We explore the dynamics of cosmological models with two coupled dark components with energy densities ${\rho }_A$ and ${\rho }_B$ and constant equation of state (EOS) parameters $w_A$ and $w_B$. We assume that the coupling is of the form $Q=Hq({\rho }_A,{\rho }_B)$, so that the dynamics of the two components turns out to be scale independent, i.e. does not depend explicitly on the Hubble scalar $H$. With this assumption, we focus on the general linear coupling $q=q_o+q_A{\rho }_A+q_B{\rho }_B$, which may be seen as arising from any $q({\rho }_A,{\rho }_B)$ at late time and leads in general to an effective cosmological constant. In the second part of the paper we consider observational constraints on the form of the coupling from SN Ia data, assuming that one of the components is cold dark matter (CDM), i.e. $w_B=0$, while for the other the EOS parameter can either have a standard ($w_A>-1$) or phantom ($w_A<-1$) value. We find that the constant part of the coupling function is unconstrained by SN Ia data and, among typical linear coupling functions, the one proportional to the dark energy density ${\rho }_A$ is preferred in the strong coupling regime, $|q_A|>1$. Models with phantom $w_A$ favor a positive coupling function, increasing ${\rho }_A$. In models with standard $w_A$, not only a negative coupling function is allowed, transferring energy to CDM, but the uncoupled subcase falls at the border of the likelihood.

This article investigates the nonlinear evolution of cosmological perturbations on sub-Hubble scales in order to evaluate the unavoidable deviations from Gaussianity that arise from the nonlinear dynamics. It shows that the dominant contribution to modes coupling in the cosmic microwave background temperature anisotropies on small angular scales is driven by the sub-Hubble nonlinear evolution of the dark matter component. The perturbation equations, involving, in particular, the first moments of the Boltzmann equation for photons, are integrated up to second order in perturbations. An analytical analysis of the solutions gives a physical understanding of the result as well as an estimation of its order of magnitude. This allows one to quantify the expected deviation from Gaussianity of the cosmic microwave background temperature anisotropy and, in particular, to compute its bispectrum on small angular scales. Restricting to equilateral configurations, we show that the nonlinear evolution accounts for a contribution that would be equivalent to a constant primordial non-Gaussianity of order $f_{\mathrm{NL}}\sim 25$ on scales ranging approximately from $\ell \sim 1000$ to $\ell \sim 3000$.

Quantum fluctuations in the post-inflationary Affleck-Dine baryogenesis model are studied. The squeezed states formalism is used to give evolution equations for the particle and antiparticle modes in the early universe. The role of expansion and parametric amplification of the quantum fluctuations on the baryon asymmetry produced is investigated.

In this paper I examine cosmological models that contain a stochastic background of nonlinear electromagnetic radiation. I show that for Born-Infeld electrodynamics the equation of state parameter, $w=P/\rho$, remains close to $1/3$ throughout the evolution of the universe if $E^2=B^2$ in the late universe to a high degree of accuracy. Theories with electromagnetic Lagrangians of the form $L=-\frac{1}{4}{F}^2+\alpha F^4$ have recently been studied in magnetic universes, where the electric field vanishes. It was shown that the $F^4$ term can produce a bounce in the early universe, avoiding an initial singularity. Here I show that the inclusion of an electric field, with $E^2\simeq B^2$ in the late universe, eliminates the bounce and the universe begins with an initial singularity. I also examine theories with Lagrangians of the form $L=-\frac{1}{4}{F}^2-{\mu }^8/F^2$, which have been shown to produce a period of late time accelerated expansion in magnetic universes. I show that, if an electric field is introduced, the accelerated phase will only occur if $E^2<3B^2$.

We study cosmological perturbations in general inflation models with multiple scalar fields and arbitrary kinetic terms, with special emphasis on the multifield extension of Dirac-Born-Infeld (DBI) inflation. We compute the second-order action governing the dynamics of linear perturbations in the most general case. Specializing to DBI inflation, we show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We also derive, in the general case, the third-order action which is useful for studying primordial non-Gaussianities generated during inflation. In the DBI case, we compute the dominant contributions to non-Gaussianities, which depend on both the adiabatic and entropy modes.

The problem of corrections to Einstein’s equations arising from averaging of inhomogeneities (backreaction) in the cosmological context has gained considerable attention recently. We present results of analyzing cosmological perturbation theory in the framework of Zalaletdinov’s fully covariant macroscopic gravity. We show that this framework can be adapted to the setting of cosmological perturbations in a manner which is free from gauge related ambiguities. We derive expressions for the backreaction which can be readily applied in any situation (not necessarily restricted to the linear perturbations considered here) where the metric can be brought to the perturbed Friedmann-Lemaître-Robertson-Walker form. In particular, these expressions can be employed in toy models studying nonlinear structure formation, and possibly also in $N$-body simulations. Additionally, we present results of example calculations which show that the backreaction remains negligible well into the matter dominated era.

Electric dipole moments (EDMs) of elementary particles and atoms probe violations of $T$ and $P$ symmetries and consequently of $CP$ if $CPT$ is an exact symmetry. We point out that EDMs can also serve as sensitive probes of $CPT$-odd, $CP$-even interactions, that are not constrained by any other existing experiments. Analyzing models with spontaneously broken Lorentz invariance, we calculate EDMs in terms of the leading $CPT$-odd operators to show that experimental sensitivity probes the scale of $CPT$ breaking as high as ${10}^{12}\mathrm{GeV}$.

Recently published measurements of the branching ratios $\mathcal{B}(\psi (1S)\to \gamma {\eta }_C(1S))$ and $\mathcal{B}(\psi (2S)\to \gamma {\eta }_C(1S))$ by the CLEO Collaboration are examined in the context of a potential model that includes both relativistic and one-loop QCD corrections to the quark-antiquark interaction. The prediction for the width $\Gamma (\psi (1S)\to \gamma {\eta }_C(1S))$ is in excellent agreement with the new data, but the prediction for $\Gamma (\psi (2S)\to \gamma {\eta }_C(1S))$ is too small. In an effort to understand this discrepancy, we derive an upper bound on $\Gamma (\psi (2S)\to \gamma {\eta }_C(1S))$ and point out its experimental value saturates this bound.

Combined analysis of recent measured $B_s-{\overline{B}}_s$ mixing and $B\to X_s\gamma$ decays provides constraints on the anomalous $\overline{t}sW$ couplings. We discuss the perspectives to examine the anomalous $\overline{t}sW$ couplings through Cabibbo-Kobayashi-Maskawa quark-mixing matrix-suppressed $t\to sW$ decays at the LHC.

It is shown that in supersymmetric $SU(N)$ models with $N>5$ the so-called “doubly lopsided” mass matrix structure can emerge in a natural way. The nontrivial flavor structure is entirely accounted for by the $SU(N)$ gauge symmetry and supersymmetry, without any “flavor symmetry.” The hierarchy among the families results directly from a hierarchy of scales in the chain of breaking from $SU(N)$ to the standard model group. A simple $SU(7)$ example is presented.

A scenario of the big-bang nucleosynthesis is analyzed within the minimal supersymmetric standard model, which is consistent with a stau-neutralino coannihilation scenario to explain the relic abundance of dark matter. We find that we can account for the possible discrepancy of the abundance of ${}^7\mathrm{Li}$ between the observation and the prediction of the big-bang nucleosynthesis by taking the mass of the neutralino as 300 GeV and the mass difference between the stau and the neutralino as $(100–120)\mathrm{MeV}$. We can therefore simultaneously explain the abundance of the dark matter and that of ${}^7\mathrm{Li}$ by these values of parameters. The lifetime of staus in this scenario is predicted to be $O(100–1000)\sec$.

We consider scale invariant theories of continuous mass fields and show how interactions of these fields with the standard model can reproduce unparticle interactions. There is no fixed point or dimensional transmutation involved in this approach. We generalize interactions of the standard model to multiple unparticles in this formalism and explicitly work out some examples, in particular, we show that the product of two scalar unparticles behaves as a normalized scalar unparticle with a dimension equal to the sum of the two composite unparticle dimensions. Extending the formalism to scale invariant interactions of continuous mass fields, we calculate three point functions of unparticles.

We investigate the severity of the sign problem in a random matrix model for QCD at finite temperature $T$ and baryon chemical potential $\mu$. We obtain an analytic expression for the average phase factor—the measure of the severity of the sign problem at arbitrary $T$ and $\mu$. We observe that the sign problem becomes less severe as the temperature is increased. We also find the domain where the sign problem is maximal—the average phase factor is zero, which is related to the pion-condensation phase in the QCD with finite isospin chemical potential. We find that, in the matrix model we studied, the critical point is located inside the domain of the maximal sign problem, making the point inaccessible to conventional reweighting techniques. We observe and describe the scaling behavior of the size and shape of the pion condensation near the chiral limit.

We examine how dynamical fermions affect both the UV and infrared structure of the QCD vacuum. We consider large ${28}^3\times 96$ lattices from the MILC collaboration, using a gluonic definition of the topological charge density, founded on a new over-improved stout-link smearing algorithm. The algorithm reproduces established results from the overlap formalism and preserves nontrivial topological objects, including instantons. At short distances we focus on the topological charge correlator, $⟨q(x)q(0)⟩$, where negative values at small $x$ reveal a sign-alternating layered structure to the topological-charge density of the QCD vacuum. We find that the magnitudes of the negative dip in the $⟨q(x)q(0)⟩$ correlator and the positive $⟨q(0{)}^2⟩$ contact term are both increased with the introduction of dynamical fermion degrees of freedom. At large distances we examine the extent to which instanton-like objects are found on the lattice, and how their distributions vary between quenched and dynamical gauge fields. We show that dynamical gauge fields contain more instanton-like objects with an average size greater than in the quenched vacuum. Finally, we directly visualize the topological charge density in order to investigate the effects of dynamical sea-quark degrees of freedom on topology.

We present results for the matrix elements relevant for proton decay in grand unified theories (GUTs). The calculation is performed at a fixed lattice spacing $a^{-1}=1.73(3)\mathrm{GeV}$ using $2+1$ flavors of domain-wall fermions on lattices of size ${16}^3\times 32$ and ${24}^3\times 64$ with a fifth dimension of length 16. We use the indirect method which relies on an effective field theory description of proton decay, where we need to estimate the low-energy constants, $\alpha =-0.0112(25){\mathrm{GeV}}^3$ and $\beta =0.0120(26){\mathrm{GeV}}^3$. We relate these low-energy constants to the proton decay matrix elements using leading order chiral perturbation theory. These can then be combined with experimental bounds on the proton lifetime to bound parameters of individual GUTs.

Inspired by the obvious discrepancies between experiment and nonrelativistic QCD (NRQCD) studies of $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ at $\sqrt{s}\simeq 10.6\mathrm{GeV}$, we investigate contributions from intermediate meson loops as long-range interaction transitions to this process. The intermediate meson loops include $D\overline{D}({\overline{D}}^{*})$, $D{\overline{D}}^{*}$ ($D$ or $D^{*}$), $D^{*}{\overline{D}}^{*}(D)$, and corresponding $D_s$ intermediate mesons. With the constraints from experimental data on the vertex couplings, we find that the intermediate meson loops account for $2.7\sim 6.7\mathrm{fb}$ of the cross sections within a reasonable range of cutoff energies of the factor parameter. We also investigate contributions from the absorptive part and find that it accounts for approximately $0.58\sim 1.38\mathrm{fb}$. These results imply that contributions from long-range interaction transitions may still play a role in such an energy region.

The strong decays of the $\pi (2070)$, $\eta (2010)$, $\eta (2100)$, $\eta (2190)$, and $\eta (2225)$ as the $4{}^{1}S_0$ quark-antiquark states are investigated in the framework of the ${}^{3}P_0$ meson decay model. It is found that the $\pi (2070)$, $\eta (2100)$, and $\eta (2225)$ appear to be the convincing $4{}^{1}S_0$ $q\overline{q}$ states, while the assignment of the $\eta (2010)$ and $\eta (2190)$ as the $4{}^{1}S_0$ isoscalar states is not favored by their widths. In the presence of the $\pi (2070)$, $\eta (2100)$, and $\eta (2225)$ being the members of the $4{}^{1}S_0$ meson nonet, the mass of the $4{}^{1}S_0$ kaon is phenomenologically determined to be about 2153 MeV. The width of this unobserved kaon is expected to be about 197 MeV in the ${}^{3}P_0$ decay model.

A complication in proving factorization theorems in Feynman gauge is that individual graphs give a superleading power of the hard scale when all the gluons inducing the hard scattering are longitudinally polarized. With the aid of an example in gluon-mediated deep-inelastic scattering, we show that, although the superleading terms cancel after a sum over graphs, there is a residual nonzero leading term from longitudinally polarized gluons. This is due to the nonzero transverse momenta of the gluons in the target. The noncancellation, due to the non-Abelian property of the gauge group, is necessary to obtain the correct form of the gluon distribution function as a gauge-invariant matrix element.

The form factors relevant to $B_q\to D_q^{*}(J^P=1^{-})\ell \nu$ ($q=s$, $d$, $u$) decays are calculated in the framework of the three point QCD sum rules approach. The heavy quark effective theory prediction of the form factors as well as $1/m_b$ corrections to those form factors are obtained. A comparison of the results for the ratio of form factors at zero recoil limit and other values of $q^2$ with the predictions of the subleading Isgur-Wise form factor application for $B\to D^{*}\ell \nu$ is presented. The total decay width and branching ratio for these decays are also evaluated using the $q^2$ dependencies of these form factors. The results are in good agreement with the constituent quark meson model and existing experimental data. The $q=s$ case can also be detected at LHC in the near future.