We present the newest statistical and numerical analysis of the matter and cosmic microwave background power spectrum with effects of the primordial magnetic field (PMF) included. New limits to the PMF strength and power spectral index are obtained based upon the accumulated data for both the matter and CMB power spectra on small angular scales. We find that a maximum develops in the probability distribution for a magnitude of the PMF of $|B_{\lambda }|=0.85\pm 1.25(\pm 1\sigma )\mathrm{nG}$ on a comoving scale of at 1 Mpc, corresponding to upper limits of $<\mathbf{2.10}\mathrm{nG}$ (68% CL) and $<\mathbf{2.98}\mathrm{nG}$ (95% CL). While for the power spectral index we find $n_B=-{2.37}_{-0.73}^{+0.88}(\pm 1\sigma )$, corresponding to upper limits of $<-\mathbf{1.19}$ (68% CL) and $<-\mathbf{0.25}$ (95% CL). This result provides new constraints on models for magnetic field generation and the physics of the early universe. We conclude that future observational programs for the CMB and matter power spectrum will likely provide not only upper limits but also lower limits to the PMF parameters.

We investigate the validity of the generalized second law of thermodynamics, in the cosmological scenario where dark energy interacts with both dark matter and radiation. Calculating separately the entropy variation for each fluid component and for the apparent horizon itself, we show that the generalized second law is always and generally valid, independently of the specific interaction form, of the fluids equation-of-state parameters and of the background geometry.

We investigate the flavor-changing interactions in an extension of the standard model with singlet quarks and singlet Higgs, which are induced by the mixing between the ordinary quarks and the singlet quarks ($q\mathrm{\text{−}}Q$ mixing). We consider the effects of the gauge and scalar interactions in the $\Delta F=2$ mixings of $K^0$, $B_d$, $B_s$, and $D^0$ mesons to show the currently allowed range of the $q\mathrm{\text{−}}Q$ mixing. Then, we investigate the new physics around the electroweak scale to the TeV scale, which is accessible to the Large Hadron Collider. Especially, the scalar coupling mediated by the singlet Higgs may provide distinct signatures for the decays of the singlet quarks and Higgs particles, which should be compared with the conventionally expected ones via the gauge and standard Higgs couplings. Observations of the singlet quarks and Higgs particles will present us with important insights on the $q\mathrm{\text{−}}Q$ mixing and Higgs mixing.

We analyze which momentum component of the gluon field induces spontaneous chiral symmetry breaking in lattice QCD. After removing the high-momentum or low-momentum component of the gluon field, we calculate the chiral condensate and observe the roles of these momentum components. The chiral condensate is found to be drastically reduced by removing the zero-momentum gluon. The reduction is about 40% of the total in our calculation condition. The nonzero-momentum infrared gluon also has a sizable contribution to the chiral condensate. From the Banks-Casher relation, this result reflects the nontrivial relation between the infrared gluon and the zero-mode quark.

Based on a sample of $58\times {10}^{6}J/\psi$ decays collected with the BESII detector at the BEPC, the $\overline{\Lambda }$ decay parameter ${\alpha }_{\overline{\Lambda }}$ for $\overline{\Lambda }\to \overline{p}{\pi }^{+}$ is measured using about 9000 $J/\psi \to \Lambda \overline{\Lambda }\to p\overline{p}{\pi }^{+}{\pi }^{-}$ decays. A fit to the joint angular distributions yields ${\alpha }_{\overline{\Lambda }}(\overline{\Lambda }\to \overline{p}{\pi }^{+})=-0.755\pm 0.083\pm 0.063$, where the first error is statistical, and the second systematic.

We study chiral symmetry breaking in the holographic D3–D7 system in a simple model with an arbitrary running coupling. We derive equations for the D7 embedding and show there is a light pion. In particular we present simple integral equations, involving just the running coupling and the quark self-energy, for the quark condensate and the pion decay constant. We compare these to the Pagels-Stokar or constituent quark model equivalent. We discuss the implications for walking technicolor theories. We also perform a similar analysis in the four-dimensional field theory whose dual is the nonsupersymmetric D3–D5 system and propose that it represents a walking theory in which the quark condensate has dimension $2+\sqrt{3}$

$SU(N)$ gauge theories, extended with adjoint fermions having periodic boundary conditions, are confining at high temperature for sufficiently light fermion mass $m$. In the high-temperature confining region, the one-loop effective potential for Polyakov loops has a $Z(N)$-symmetric confining minimum. String tensions associated with Polyakov loops are calculable in perturbation theory, and display a novel scaling behavior in which higher representations have smaller string tensions than the fundamental representation. In the magnetic sector, the Polyakov loop plays a role similar to a Higgs field, leading to an apparent breaking of $SU(N)$ to $U(1{)}^{N-1}$. This in turn yields a dual effective theory where magnetic monopoles give rise to string tensions for spatial Wilson loops. The spatial string tensions arise semiclassically from kink solutions of the dual system. We prove that the spatial string tensions ${\sigma }_k^{(s)}$ associated with each $N$-ality $k$ are constrained by a rigorous upper bound. This bound is saturated for $N=2$ and 3, but is insufficient to determine the spatial string tension scaling law for $N\ge 4$. Lattice simulations indicate that the high-temperature confining region is smoothly connected to the confining region of low-temperature pure $SU(N)$ gauge theory. However, our results show that the string tension scaling behavior of the low-temperature region does not hold for the electric sector in the high-temperature region, and may not hold in the magnetic sector. The predicted change in the behavior of the electric sector should be readily distinguishable in lattice simulations.

We study the effects that a nonzero strong-$CP$-violating parameter $\theta$ would have on the deuteron and diproton binding energies and on the triple-alpha process. Both these systems exhibit fine-tuning, so it is plausible that a small change in the nuclear force would produce catastrophic consequences. Such a nuclear force is here understood in the framework of an effective Lagrangian for pions and nucleons, and the strength of the interaction varies with $\theta$. We find that the effects are not too dramatic.

In [T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995).] it was shown that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. More recently, in the attempt to extend the same approach to the case of $f(R)$ theories of gravity, it was found that a nonequilibrium setting is indeed required in order to fully describe both this theory as well as classical general relativity (GR) [C. Eling, R. Guedens, and T. Jacobson, Phys. Rev. Lett. 96, 121301 (2006).]. Here, elaborating on this point, we show that the dissipative character leading to nonequilibrium spacetime thermodynamics is actually related—both in GR as well as in $f(R)$ gravity—to nonlocal heat fluxes associated with the purely gravitational/internal degrees of freedom of the theory. In particular, in the case of GR we show that the internal entropy production term is identical to the so-called tidal heating term of Hartle-Hawking. Similarly, for the case of $f(R)$ gravity, we show that dissipative effects can be associated with the generalization of this term plus a scalar contribution whose presence is clearly justified within the scalar-tensor representation of the theory. Finally, we show that the allowed gravitational degrees of freedom can be fixed by the kinematics of the local spacetime causal structure, through the specific equivalence principle formulation. In this sense, the thermodynamical description seems to go beyond Einstein’s theory as an intrinsic property of gravitation.

We derive a scalar field theory of the deformed special relativity type, living on noncommutative $\kappa$-Minkowski space-time and with a $\kappa$-deformed Poincaré symmetry, from the SO(4,1) group field theory defining the transition amplitudes for topological BF theory in 4 space-time dimensions. This is done at a nonperturbative level of the spin foam formalism working directly with the group field theory (GFT). We show that matter fields emerge from the fundamental model as perturbations around a specific phase of the GFT, corresponding to a solution of the fundamental equations of motion, and that the noncommutative field theory governs their effective dynamics.

The self-adjointness of an evolution operator ${\Theta }_{\Lambda }$ corresponding to the model of the flat FRW universe with massless scalar field and cosmological constant quantized in the framework of loop quantum cosmology is studied in the case $\Lambda >0$. It is shown that, for $\Lambda <{\Lambda }_c\approx 10.3{\ell }_{\mathrm{Pl}}^{-2}$, the operator admits many self-adjoint extensions, each of the purely discrete spectrum. On the other hand for $\Lambda \ge {\Lambda }_c$ the operator is essentially self-adjoint, however the physical Hilbert space of the model does not contain any physically interesting states.

We derive the equation of state of tracker fields, which are typical examples of freezing quintessence (quintessence with the equation of state approaching toward $-1$), taking into account of the late-time departure from the tracker solution due to the nonzero density parameter of dark energy ${\Omega }_{\varphi }$. We calculate the equation of state as a function of ${\Omega }_{\varphi }$ for constant $\Gamma =V{V}^{\prime \prime }/(V^{\prime }{)}^2$ (during matter era) models. The derived equation of state contains a single parameter, $w_{(0)}$, which parametrizes the equation of state during the matter-dominated epoch. We derive observational constraints on $w_{(0)}$ and find that observational data are consistent with the cosmological constant: $-1.11<w_{(0)}<-0.96(1\sigma )$.

We continue the analysis of perturbations in vector inflation. The dominant theme of this paper is the long wavelength limit of perturbations in small fields inflation and the controversial issue of its linear stability. We explain the nature of longitudinal modes, describe how they evolve, and show that they are not as harmful as it could seem at the first glance. On the other hand, the gravitational waves’ instability in large fields models is shown explicitly. It strongly limits a potential applicability of the recently proposed $\delta N$-type approach to vector inflationary perturbations. Finally, we expose a problem of an extra (gravitational) degree of freedom which appears whenever the vector fields are nonminimally coupled to gravity.

We display some simple cosmological solutions of gravity theories with quadratic Ricci curvature terms added to the Einstein-Hilbert Lagrangian which exhibit anisotropic inflation. The Hubble expansion rates are constant and unequal in three orthogonal directions. We describe the evolution of the simplest of these homogeneous and anisotropic cosmological models from its natural initial state and evaluate the deviations they will create from statistical isotropy in the fluctuations produced during a period of anisotropic inflation. The anisotropic inflation is not a late-time attractor in these models but the rate of approach to a final isotropic de Sitter state is slow and is conducive to the creation of observable anisotropic statistical effects in the microwave background. The statistical anisotropy would not be scale invariant and the level of statistical anisotropy will grow with scale.

We explore the effect of a cubic correction $g_{\mathrm{NL}}{\varphi }^3$ on the mass function and bias of dark matter haloes extracted from a series of large N-body simulations and compare it to theoretical predictions. Such cubic terms can be motivated in scenarios like the curvaton model, in which a large cubic correction can be produced while simultaneously keeping the quadratic $f_{\mathrm{NL}}{\varphi }^2$ correction small. The deviation from the Gaussian halo mass function is in reasonable agreement with the theoretical predictions. The scale-dependent bias correction $\Delta b_{\kappa }(k,g_{\mathrm{NL}})$ measured from the auto- and cross-power spectrum of haloes, is similar to the correction in $f_{\mathrm{NL}}$ models, but the amplitude is lower than theoretical expectations. Using the compilation of LSS data in [A. Slosar et al., J. Cosmol. Astropart. Phys. 08 (2008) 031], we obtain for the first time a limit on $g_{\mathrm{NL}}$ of $-3.5\times {10}^5<g_{\mathrm{NL}}<+8.2\times {10}^5$ (at 95% CL). This limit will improve with the future LSS data by 1–2 orders of magnitude, which should test many of the scenarios of this type.

We explore general features of thermodynamic quantities and hadron mass spectra in a possible phase where chiral $SU(2{)}_L\times SU(2{)}_R$ symmetry is spontaneously broken while its center $Z_2$ symmetry remains unbroken. In this phase, chiral symmetry breaking is driven by a quartic quark condensate although a bilinear quark condensate vanishes. A Ginzburg-Landau free energy leads to a new tricritical point between the $Z_2$ broken and unbroken phases. Furthermore, a critical point can appear even in the chiral limit where explicit breaking is turned off, instead of a tricritical point at which restoration of chiral and its center symmetries takes place simultaneously. The net quark number density exhibits an abrupt change near the restoration of the center symmetry rather than that of the chiral symmetry. Hadron masses in possible phases are also studied in a linear sigma model. We show that, in the $Z_2$ symmetric phase, the $\overline{q}q$-type scalar meson with zero isospin $I=0$ splits from the $\overline{q}q$-type pseudoscalar meson with $I=1$.

We study the equation of state of a strongly interacting theory of relativistic bosons and chiral fermions in the vicinity and above the chiral phase-transition temperature. Our model resembles presently used low-energy models of QCD in many ways, but its simplicity allows us to study systematically various approximation schemes by means of a derivative expansion. In particular, we compare the results for the phase-transition temperature, equation of state, and the thermal mass of the scalar fields obtained in various approximations. We find that the large-$N_c$ approximation, being the zeroth order of our approximation, deviates significantly from approximation schemes in which effects of (pseudo-) Goldstone modes have been taken into account, even at high temperatures and even if we allow for a finite explicit symmetry breaking. The important role of the (pseudo-) Goldstone modes is also manifested in the phenomenon of “local order” which is missing in large-$N_c$ studies.

Decays of ground state $B_c$ meson $B_c\to J/\psi +n\pi$ are considered. Using existing parametrizations for $B_c\to J/\psi$ form factors and $W^{*}\to n\pi$ spectral functions we calculate branching fractions and transferred momentum distributions of $B_c\to J/\psi +n\pi$ decays for $n=1$, 2, 3, 4. Inclusive decays $B_c\to J/\psi +\overline{u}d$ and polarization asymmetries of final charmonium are also investigated. The results presented in our paper can be used to study form factors of $B_c\to J/\psi$ transitions, $\pi$-meson system spectral functions, and give the opportunity to check the factorization theorem.