Calculations of cosmological hydrogen recombination are vital for the extraction of cosmological parameters from cosmic microwave background (CMB) observations, and for imposing constraints to inflation and reionization. The Planck mission and future experiments will make high precision measurements of CMB anisotropies at angular scales as small as $\ell \sim 2500$, necessitating a calculation of recombination with fractional accuracy of $\approx {10}^{-3}$. Recent work on recombination includes two-photon transitions from high excitation states and many radiative transfer effects. Modern recombination calculations separately follow angular momentum sublevels of the hydrogen atom to accurately treat nonequilibrium effects at late times ($z<900$). The inclusion of extremely high-$n$ ($n\gtrsim 100$) states of hydrogen is then computationally challenging, preventing until now a determination of the maximum $n$ needed to predict CMB anisotropy spectra with sufficient accuracy for Planck. Here, results from a new multilevel-atom code (RecSparse) are presented. For the first time, “forbidden” quadrupole transitions of hydrogen are included, but shown to be negligible. RecSparse is designed to quickly calculate recombination histories including extremely high-$n$ states in hydrogen. Histories for a sequence of values as high as $n_{\max }=250$ are computed, keeping track of all angular momentum sublevels and energy shells of the hydrogen atom separately. Use of an insufficiently high $n_{\max }$ value (e.g., $n_{\max }=64$) leads to errors (e.g., $1.8\sigma$ for Planck) in the predicted CMB power spectrum. Extrapolating errors, the resulting CMB anisotropy spectra are converged to $\sim 0.5\sigma$ at Fisher-matrix level for $n_{\max }=128$, in the purely radiative case.

In Regge phenomenology, we first study the spectra of charmonium and bottomonium in the $(n,M^2)$ plane and predict masses of some charmonium and bottomonium states which have not been observed now. Then, with the aid of the additivity of intercepts and inverse slopes, we calculate the masses of ground $S$-wave and $P$-wave $c\overline{b}$ meson states and their first radial excited states. The predictions are in reasonable agreement with the existing experimental data and those suggested in many other approaches. The predictions may be useful for the discovery of the unobserved $c\overline{c}$, $b\overline{b}$, and $c\overline{b}$ mesons and the $J^P$ assignment of these states.

We study the possibility of family unification on the basis of $SO(2N)$ gauge theory on the five-dimensional space-time, $M^4\times S^1/Z_2$. Several $SO(10)$, $SU(4)\times SU(2{)}_L\times SU(2{)}_R$, or $SU(5)$ multiplets come from a single bulk multiplet of $SO(2N)$ after the orbifold breaking. Other multiplets including brane fields are necessary to compose three families of quarks and leptons.

In the recently proposed dark left-right gauge model of particle interactions, the left-handed fermion doublet $(\nu ,e{)}_{\mathrm{L}}$ is connected to its right-handed counterpart $(n,e{)}_{\mathrm{R}}$ through a scalar bidoublet, but ${\nu }_{\mathrm{L}}$ couples to $n_{\mathrm{R}}$ only through ${\varphi }_1^0$ which has no vacuum expectation value. The usual $R$ parity, i.e. $R=(-{)}^{3B+L+2j}$, can be defined for this nonsupersymmetric model so that both $n$ and ${\Phi }_1$ are odd together with $W_{\mathrm{R}}^{\pm }$. The lightest $n$ is thus a viable dark-matter candidate (scotino). Here we explore the phenomenology associated with the $SU(2{)}_{\mathrm{R}}$ gauge group of this model, which allows it to appear at the TeV energy scale. The exciting possibility of $Z^{\prime }\to 8$ charged leptons is discussed.

The Coulomb-gauge ghost propagator and the color-Coulomb potential are computed in an ensemble of configurations derived from our recently proposed Yang-Mills vacuum wave functional in $2+1$ dimensions. The results are compared to the corresponding values obtained by standard Monte Carlo simulations in three Euclidean dimensions. The agreement is quite striking for the Coulomb-gauge ghost propagator. The color-Coulomb potential rises linearly at large distances, but its determination suffers from rather large statistical fluctuations, due to configurations with very low values of ${\mu }_0$, the lowest eigenvalue of the Coulomb-gauge Faddeev-Popov operator. However, if one imposes cuts on the data, effectively leaving out configurations with very low ${\mu }_0$, the agreement of the potential in both sets of configurations is again satisfactory, although the error bars grow systematically as the cutoff is eliminated.

Within the framework of the perturbative QCD approach based on ${\mathbf{k}}_{\mathbf{T}}$ factorization, we investigate the charmless decay mode $B\to K_0^{*}(1430)\varphi$. Under two different scenarios (S1 and S2) for the description of scalar meson $K_0^{*}(1430)$, we explore the branching fractions and related $CP$ asymmetries. Besides the dominant contributions from the factorizable emission diagrams, penguin operators in the annihilation diagrams could also provide considerable contributions. The central values of our predictions are larger than those from the QCD factorization in both scenarios. Compared with the experimental measurements of the BaBar Collaboration, the result of the neutral channel in the S1 agrees with experimental data, while the result of the charged one is a bit smaller than the data. In the S2 scenario, although the central value for the branching fractions of both channels is much larger than the data, the predictions could agree with the data due to the large uncertainties to the branching fractions from the hadronic input parameters. The $CP$ asymmetry in the charged channel is small and not sensitive to the Cabibbo-Kobayashi-Maskawa angle $\gamma$. With accurate data in the near future from the various $B$ factories, these predictions will be under stringent tests.

The Polyakov-quark-meson model, which combines chiral as well as deconfinement aspects of strongly interacting matter, is introduced for three light quark flavors. An analysis of the chiral and deconfinement phase transition of the model and its thermodynamics at finite temperatures is given. Three different forms of the effective Polyakov-loop potential are considered. The findings of the $2+1$ flavor model investigations are compared to corresponding recent QCD lattice simulations of the RBC-Bielefeld, HotQCD and Wuppertal-Budapest collaborations. The influence of the heavier quark masses, which are used in the lattice calculations, is taken into account. In the transition region the bulk thermodynamics of the Polyakov-quark-meson model agrees well with the lattice data.

Using the gauge-gravity duality, we compute the leading order hadronic (HLO) contribution to the anomalous magnetic moment of muon, $a_{\mu }^{\mathrm{HLO}}$. Holographic renormalization is used to obtain a finite vacuum polarization. We find $a_{\mu }^{\mathrm{HLO}}=470.5\times {10}^{-10}$ in anti-de Sitter/QCD with two light flavors, which is compared with the currently revised BABAR data estimated from $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ events, $a_{\mu }^{\mathrm{HLO}}[\pi \pi ]=(514.1\pm 3.8)\times {10}^{-10}$.

Collective flavor transformations in supernovae, caused by neutrino-neutrino interactions, are essentially a two-flavor phenomenon driven by the atmospheric mass difference and the small mixing angle ${\theta }_{13}$. In the two-flavor approximation, the initial evolution depends logarithmically on ${\theta }_{13}$ and the system remains trapped in an unstable fixed point for ${\theta }_{13}=0$. However, any effect breaking exact ${\nu }_{\mu }-{\nu }_{\tau }$ equivalence triggers the conversion. Such three-flavor perturbations include radiative corrections to weak interactions, small differences between the ${\nu }_{\mu }$ and ${\nu }_{\tau }$ fluxes, or nonstandard interactions. Therefore, extremely small values of ${\theta }_{13}$ are in practice equivalent, the fate of the system depending only on the neutrino spectra and their mass ordering.

We consider a model for quark and lepton masses and mixings based on $S_4$ flavor symmetry. The model contains six Higgs doublets where three of them give mass to the leptons, and the other three gives mass to the quarks. Charged fermion and quark masses arise from renormalizable interactions while neutrino Majorana masses are generated through effective dimension five Weinberg operator. From the study of the minimization of the scalar potential we found a residual $\mu \leftrightarrow \tau$ symmetry in the neutrino sector predicting zero reactor angle and maximal atmospheric angle and for the quark sector we found a four-zero texture. We give a fit of the mass hierarchies and mixing angles in the quark sector.

We establish the set of independent variables suitable to monitor the complicated evolution of the spinning compact binary during the inspiral. Our approach is valid up to the second post-Newtonian order, including leading order spin-orbit, spin-spin and mass quadrupole-mass monopole effects, for generic (noncircular, nonspherical) orbits. Then, we analyze the conservative spin dynamics in terms of these variables. We prove that the only binary black hole configuration allowing for spin precessions with equal angular velocities about a common instantaneous axis roughly aligned to the normal of the osculating orbit, is the equal mass and parallel (aligned or antialigned) spin configuration. This analytic result puts limitations on what particular configurations can be selected in numerical investigations of compact binary evolutions, even in those including only the last orbits of the inspiral.

Building on a recent paper in which we computed the canonical Hamiltonian of a spinning test particle in curved spacetime, at linear order in the particle’s spin, we work out an improved effective-one-body (EOB) Hamiltonian for spinning black-hole binaries. As in previous descriptions, we endow the effective particle not only with a mass $\mu$, but also with a spin ${\mathbf{S}}_{*}$. Thus, the effective particle interacts with the effective Kerr background (having spin ${\mathbf{S}}_{\mathrm{Kerr}}$) through a geodesic-type interaction and an additional spin-dependent interaction proportional to ${\mathbf{S}}_{*}$. When expanded in post-Newtonian orders, the EOB Hamiltonian reproduces the leading order spin-spin coupling and the spin-orbit coupling through 2.5 post-Newtonian order, for any mass ratio. Also, it reproduces all spin-orbit couplings in the test-particle limit. Similarly to the test-particle limit case, when we restrict the EOB dynamics to spins aligned or antialigned with the orbital angular momentum, for which circular orbits exist, the EOB dynamics has several interesting features, such as the existence of an innermost stable circular orbit, a photon circular orbit, and a maximum in the orbital frequency during the plunge subsequent to the inspiral. These properties are crucial for reproducing the dynamics and gravitational-wave emission of spinning black-hole binaries, as calculated in numerical relativity simulations.

We study the statistical distributions of the spins of generic black-hole binaries during the inspiral and merger, as well as the distributions of the remnant mass, spin, and recoil velocity. For the inspiral regime, we start with a random uniform distribution of spin directions ${\overrightarrow{S}}_1$ and ${\overrightarrow{S}}_2$ over the sphere and magnitudes $|{\overrightarrow{S}}_1/m_1^2|=|{\overrightarrow{S}}_2/m_2^2|=0.97$ for different mass ratios, where ${\overrightarrow{S}}_i$ and $m_i$ are the spin-angular momentum and mass of the $i$th black hole. Starting from a fiducial initial separation of $R_i=50M$, we perform 3.5-post-Newtonian-order evolutions down to a separation of $R_f=5M$, where $M=m_1+m_2$, the total mass of the system. At this final fiducial separation, we compute the angular distribution of the spins with respect to the final orbital angular momentum, $\overrightarrow{L}$. We perform ${16}^4=65536$ simulations for six mass ratios between $q=1$ and $q=1/16$ and compute the distribution of the angles $\widehat{\overrightarrow{L}}·\widehat{\overrightarrow{\Delta }}$ and $\widehat{\overrightarrow{L}}·\widehat{\overrightarrow{S}}$, directly related to recoil velocities and total angular momentum. We find a small but statistically significant bias of the distribution towards counteralignment of both scalar products. A post-Newtonian analysis shows that radiation-reaction-driven dissipative effects on the orbital angular momentum lead to this bias. To study the merger of black-hole binaries, we turn to full numerical techniques. In order to make use of the numerous simulations now available in the literature, we introduce empirical formulas to describe the final remnant black-hole mass, spin, and recoil velocity for merging black-hole binaries with arbitrary mass ratios and spins. Our formulas are based on the post-Newtonian scaling, to model the plunge phase, with amplitude parameters chosen by a least-squares fit of recently available fully nonlinear numerical simulations, supplemented by inspiral losses from infinity to the innermost stable circular orbit. We then evaluate those formulas for randomly chosen directions of the individual spins and magnitudes as well as the binary’s mass ratio. The number of evaluations has been chosen such that there are 10 configurations per each dimension of this parameter space, i.e. ${10}^7$. We found that the magnitude of the recoil velocity distribution decays exponentially as $P(v)\sim \exp (-v/2500\mathrm{km}{\mathrm{s}}^{-1})$ with mean velocity $⟨v⟩=630\mathrm{km}{\mathrm{s}}^{-1}$ and standard deviation $\sqrt{⟨v^2⟩-⟨v{⟩}^2}=534\mathrm{km}{\mathrm{s}}^{-1}$, leading to a 23% probability of recoils larger than $1000\mathrm{km}{\mathrm{s}}^{-1}$, and a highly peaked angular distribution along the final orbital axis. The studies of the distribution of the final black-hole spin magnitude show a universal distribution highly peaked at $S_f/m_f^2=0.73$ and a 25° misalignment with respect to the final orbital angular momentum, just prior to full merger of the holes. We also compute the statistical dependence of the magnitude of the recoil velocity with respect to the ejection angle. The spin and recoil velocity distributions are also displayed as a function of the mass ratio. Finally, we compute the effects of the observer orientation with respect to the recoil velocity vector to take into account the probabilities to measure a given redshifted (or blueshifted) radial velocity of accretion disks with respect to host galaxies.

In this article we study a general class of nonrotating thin-shell wormholes with cylindrical symmetry. We consider two physically sound definitions of the flare-out condition and we show that the less restrictive one allows for the construction of wormholes with positive energy density at the throat. We also analyze the mechanical stability of these objects under perturbations preserving the symmetry, proving that previous results are particular cases of a general property. We present examples of wormholes corresponding to Einstein-Maxwell spacetimes.

We consider an inflationary curvaton scenario, where the curvaton decays into two noninteracting relativistic fluids and later during the cosmological evolution one of them becomes nonrelativistic, forming a dark matter component of the Universe. We study the thermic properties and the generation of non-Gaussianity in this three-fluid curvaton model. By solving the evolution of the system and using several cosmological conditions we find that the allowed parameter space is strongly constrained. The naturalness of this curvaton scenario is also discussed.

We examine the possibility of achieving quintessential inflation, where the same field serves as both inflaton and quintessence, in the context of a five-dimensional braneworld. Braneworld cosmology provides an appropriate environment as it permits inflation with much steeper potentials than the conventional scenario, which is favorable to a late-time quintessence. We explore a wide space of models, together with contemporary observational data, to determine in which contexts such a picture is possible. We find that such a scenario, although attractive, is in fact impossible to achieve for the potentials studied due to the restrictiveness of current data.

The integrated Sachs-Wolfe (ISW) effect is an important implication for dark energy. In this paper, we have calculated the power spectrum of the ISW effect in the time varying vacuum cosmological model, where the model parameter $\beta =4.407$ is obtained by the observational constraint of the growth rate. It is found that the source of the ISW effect is not only affected by the different evolutions of the Hubble function $H(a)$ and the dimensionless matter density ${\Omega }_m(a)$, but also by the different growth function $D_{+}(a)$, all of which are changed due to the presence of a matter production term in the time varying vacuum model. However, the difference of the ISW effect in the $\Lambda (t)\mathrm{CDM}$ model and the $\Lambda \mathrm{CDM}$ model is lessened to a certain extent because of the integration from the time of last scattering to the present. It is implied that the observations of the galaxies with high redshift are required to distinguish the two models.

The inhibition of the total HI $n\leftrightarrow 1$ transition rate by delayed resonant reabsorption of HI $(n+1)\to 1$ photons by HI $n\to 1$ line which is possible due to cosmological redshift is considered semianalytically. The method taking into account this effect in the frame of simple three-level approximation model of recombination is suggested. It is confirmed that the resonant feedbacks affect ionization fraction at the level about 0.2% for the epoch of last scattering. Similar consideration of $\mathrm{HeI}2{}^{1}P\leftrightarrow 1{}^{1}S\Rightarrow \mathrm{HeI}2{}^{3}P\leftrightarrow 1{}^{1}S$ feedback for helium is provided. It is confirmed that allowance of this feedback leads to an increase of predicted free electron fraction by 0.12% at $z\simeq 2300$. It is shown that taking into account absorption and thermalization of HeI $2{}^{1}P\leftrightarrow 1{}^{1}S$ resonant superequilibrium photons (during their redshifting to the HeI $2{}^{3}P\leftrightarrow 1{}^{1}S$ frequency) by a small amount of neutral hydrogen (${10}^{-7}–{10}^{-4}$ of total number of hydrogen atoms and ions) existing in the helium recombination epoch is important for correct consideration of this helium feedback.

We perform a multilepton channel analysis in the context of the Large Hadron Collider (LHC) for Wilkinson Microwave Anisotropy Probe compatible points in a model with nonuniversal scalar masses, which admits a Higgs funnel region of supersymmetry dark matter even for a small $\tan \beta$. In addition to two- and three-lepton final states, four-lepton events, too, are shown to be useful for this purpose. We also compare the collider signatures in similar channels for Wilkinson Microwave Anisotropy Probe compatible points in the minimal supergravity (mSUGRA) framework with similar gluino masses. Some definite features of such nonuniversal scenario emerge from the analysis.

We present the results of the physical point simulation in $2+1$ flavor lattice QCD with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $\beta =1.9$ on a ${32}^3\times 64$ lattice. The physical quark masses together with the lattice spacing is determined with $m_{\pi }$, $m_K$ and $m_{\Omega }$ as physical inputs. There are two key algorithmic ingredients to make possible the direct simulation at the physical point: One is the mass-preconditioned domain-decomposed HMC algorithm to reduce the computational cost. The other is the reweighting technique to adjust the hopping parameters exactly to the physical point. The physics results include the hadron spectrum, the quark masses and the pseudoscalar meson decay constants. The renormalization factors are nonperturbatively evaluated with the Schrödinger functional method. The results are compared with the previous ones obtained by the chiral extrapolation method.