in the confined phase, we find $SU(3)$ spatial string tensions compatible with lattice simulations in the temperature interval $1.5T_c<T<2.5T_c$. Use of the effective theory to analyze experiments on heavy ion collisions will provide applications and further tests of these ideas.

Treating the production of electron and positron pairs by a strong electric field from the vacuum as a quantum tunneling process we derive, in semiclassical approximation, a general expression for the pair-production rate in a $z$-dependent electric field $E(z)$ pointing in the $z$ direction. We also allow for a smoothly varying magnetic field parallel to $E(z)$. The result is applied to a confined field $E(z)\ne 0$ for $|z|\lesssim \ell$, a semiconfined field $E(z)\ne 0$ for $z\gtrsim 0$, and a linearly increasing field $E(z)\sim z$. The boundary effects of the confined fields on pair-production rates are exhibited. A simple variable change in all formulas leads to results for electric fields depending on time rather than space. In addition, we discuss tunneling processes in which empty atomic bound states are spontaneously filled by negative-energy electrons from the vacuum under positron emission. In particular, we calculate the rate at which the atomic levels of a bare nucleus of finite-size $r_{\mathrm{n}}$ and large $Z\gg 1$ are filled by spontaneous pair creation.

We show that the application of a novel gauge-invariant truncation scheme to the Schwinger-Dyson equations of QCD leads, in the Landau gauge, to an infrared finite gluon propagator and a divergent ghost propagator, in qualitative agreement with recent lattice data.

The behavior of Wilson loops with fractional charge is used to study the $\theta$ dependence of the free energy density $\epsilon (\theta )$ for the $C{P}^1$, $C{P}^5$, and $C{P}^9$ sigma models in two space-time dimensions. The function $\epsilon (\theta )$ is extracted from the area law for a Wilson loop of charge $q=\theta /2\pi$. For $C{P}^1$, $\epsilon (\theta )$ is smooth in the region $\theta \approx \pi$ and well described by a dilute instanton gas throughout the range $0<\theta <2\pi$. For $C{P}^5$ and $C{P}^9$ the energy exhibits a clear cusp and evidence for discrete, degenerate vacua at $\theta =\pi$, as expected from large $N$ arguments. For $C{P}^9$ the $\theta$ dependence is in good quantitative agreement with the leading-order large $N$ prediction $\epsilon (\theta )=\frac{1}{2}{\chi }_t{\theta }^2$ throughout the range $0<\theta <\pi$.

We study various correlation functions (two- and three-point functions) in a large $N$ matrix model of six commuting matrices with a numerical Monte Carlo algorithm. This is equivalent to a model of a gas of particles in six dimensions with a confining quadratic potential and logarithmic repulsions at finite temperature, where we are measuring the leading-order nongaussianities in the thermal fluctuations. This is a simplified model of the low-energy dynamics of $\mathcal{N}=4\mathrm{SYM}$ at strong coupling. We find strong evidence that the simplified matrix model matches with the dual gravitational description of three-point functions in the AdS/CFT correspondence.

In this paper we implement an improved (error-sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the Wilkinson Microwave Anisotropy Probe (WMAP) 3 year data to determine the primordial power spectrum assuming different points in the cosmological parameter space for a flat $\Lambda \mathrm{CDM}$ cosmological model. We also present the preliminary results of the cosmological parameter estimation by assuming a free form of the primordial spectrum, for a reasonably large volume of the parameter space. The recovered spectrum for a considerably large number of the points in the cosmological parameter space has a likelihood far better than a “best fit” power law spectrum up to $\Delta {\chi }_{\mathrm{eff}}^2\approx -30$. We use discrete wavelet transform (DWT) for smoothing the raw recovered spectrum from the binned data. The results obtained here reconfirm and sharpen the conclusion drawn from our previous analysis of the WMAP 1st year data. A sharp cut off around the horizon scale and a bump after the horizon scale seem to be a common feature for all of these reconstructed primordial spectra. We have shown that although the WMAP 3 year data prefers a lower value of matter density for a power law form of the primordial spectrum, for a free form of the spectrum, we can get a very good likelihood to the data for higher values of matter density. We have also shown that even a flat cold dark matter model, allowing a free form of the primordial spectrum, can give a very high likelihood fit to the data. Theoretical interpretation of the results is open to the cosmology community. However, this work provides strong evidence that the data retains discriminatory power in the cosmological parameter space even when there is full freedom in choosing the primordial spectrum.

We study the impact of a stochastic background of primordial magnetic fields on the scalar contribution of cosmic microwave background (CMB) anisotropies and on the matter power spectrum. We give the correct initial conditions for cosmological perturbations and the exact expressions for the energy density and Lorentz force associated to the stochastic background of primordial magnetic fields, given a power-law for their spectra cut at a damping scale. The dependence of the CMB temperature and polarization spectra on the relevant parameters of the primordial magnetic fields is illustrated.

We study the phase space of initial conditions for brane inflation, and find that including the effects of the Dirac-Born-Infeld (DBI) kinetic term dramatically improves previous estimates on the amount of fine-tuning of initial conditions necessary for inflation, even for models dominated by slow roll. Two effects turn out to be important for the phase space analysis: restrictions on the total available phase space due to UV effects in brane inflation, and the extension of the inflationary attractor to the DBI inflationary regime. We compare the amount of initial conditions fine-tuning required for a brane-inflation model and its standard field theory counterpart and find that brane inflation decreases the required tuning by several orders of magnitude.

The primary optical caustic surface behind a Kerr black hole is a four-cusped tube displaced from the line of sight. We derive the caustic surface in the nearly asymptotic region far from the black hole through a Taylor expansion of the lightlike geodesics up to and including fourth-order terms in $m/b$ and $a/b$, where $m$ is the black hole mass, $a$ the spin, and $b$ the impact parameter. The corresponding critical locus in the observer’s sky is elliptical and a pointlike source inside the caustics will be imaged as an Einstein cross. With regard to lensing near critical points, a Kerr lens is analogous to a circular lens perturbed by a dipole and a quadrupole potential. The caustic structure of the supermassive black hole in the Galactic center could be probed by lensing of low mass x-ray binaries in the galactic inner regions or by hot spots in the accretion disk.

The effects of absorption in the gas, and of density variations on the sensitivity of gas-filled solar-axion helioscopes, are theoretically investigated. It is concluded that the 10-meter long CAST helioscope, the most sensitive experiment to date, is near the limit of sensitivity in axion mass. Increasing the length, gas density, or tilt angle all have negative influences and will not improve the sensitivity.

Direct detection experiments rule out fermion dark matter that is a chiral representation of the electroweak gauge group. Nonchiral real, complex and singlet representations, however, provide viable fermion dark-matter candidates. Although any one of these candidates will be virtually impossible to detect at the LHC, it is shown that they may be detected at future planned direct detection experiments. For the real case, an irreducible radiative coupling to quarks may allow a detection. The complex case in general has an experimentally ruled out tree-level coupling to quarks via $Z$-boson exchange. However, in the case of two $SU(2{)}_L$ doublets, a higher-dimensional coupling to the Higgs can suppress this coupling, and a remaining irreducible radiative coupling may allow a detection. Singlet dark matter could be detected through a coupling to quarks via Higgs exchange. Since all nonchiral dark matter can have a coupling to the Higgs, at least some of its mass can be obtained from electroweak symmetry breaking, and this mass is a useful characterization of its direct detection cross section.

We study the QCD charge asymmetry in $t\overline{t}$ production at the Tevatron. We investigate the role of higher orders in perturbation theory by considering the resummation of potentially large logarithmic corrections that arise near partonic threshold. This requires us to employ the rapidity-dependent anomalous dimension matrices that describe color mixing due to soft-gluon emission in both quark- and gluon-initiated processes. The charge asymmetry appears directly in the resummed cross section at next-to-leading logarithm (NLL), and we find that the first-order expansion of the NLL-resummed charge asymmetry reproduces the known fixed-order result for the asymmetry well. Beyond its lowest order, the asymmetric component of the cross section is enhanced by the same leading-logarithmic threshold corrections as the total cross section. As a result, the charge asymmetry is robust with respect to the higher-order perturbative corrections generated by threshold resummation. We observe that the asymmetry increases with pair mass and with scattering angle.

We calculate several differential distributions for exclusive double-diffractive ${\chi }_c(0^{++})$ production in the proton-antiproton collisions at the Tevatron and in proton-proton collisions at RHIC and LHC. We use unintegrated gluon distributions (UGDFs) within the $k_t$-factorization approach. The $g^{*}{g}^{*}\to {\chi }_c(0^{++})$ transition vertex is calculated as a function of gluon virtualities via the standard perturbative nonrelativistic QCD technique. The off shell effects are discussed and quantified. They lead to a reduction of the cross section by a factor of 2–5, depending on the position in the phase space and UGDFs. Different models of UGDFs are used and the results are shown and discussed. The cross section for the diffractive component depends strongly on UGDFs. Transverse momentum distribution of ${\chi }_c(0)$ shows a well localized minimum. We calculate also the differential distributions for the ${\gamma }^{*}{\gamma }^{*}\to {\chi }_c(0^{++})$ fusion mechanism. The integrated cross section for photon-photon fusion is much smaller than that of diffractive origin. The two components have very different dependence on the momentum transfers $t_1$, $t_2$ in the nucleon lines as well as azimuthal-angle correlations between both outgoing nucleons.