We investigate the dynamics of superinflation in two versions of loop quantum cosmology, one in which the Friedmann equation is modified by the presence of inverse volume corrections, and one in which quadratic corrections are important. Computing the tilt of the power spectrum of the perturbed scalar field in terms of fast-roll parameters, we conclude that the first case leads to a power spectrum that is scale invariant for steep power law negative potentials and for the second case, scale invariance is obtained for positive potentials that asymptote to a constant value for large values of the scalar field. It is found that in both cases, the horizon problem is solved with only a few e-folds of superinflationary evolution.

We consider direct dark matter detection rates and investigate the difference between a standard Maxwell-Boltzmann velocity distribution and a “realistic” distribution like the ones extracted from numerical $N$-body simulations. Sizable differences are observed when such results are compared to the standard Maxwell-Boltzmann distribution. For a light target both the total rate and the annual modulation are reduced by $\sim 25\%$. For a heavy target the total rate is virtually unchanged, whereas the annual modulation is modified by up to 50%, depending on the weakly interacting massive particle mass and detector energy threshold. We also consider the effect of a possible velocity anisotropy, and the effect is found to be largest for a light target. For the realistic velocity distribution the anisotropy may reduce the annual modulation, in contrast to the Maxwell-Boltzmann case.

We compute the static potential associated with the locally $1/2$ BPS Wilson loop in $\mathcal{N}=4$ supersymmetric Yang-Mills theory with $\mathcal{O}({\lambda }^2/r)$ accuracy. We also resum the leading logarithms, of $\mathcal{O}({\lambda }^{n+1}{ln}^n\lambda /r)$, and show the structure of the renormalization group equation at next-to-leading order in the multipole expansion. In order to obtain these results it is crucial to use an effective theory for the ultrasoft degrees of freedom. We develop this theory up to next-to-leading order in the multipole expansion. Using the same formalism we also compute the leading logarithms, of $\mathcal{O}({\lambda }^{n+1}{ln}^n\lambda /r)$, of the static potential associated with an ordinary Wilson loop in the same theory.

A natural extension of the standard $\mathrm{SU}(2{)}_{\mathrm{L}}\times \mathrm{U}(1{)}_{\mathrm{Y}}$ gauge model to accommodate massive neutrinos is to introduce one Higgs triplet and three right-handed Majorana neutrinos, leading to a $6\times 6$ neutrino mass matrix which contains three $3\times 3$ submatrices, $M_{\mathrm{L}}$, $M_{\mathrm{D}}$ and $M_{\mathrm{R}}$. We show that three light Majorana neutrinos (i.e., the mass eigenstates of ${\nu }_e$, ${\nu }_{\mu }$, and ${\nu }_{\tau }$) are exactly massless in this model, if and only if $M_{\mathrm{L}}=M_{\mathrm{D}}{M}_{\mathrm{R}}^{-1}{M}_{\mathrm{D}}^T$ exactly holds. This no-go theorem implies that small but nonvanishing neutrino masses may result from a significant but incomplete cancellation between $M_{\mathrm{L}}$ and $M_{\mathrm{D}}{M}_{\mathrm{R}}^{-1}{M}_{\mathrm{D}}^T$ terms in the Type-II seesaw formula, provided three right-handed Majorana neutrinos are of $\mathcal{O}(1)\mathrm{TeV}$ and experimentally detectable at the LHC. We propose three simple Type-II seesaw scenarios with the $A_4\times \mathrm{U}(1{)}_{\mathrm{X}}$ flavor symmetry and its explicit breaking to interpret the observed neutrino mass spectrum and neutrino mixing pattern. Such a TeV-scale neutrino model can be tested in two complementary ways: (1) searching for possible collider signatures of lepton number violation induced by the right-handed Majorana neutrinos and doubly-charged Higgs particles; and (2) searching for possible consequences of unitarity violation of the $3\times 3$ neutrino mixing matrix in the future long-baseline neutrino oscillation experiments.

Higgs boson production in association with a high $p_T$ photon at the CERN Large Hadron Collider is analyzed, in the framework of the MSSM model, for the heavier neutral Higgs bosons. The request of an additional photon in the exclusive Higgs boson final state selects $b$-quark pairs among the possible initial partonic states, since gluon-gluon initial states are not allowed by C-parity conservation. Hence, the measurement of cross sections for neutral Higgs boson plus photon production can provide a clean probe of the $b$-quark density in the proton as well as of the $b$-quark Yukawa coupling. The suppression of the production rates by the $b$-quark electromagnetic coupling can be compensated by the enhanced Higgs boson Yukawa coupling to $b$’s in the large $\tan \beta$ regime. The Higgs boson decay into a tau-lepton pair is considered, and irreducible backgrounds with corresponding signal significances are evaluated.

The $I=2$ $\pi \pi$ scattering length is calculated in fully dynamical lattice QCD with domain-wall valence quarks on the asqtad-improved coarse MILC configurations (with fourth-rooted staggered sea quarks) at four light-quark masses. Two- and three-flavor mixed-action chiral perturbation theory at next-to-leading order is used to perform the chiral and continuum extrapolations. At the physical charged pion mass, we find $m_{\pi }{a}_{\pi \pi }^{I=2}=-0.04330\pm 0.00042$, where the error bar combines the statistical and systematic uncertainties in quadrature.

Existence of color sextet diquark Higgs fields with TeV masses will indicate a fundamentally different direction for unification than conventional grand unified theories. One class of models where they appear naturally is the supersymmetric $SU(2{)}_L\times SU(2{)}_R\times SU(4{)}_c$ model embedding the seesaw mechanism for neutrino mass with seesaw scale around ${10}^{11}\mathrm{GeV}$. The diquark Higgs fields in this model couple only to up-type quarks. We discuss phenomenological constraints on these fields and show that they could be detected at LHC via their decay to either $tt$ or single $\mathrm{\text{top}}+\mathrm{\text{jet}}$. We also find that existing Tevatron data gives a lower bound on its mass somewhere in the 400–500 GeV, for reasonable values of its coupling.

We show that regular changes of signature on brane worlds in ${\mathrm{AdS}}_5$ bulks may account for some types of the recently fashionable sudden singularities. Therefore, the possibility that the Universe seems to approach a future sudden singularity at an accelerated rate of expansion might simply be an indication that our brane world is about to change from Lorentzian to Euclidean signature. Both the brane and the bulk remain fully regular everywhere. We present a model in which the weak and strong energy conditions hold on the brane, in contrast with the standard cosmologies leading to the analogous kinematical behavior (that is, with a diverging Hubble factor).

Recent computations of scattering amplitudes show that $\mathcal{N}=8$ supergravity is surprisingly well behaved in the ultraviolet and may even be ultraviolet finite in perturbation theory. The novel cancellations necessary for ultraviolet finiteness first appear at one loop in the guise of the “no-triangle hypothesis.” We study one-loop amplitudes in pure Einstein gravity and point out the existence of cancellations similar to those found previously in $\mathcal{N}=8$ supergravity. These cancellations go beyond those found in the one-loop effective action. Using unitarity, this suggests that generic theories of quantum gravity based on the Einstein-Hilbert action may be better behaved in the ultraviolet at higher loops than suggested by naive power counting, though without additional (supersymmetric) cancellations they diverge. We comment on future studies that should be performed to support this proposal.

We explore the geometric phase in $\mathcal{N}=(2,2)$ supersymmetric quantum mechanics. The Witten index ensures the existence of degenerate ground states, resulting in a non-Abelian Berry connection. We exhibit a nonrenormalization theorem which prohibits the connection from receiving perturbative corrections. However, we show that it does receive corrections from BPS instantons. We compute the one-instanton contribution to the Berry connection for the massive $C{P}^1$ sigma-model as the potential is varied. This system has two ground states and the associated Berry connection is the smooth $SU(2)$ ’t Hooft-Polyakov monopole.

We use a combination of numerical and analytical methods, exploiting the equations derived in a preceding paper, to classify all spherically symmetric self-similar solutions which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state $p=(\gamma -1)\mu$ with $0<\gamma <2/3$. The expansion of the Friedmann universe is accelerated in this case. We find a one-parameter family of self-similar solutions representing a black hole embedded in a Friedmann background. This suggests that, in contrast to the positive pressure case, black holes in a universe with dark energy can grow as fast as the Hubble horizon if they are not too large. There are also self-similar solutions which contain a central naked singularity with negative mass and solutions which represent a Friedmann universe connected to either another Friedmann universe or some other cosmological model. The latter are interpreted as self-similar cosmological white hole or wormhole solutions. The throats of these wormholes are defined as two-dimensional spheres with minimal area on a spacelike hypersurface and they are all nontraversable because of the absence of a past null infinity.

Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state $p=(\gamma -1)\mu$ with $0<\gamma <2/3$. This corresponds to a “dark energy” fluid and the Friedmann solution is accelerated in this case due to antigravity. This extends the previous analysis of spherically symmetric self-similar solutions for fluids with positive pressure ($\gamma >1$). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically “quasi-Friedmann,” in the sense that they exhibit an angle deficit at large distances. In the $0<\gamma <2/3$ case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions.

It has been suggested that infrared gravitons in de Sitter space may lead to a secular screening of the effective cosmological constant. This seems to clash with the naive expectation that the curvature scalar should stay constant due to the Heisenberg equation of motion. Here, we show that the tadpole correction to the local expansion rate, which has been used in earlier analyses as an indicator of a decaying effective $\Lambda$, is not gauge invariant. On the other hand, we construct a gauge-invariant operator which measures the renormalized curvature scalar smeared over an arbitrary window function, and we find that there is no secular screening of this quantity (to any given order in perturbation theory).

We calculate the quantum radiation from the 5-dimensional charged rotating black rings by demanding the radiation eliminate the possible anomalies on the horizons. It is shown that the temperature, energy flux, and angular-momentum flux exactly coincide with those of the Hawking radiation. The black rings considered in this paper contain the Myers-Perry black hole as a limit, and the quantum radiation for this black hole, obtained in the literature, is recovered in the limit. The results support the picture that the Hawking radiation can be regarded as the anomaly eliminator on horizons and suggest its general applicability to the higher-dimensional black holes discovered recently.

We use a post-Newtonian diagnostic tool to examine numerically generated quasiequilibrium initial data sets for nonspinning double neutron star and neutron star–black hole binary systems. The post-Newtonian equations include the effects of tidal interactions, parametrized by the compactness of the neutron stars and by suitable values of “apsidal” constants, which measure the degree of distortion of stars subjected to tidal forces. We find that the post-Newtonian diagnostic agrees well with the double neutron star initial data, typically to better than half a percent except where tidal distortions are becoming extreme. We show that the differences could be interpreted as representing small residual eccentricity in the initial orbits. In comparing the diagnostic with preliminary numerical data on neutron star–black hole binaries, we find less agreement.

Generalizing the method of Wilczek and collaborators we provide a derivation of Hawking radiation from charged black holes using only covariant gauge and gravitational anomalies. The reliability and universality of the anomaly cancellation approach to Hawking radiation is also discussed.

Modified gravity provides a possible explanation for the currently observed cosmic acceleration. In this paper, we study general classes of modified gravity models. The Einstein-Hilbert action is modified by using general functions of the Ricci and the Gauss-Bonnet scalars, both in the metric and in the Palatini formalisms. We do not use an explicit form for the functions, but a general form with a valid Taylor expansion up to second order about redshift zero in the Riemann-scalars. The coefficients of this expansion are then reconstructed via the cosmic expansion history measured using current cosmological observations. These are the quantities of interest for theoretical considerations relating to ghosts and instabilities. We find that current data provide interesting constraints on the coefficients. The next-generation dark energy surveys should shrink the allowed parameter space for modified gravity models quite dramatically.

Cosmological tensor perturbations equations are derived for Hamiltonian cosmology based on Ashtekar’s formulation of general relativity, including typical quantum gravity effects in the Hamiltonian constraint as they are expected from loop quantum gravity. This translates to corrections of the dispersion relation for gravitational waves. The main application here is the preservation of causality which is shown to be realized due to the absence of anomalies in the effective constraint algebra used.

We discuss observational consequences of $f(R)$ dark energy scenarios that satisfy local gravity constraints (LGC) as well as conditions of the cosmological viability. The model we study is given by $m(r)=C(-r-1{)}^p$ ($C>0$, $p>1$) with $m=R{f}_{,RR}/f_{,R}$ and $r=-R{f}_{,R}/f$, which covers viable $f(R)$ models proposed so far in a high-curvature region designed to be compatible with LGC. The equation of state of dark energy exhibits a divergence at a redshift $z_c$ that can be as close as a few while satisfying sound horizon constraints of the cosmic microwave background (CMB). We study the evolution of matter density perturbations in detail and place constraints on model parameters from the difference of spectral indices of power spectra between CMB and galaxy clustering. The models with $p\ge 5$ can be consistent with those observational constraints as well as LGC. We also discuss the evolution of perturbations in the Ricci scalar $R$ and show that an oscillating mode (scalaron) can easily dominate over a matter-induced mode as we go back to the past. This violates the stability of cosmological solutions, thus posing a problem about how the overproduction of scalarons should be avoided in the early universe.

We give a gravitational upper limit for the mass of static degenerate fermionic dark matter objects. The treatment we use includes fully relativistic equations for describing the static solutions of these objects. We study the influence of the annihilation of the particles on this mass limit. We give the change of its value over the age of the Universe with annihilation cross sections relevant for such fermions constituting the dark matter. Our calculations take into account the possibility of Dirac as well Majorana spinors.