Complicated cosmic string loops will fragment until they reach simple, nonintersecting (“stable”) configurations. Through extensive numerical study we characterize these attractor loop shapes including their length, velocity, kink, and cusp distributions. We find that an initial loop containing $M$ harmonic modes will, on average, split into $3M$ stable loops. These stable loops are approximately described by the degenerate kinky loop, which is planar and rectangular, independently of the number of modes on the initial loop. This is confirmed by an analytic construction of a stable family of perturbed degenerate kinky loops. The average stable loop is also found to have a 40% chance of containing a cusp. We examine the properties of stable loops of different lengths and find only slight variation. Finally we develop a new analytic scheme to explicitly solve the string constraint equations.

We examine the evolution of a universe comprising two fluids which interact via a term proportional to the product of their densities. In the case of two matter fluids, it is shown that the ratio of the densities tends to a constant after an initial cooling-off period. We then obtain a complete solution for the cosmological constant ($w=-1$) scenario and show that periodic solutions can occur if $w<-1$. We further demonstrate that the ratio of the dark matter and dark energy densities is confined to a bounded interval and that this ratio can be $O(1)$ at infinitely many times in the history of the universe, thus solving the coincidence problem. Finally, we show that, for a certain choice of parameters, the model is a viable fit to observational constraints, and we give a detailed discussion of the past and future evolution of the universe in this particular case.

We demonstrate novel features in the behavior of the second- and third-order nonlinearity parameters of the curvature perturbation, namely $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$, arising from nonlinear motion of the curvaton field. We investigate two classes of potentials for the curvaton—the first has tiny oscillations superimposed upon the quadratic potential. The second is characterized by a single “feature” separating two quadratic regimes with different mass scales. The feature may either be a bump or a flattening of the potential. In the case of the oscillatory potential, we find that, as the width and height of superimposed oscillations increase, both $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ deviate strongly from their expected values from a quadratic potential. $f_{\mathrm{NL}}$ changes sign from positive to negative as the oscillations in the potential become more prominent. Hence, this model can be severely constrained by convincing evidence from observations that $f_{\mathrm{NL}}$ is positive. $g_{\mathrm{NL}}$, on the other hand, acquires very large negative values. Further, this model can give rise to a large running of $f_{\mathrm{NL}}$, with respect to scale. For the single-feature potential, we find that $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ exhibit oscillatory behavior as a function of the parameter that controls the feature. The running of $f_{\mathrm{NL}}$ with respect to scale is found to be small.

We investigate chiral and deconfinement transitions in the framework of the strong coupling lattice QCD for color SU(3) with one species of unrooted staggered fermion at finite temperature and quark chemical potential. We take account of the leading order Polyakov loop terms as well as the next-to-next-to-leading order ($1/g^4$) fermionic terms of the strong coupling expansion in the effective action. We investigate the Polyakov loop effects by comparing two approximation schemes, a Haar measure method (no fluctuation from the mean field) and a Weiss mean-field method (with fluctuations). The effective potential is obtained in both cases, and we analytically clarify the Polyakov loop contributions to the effective potential. The Polyakov loop is found to suppress the chiral condensate and to reduce the chiral transition temperature at $\mu =0$, and the chiral transition temperature roughly reproduces the Monte Carlo results at $\beta =2N_c/g^2\lesssim 4$. The deconfinement transition is found to be the crossover and first order for light ($a{m}_0\lesssim 4$ at $\beta =4$) and heavy quark masses, respectively.

The Cahn effect and the unintegrated unpolarized parton distribution function $f_1^q(x,{\mathbf{p}}_T)$ are studied in a covariant approach. The Cahn effect is compared with some other effects due to the parton intrinsic motion. The comparison suggests that the present understanding of parton transverse momenta and intrinsic motion in general is still rather incomplete. The new relation for $f_1^q(x,{\mathbf{p}}_T)$ is obtained in the framework of the covariant parton model from which a prediction for this distribution function follows.

We present a study of the $P$-wave spin-triplet charmonium ${\chi }_{cJ}$ decays ($J=0$, 1, 2) into ${\pi }^0{\pi }^0{\pi }^0{\pi }^0$. The analysis is based on $106\times {10}^6$ ${\psi }^{\prime }$ decays recorded with the BESIII detector at the BEPCII electron positron collider. The decay into the ${\pi }^0{\pi }^0{\pi }^0{\pi }^0$ hadronic final state is observed for the first time. We measure the branching fractions $B({\chi }_{c0}\to {\pi }^0{\pi }^0{\pi }^0{\pi }^0)=(3.34\pm 0.06\pm 0.44)\times {10}^{-3}$, $B({\chi }_{c1}\to {\pi }^0{\pi }^0{\pi }^0{\pi }^0)=(0.57\pm 0.03\pm 0.08)\times {10}^{-3}$, and $B({\chi }_{c2}\to {\pi }^0{\pi }^0{\pi }^0{\pi }^0)=(1.21\pm 0.05\pm 0.16)\times {10}^{-3}$, where the uncertainties are statistical and systematical, respectively.

The rest frame subjet algorithm is introduced to define the subjets for the SISCone jet; with this algorithm, an infrared and collinear safe jet shape observable $N$-subjettiness ${\tau }_N^j$ is defined to discriminate the fat jet, from a highly boosted color singlet particle decaying to $N$ partons, from the QCD jet. Using rest frame subjets and ${\tau }_2^j$ on dijets from highly boosted $H/W/Z$ bosons through $pp\to HW,HZ$ with $m_H=120\mathrm{GeV}$, we found that the statistical significance of the signal, from the fully hadronic channels, is about $2\sigma$ for 14 TeV collisions with $\mathcal{L}\sim 30{\mathrm{fb}}^{-1}$.

We generalize the most extensively used Gunion-Bertsch formula for the soft gluon emission in a perturbative QCD. We show that the corrections arising due to this generalization could be very important for the phenomenology of the hot and dense matter produced in the heavy-ion collisions.

We obtain the following analytical formula which describes the dependence of the electric potential of a pointlike charge on the distance away from it in the direction of an external magnetic field $B$: $\mathbf{\Phi }(z)=e/|z|[1-\exp (-\sqrt{6m_e^2}|z|)+\exp (-\sqrt{(2/\pi )e^{3}B+6m_e^2}|z|)]$. The deviation from Coulomb’s law becomes essential for $B>3\pi B_{\mathrm{cr}}/\alpha =3\pi m_e^2/e^3\approx 6\times {10}^{16}\mathrm{G}$. In such superstrong fields, electrons are ultrarelativistic except those which occupy the lowest Landau level (LLL) and which have the energy ${\epsilon }_0^2=m_e^2+p_z^2$. The energy spectrum on which LLL splits in the presence of the atomic nucleus is found analytically. For $B>3\pi B_{\mathrm{cr}}/\alpha$ it differs substantially from the one obtained without accounting for the modification of the atomic potential.

We construct all the bulk and boundary unitary cubic curvature parity invariant gravity theories in three dimensions in (anti)-de Sitter spaces. For bulk unitarity, our construction is based on the principle that the free theory of the cubic curvature theory reduces to one of the three known unitary theories which are the cosmological Einstein-Hilbert theory, the quadratic theory of the scalar curvature, or the new massive gravity (NMG). Bulk and boundary unitarity in NMG is in conflict; therefore, cubic theories that are unitary both in the bulk and on the boundary have free theories that reduce to the other two alternatives. We also study the unitarity of the Born-Infeld extensions of NMG to all orders in curvature.

We derive the equations of motion for Palatini $F(\mathcal{R})$ gravity by applying an entropy balance law $TdS=\delta Q+\delta N$ to the local Rindler wedge that can be constructed at each point of spacetime. Unlike previous results for metric $F(R)$, there is no bulk viscosity term in the irreversible flux $\delta N$. Both theories are equivalent to particular cases of Brans-Dicke scalar-tensor gravity. We show that the thermodynamical approach can be used ab initio also for this class of gravitational theories and it is able to provide both the metric and scalar equations of motion. In this case, the presence of an additional scalar degree of freedom and the requirement for it to be dynamical naturally imply a separate contribution from the scalar field to the heat flux $\delta Q$. Therefore, the gravitational flux previously associated to a bulk viscosity term in metric $F(R)$ turns out to be actually part of the reversible thermodynamics. Hence we conjecture that only the shear viscosity associated with Hartle-Hawking dissipation should be associated with irreversible thermodynamics.

We perform a comprehensive analysis of the spectrum of proper oscillations (quasinormal modes), transmission/reflection coefficients, and Hawking radiation for a massive charged scalar field in the background of the Kerr-Newman black hole immersed in an asymptotically homogeneous magnetic field. There are two main effects: the Zeeman shift of the particle energy in the magnetic field and the difference of values of an electromagnetic potential between the horizon and infinity, i.e. the Faraday induction. We have shown that “turning on” the magnetic field induces a stronger energy-emission rate and leads to “recharging” of the black hole. Thus, a black hole immersed in a magnetic field evaporates much quicker, achieving thereby an extremal state in a shorter period of time. Quasinormal modes are moderately affected by the presence of a magnetic field which is assumed to be relatively small compared to the gravitational field of the black hole.

The simplest models of inflation based on slow roll produce nearly scale invariant primordial power spectra (PPS). But there are also numerous models that predict radically broken scale invariant PPS. In particular, markedly cuspy dips in the PPS correspond to nulls where the perturbation amplitude, hence PPS, goes through a zero at a specific wave number. Near this wave number, the true quantum nature of the generation mechanism of the primordial fluctuations may be revealed. Naively these features may appear to arise from fine-tuned initial conditions. However, we show that this behavior arises under fairly generic set of conditions involving super-Hubble scale evolution of perturbation modes during inflation. We illustrate this with the well-studied examples of punctuated inflation and the Starobinsky-break model.

Present treatments of eternal inflation regulate infinities by imposing a geometric cutoff. We point out that some matter systems reach the cutoff in finite time. This implies a nonzero probability for a novel type of catastrophe. According to the most successful measure proposals, our galaxy is likely to encounter the cutoff within the next $5\times {10}^9$ years.

General relativistic corrections to the expansion rate of the Universe arise when the Einstein equations are averaged over a spatial volume in a locally inhomogeneous cosmology. It has been suggested that they may contribute to the observed cosmic acceleration. In this paper, we propose a new scheme that utilizes numerical simulations to make a realistic estimate of the magnitude of these corrections for general inhomogeneities in ($3+1$) spacetime. We then quantitatively calculate the volume averaged expansion rate using N-body large-scale structure simulations and compare it with the expansion rate in a standard FRW cosmology. We find that in the weak gravitational field limit, the converged corrections are slightly larger than the previous claimed ${10}^{-5}$ level, but not large enough nor even of the correct sign to drive the current cosmic acceleration. Nevertheless, the question of whether the cumulative effect can significantly change the expansion history of the Universe needs to be further investigated with strong-field relativity.

Observation of even a single massive cluster, especially at high redshift, can falsify the standard cosmological framework consisting of a cosmological constant and cold dark matter ($\Lambda \mathrm{CDM}$) with Gaussian initial conditions by exposing an inconsistency between the well-measured expansion history and the growth of structure it predicts. Through a likelihood analysis of current cosmological data that constrain the expansion history, we show that the $\Lambda \mathrm{CDM}$ upper limits on the expected number of massive, distant clusters are nearly identical to limits predicted by all quintessence models where dark energy is a minimally coupled scalar field with a canonical kinetic term. We provide convenient fitting formulas for the confidence level at which the observation of a cluster of mass $M$ at redshift $z$ can falsify $\Lambda \mathrm{CDM}$ and quintessence given cosmological parameter uncertainties and sample variance, as well as for the expected number of such clusters in the light cone and the Eddington bias factor that must be applied to observed masses. By our conservative confidence criteria, which equivalently require masses 3 times larger than typically expected in surveys of a few hundred square degrees, none of the presently known clusters falsify these models. Various systematic errors, including uncertainties in the form of the mass function and differences between supernova light curve fitters, typically shift the exclusion curves by less than 10% in mass, making current statistical and systematic uncertainties in cluster mass determination the most critical factor in assessing falsification of $\Lambda \mathrm{CDM}$ and quintessence.

We show that the lowest part of the eigenvalue density of the staggered fermion operator in lattice ${\mathrm{QCD}}_3$ at small lattice coupling constant $\beta$ has exactly the same shape as in ${\mathrm{QCD}}_4$. This observation is quite surprising, since universal properties of the ${\mathrm{QCD}}_3$ Dirac operator are expected to be described by a nonchiral matrix model. We show that this effect is related to the specific nature of the staggered fermion discretization and that the eigenvalue density evolves toward the nonchiral random matrix prediction when $\beta$ is increased and the continuum limit is approached. We propose a two-matrix model with one free parameter which interpolates between the two limits and very well mimics the pattern of evolution with $\beta$ of the eigenvalue density of the staggered fermion operator in ${\mathrm{QCD}}_3$.

We calculate the coupling constants of the decay modes $1^{-+}\to \rho \pi$, $f_1\pi$, $b_1\pi$, $\eta \pi$, ${\eta }^{\prime }\pi$, $a_1\pi$, $f_1\eta$ within the framework of the light-cone QCD sum rule. Then we calculate the partial width of these decay channels, which differ greatly from the existing calculations using phenomenological models. For the isovector $1^{-+}$ state, the dominant decay modes are $\rho \pi$, $f_1\pi$. For its isoscalar partner, its dominant decay mode is $a_1\pi$. We also discuss the possible search of the $1^{-+}$ state at BESIII, for example through the decay chains $J/\psi ({\psi }^{\prime })\to {\pi }_1+\gamma$ or $J/\psi ({\psi }^{\prime })\to {\pi }_1+\rho$, where ${\pi }_1$ can be reconstructed through the decay modes ${\pi }_1\to \rho \pi \to {\pi }^{+}{\pi }^{-}{\pi }^0$ or ${\pi }_1\to f_1(1285){\pi }^0$. Hopefully the present work will be helpful to the experimental establishment of the $1^{-+}$ hybrid meson.