The next generation of weak lensing surveys will trace the growth of large scale perturbations through a sequence of epochs, offering an opportunity to test general relativity on cosmological scales. We review in detail the parametrization used in MGCAMB to describe the modified growth expected in alternative theories of gravity and generalized dark energy models. We highlight its advantages and examine several theoretical aspects. In particular, we show that the same set of equations can be consistently used on superhorizon and subhorizon linear scales. We also emphasize the sensitivity of data to scale-dependent features in the growth pattern, and propose using principal component analysis to converge on a practical set of parameters which is most likely to detect departures from general relativity. The connection with other parametrizations is also discussed.

By a spherical gravitating condenser we mean two concentric charged shells made of perfect fluids restricted by the condition that the electric field is nonvanishing only between the shells. Flat space is assumed inside the inner shell. By using Israel’s formalism we first analyze the general system of $N$ shells and then concentrate on the two-shell condensers. Energy conditions are taken into account; physically interesting cases are summarized in two tables, but also more exotic situations in which, for example, the inner shell may occur below the inner horizon of the corresponding Reissner-Nordström geometry or the spacetime is curved only inside the condenser are considered. Classical limits are mentioned.

Stimulated by recent work by Sumino, on the basis of a model in which effective Yukawa coupling constants are described by vacuum expectation values of a scalar $\Phi$ with $3\times 3$ components, a possible form of the scalar potential $V(\Phi )$ which can well describe the observed charged lepton mass spectrum is investigated without referring to a specific flavor symmetry model. A general relation among eigenvalues of $⟨\Phi ⟩$ is derived without referring to an explicit form of $V(\Phi )$.

The Large Electron-Positron (LEP) collider experiments have constrained the mass of the standard model (SM) Higgs boson to be above 114.4 GeV. This bound applies to all extensions of the SM where the coupling of a Higgs boson to the $Z$ boson and also the Higgs decay profile do not differ much from the SM one. However, in scenarios with extended Higgs sectors, this coupling can be made very small by a suitable choice of the parameters of the model. In such cases, the lightest $CP$-even Higgs boson mass can in turn be made very small. Such a very light Higgs state, with a mass of the order of the $Z$ boson one or even smaller, could have escaped detection at LEP. In this work we perform a detailed parton level study on the feasibility of the detection of such a very light Higgs particle at the Large Hadron Collider (LHC) in the production process $pp\to hj\to {\tau }^{+}{\tau }^{-}j$, where $j$ is a resolved jet. We conclude that there are several models where such a Higgs state could be detected at the LHC with early data.

We investigate the connection between color confinement and thermal Abelian monopoles populating the deconfined phase of SU(2) Yang-Mills theory, by studying how the statistical properties of the monopole ensemble change as the confinement/deconfinement temperature is approached from above. In particular, we study the distribution of monopole currents with multiple wrappings in the Euclidean time direction, corresponding to two or more particle permutations, and show that multiple wrappings increase as the deconfinement temperature is approached from above, in a way compatible with a condensation of such objects happening right at the deconfining transition. We also address the question of the thermal monopole mass, showing that different definitions give consistent results only around the transition, where the monopole mass goes down and becomes of the order of the critical temperature itself.

The degenerate leptogenesis is studied when the degeneracy in two of the heavy right-handed neutrinos [the third one is irrelevant if $\mu -\tau$ symmetry is assumed] is due to $\overline{L}\equiv (L_e-L_{\mu }-L_{\tau })$ discrete symmetry. It is shown that a sizable leptogenesis asymmetry ($\epsilon \ge {10}^{-6}$) is possible. The level of degeneracy required also predicts the Majorana phase needed for the asymmetry and this prediction is testable since it is the same phase, which appears in the double $\beta$ decay. Implications of nonzero reactor angle ${\theta }_{13}$ are discussed. It is shown that the contribution from ${sin}^2{\theta }_{13}$ to the leptogenesis asymmetry parameter may even dominate. An accurate measurement of ${sin}^2{\theta }_{13}$ would have important implications for the mass degeneracy of heavy right-handed neutrinos.

We present a measurement of the top-quark pair-production cross section in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ using a data sample corresponding to $1.7{\mathrm{fb}}^{-1}$ of integrated luminosity collected with the Collider Detector at Fermilab. We reconstruct $t\overline{t}$ events in the $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ channel, consisting of $e\nu +\mathrm{\text{jets}}$ and $\mu \nu +\mathrm{\text{jets}}$ final states. The dominant background is the production of $W$ bosons in association with multiple jets. To suppress this background, we identify electrons from the semileptonic decay of heavy-flavor jets (“soft electron tags”). From a sample of 2196 candidate events, we obtain 120 tagged events with a background expectation of $51\pm 3$ events, corresponding to a cross section of ${\sigma }_{t\overline{t}}=7.8\pm 2.4(\mathrm{stat})\pm 1.6(\mathrm{syst})\pm 0.5(\mathrm{lumi})\mathrm{pb}$. We assume a top-quark mass of $175\mathrm{GeV}/c^2$. This is the first measurement of the $t\overline{t}$ cross section with soft electron tags in run II of the Tevatron.

We study spiky string solutions in ${\mathrm{AdS}}_3\times S^1$ that are characterized by two spins $S$, $J$ as well as winding $m$ in $S^1$ and spike number $n$. We construct explicitly two-cut solutions by using the $SL(2)$ asymptotic Bethe ansatz equations at leading order in strong coupling. Unlike the folded spinning string, these solutions have asymmetric distributions of Bethe roots. The solutions match the known spiky string classical results obtained directly from string theory for arbitrary semiclassical parameters, including $\mathcal{J}=0$ and any value of $\mathcal{S}$, namely, short and long strings. At large spins and winding number the string touches the boundary, and we find a new scaling limit with the energy given as $\mathcal{E}-\mathcal{S}=\frac{n}{2\pi }\sqrt{1+[(4{\pi }^2)/n^2]({\mathcal{J}}^2/{ln}^2\mathcal{S}+m^2/{ln}^2\mathcal{S})}\ln \mathcal{S}$. This is a generalization of the known scaling for the folded spinning string.

We present a more detailed picture of the infrared regime of Landau-gauge Yang-Mills theory. This is done within a novel framework that allows one to take into account the influence of finite scales within an infrared power counting analysis. We find that there are two qualitatively different infrared fixed points of the full system of Dyson-Schwinger equations. The first extends the known scaling solution, where the ghost dynamics is dominant and gluon propagation is strongly suppressed. It features in addition to the strong divergences of gluonic vertex functions in the previously considered uniform scaling limit, when all external momenta tend to zero, also weaker kinematic divergences, when only some of the external momenta vanish. The second solution represents the recently proposed decoupling scenario where the gluons become massive and the ghosts remain bare. In this case we find that none of the vertex functions is enhanced, so that the infrared dynamics is entirely suppressed. Our analysis also provides a strict argument why the Landau-gauge gluon dressing function cannot be infrared divergent.

We fabricate gravitino vertex interactions, using as only input on-shell Yang-Mills amplitudes and the Kawai-Lewellen-Tye gauge theory/gravity relations, aiming to achieve a better understanding of Kawai-Lewellen-Tye factorizations for gravitinos at an off-shell Lagrangian level. A useful by-product of this analysis is simpler tree-level Feynman rules for gravitino scattering than in traditional gauges. All results are explicitly verified until five-point scattering.

We give an analytical derivation of the mass gap of the vector $O(N)$ sigma model in two dimensions and investigate a large-order behavior of the weak-coupling asymptotic expansion for the energy. For sufficiently large $N$ the series is sign-oscillating, which is expected from the large $N$ solution of the sigma model. However, for $N=3$ and $N=4$ the series have positive coefficients.

We give an explicit example of the embedding of a near-BPS low-energy $(U(1)\times USp(2M))/{\mathbb{Z}}_2$ gauge theory into a high-energy theory with a simple gauge group and adjoint matter content. This system possesses degenerate monopoles arising from the high-energy symmetry breaking as well as non-Abelian vortices due to the symmetry breaking at low energies. These solitons of different codimensions are related by the exact homotopy sequences.

We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of anisotropic nonadiabatic radiating and dissipative distributions in general relativity. Dissipation is described by viscosity and free-streaming radiation, assuming an equation of state to model anisotropy induced by the shear viscosity. We match the interior solution, in noncomoving coordinates, with the Vaidya exterior solution. Two simple models are presented, based on the Schwarzschild and Tolman VI solutions, in the nonadiabatic and adiabatic limit. In both cases, the eventual collapse or expansion of the distribution is mainly controlled by the anisotropy induced by the viscosity.

A possible solution to the dark energy problem is that Einstein’s theory of general relativity is modified. A suite of models have been proposed that, in general, are unable to predict the correct amount of large scale structure in the distribution of galaxies or anisotropies in the cosmic microwave background. It has been argued, however, that it should be possible to constrain a general class of theories of modified gravity by focusing on properties such as the growing mode, gravitational slip, and the effective, time-varying Newton’s constant. We show that assuming certain physical requirements such as stability, metricity, and gauge invariance, it is possible to come up with consistency conditions between these various parameters. In this paper we focus on theories which have, at most, second derivatives in the metric variables and find restrictions that shed light on current and future experimental constraints without having to resort to a (as yet unknown) complete theory of modified gravity. We claim that future measurements of the growth of structure on small scales (i.e. from $1–200h^{-1}\mathrm{Mpc}$) may lead to tight constraints on both dark energy and modified theories of gravity.

We update the constraints on the fraction of the Universe going into primordial black holes in the mass range ${10}^9–{10}^{17}\mathrm{g}$ associated with the effects of their evaporations on big bang nucleosynthesis and the extragalactic photon background. We include for the first time all the effects of quark and gluon emission by black holes on these constraints and account for the latest observational developments. We then discuss the other constraints in this mass range and show that these are weaker than the nucleosynthesis and photon background limits, apart from a small range ${10}^{13}–{10}^{14}\mathrm{g}$, where the damping of cosmic microwave background anisotropies dominates. Finally we review the gravitational and astrophysical effects of nonevaporating primordial black holes, updating constraints over the broader mass range $1–{10}^{50}\mathrm{g}$.

It is possible that there exist some interactions between dark energy (DE) and dark matter (DM), and a suitable interaction can alleviate the coincidence problem. Several phenomenological interacting forms are proposed and are fitted with observations in the literature. In this paper we investigate the possible interaction in a way independent of specific interacting forms by the use of observational data (supernovae, BAO, CMB, and Hubble parameter). We divide the whole range of redshift into a few bins and set the interacting term $\delta (z)$ to be a constant in each redshift bin. We consider four parametrizations of the equation of state $w_{de}$ for DE and find that $\delta (z)$ is likely to cross the noninteracting ($\delta =0$) and have an oscillation form. It suggests that to study the interaction between DE and DM, more general phenomenological forms of the interacting term should be considered.

The nature of dark energy can be probed not only through its equation of state but also through its microphysics, characterized by the sound speed of perturbations to the dark energy density and pressure. As the sound speed drops below the speed of light, dark energy inhomogeneities increase, affecting both cosmic microwave background and matter power spectra. We show that current data can put no significant constraints on the value of the sound speed when dark energy is purely a recent phenomenon, but can begin to show more interesting results for early dark energy models. For example, the best fit model for current data has a slight preference for dynamics [$w(a)\ne -1$], degrees of freedom distinct from quintessence ($c_s\ne 1$), and early presence of dark energy [${\Omega }_{\mathrm{de}}(a\ll 1)\ne 0$]. Future data may open a new window on dark energy by measuring its spatial as well as time variation.

It has been argued that the effect of cosmological structure formation on the average expansion rate is negligible, because the linear approximation to the metric remains applicable in the regime of nonlinear density perturbations. We discuss why the arguments based on the linear theory are not valid. We emphasize the difference between Newtonian gravity and the weak field, small velocity limit of general relativity in the cosmological setting.

We derive a condition on the Lagrangian density describing a generic, single, noncanonical scalar field, by demanding that the intrinsic, nonadiabatic pressure perturbation associated with the scalar field vanishes identically. Based on the analogy with perfect fluids, we refer to such fields as perfect scalar fields. It is common knowledge that models that depend only on the kinetic energy of the scalar field (often referred to as pure kinetic models) possess no nonadiabatic pressure perturbation. While we are able to construct models that seemingly depend on the scalar field and also do not contain any nonadiabatic pressure perturbation, we find that all such models that we construct allow a redefinition of the field under which they reduce to pure kinetic models. We show that, if a perfect scalar field drives inflation, then, in such situations, the first slow roll parameter will always be a monotonically decreasing function of time. We point out that this behavior implies that these scalar fields cannot lead to features in the inflationary, scalar perturbation spectrum.