We study the coincidence problem of late cosmic acceleration by assuming that the present ratio between dark matter and dark energy is a slowly varying function of the scale factor. As the dark energy component we consider two different candidates, first a quintessence scalar field, and then a tachyon field. In either case analytical solutions for the scale factor, the field, and the potential are derived. Both models show a good fit to the recent magnitude-redshift supernovae data. However, the likelihood contours disfavor the tachyon field model as it seems to prefer a excessively high value for the matter component.

We present some phenomenology of a new class of intersecting D-brane models. Soft supersymmetry (SUSY) breaking terms for these models are calculated in the $u$-moduli dominant SUSY breaking approach (in type IIA). In this case, the dependence of the soft terms on the Yukawas and Wilson lines drops out. These soft terms have a different pattern compared to the usual heterotic string models. Phenomenological implications for dark matter are discussed.

We consider the non-Abelian Bianchi identities in SU(2) pure Yang-Mills theory in $D=3,4$ focusing on the possibility of their violation and the significance of the chromomagnetic fields degeneracy points. We show that the recently proposed non-Abelian Stokes theorem allows one to formulate the Bianchi identities in terms of the physical fluxes and their relative color orientations. Then the violation of Bianchi identities becomes a well defined concept ultimately related to the degeneracy points. The locality and gauge invariance of our approach allows one to study the problem numerically. We present evidence that in $D=4$ the suppression of the Bianchi identities violation is likely to destroy confinement, while the removal of the degeneracy points drives the theory to the topologically nontrivial sector. However, confronting the results obtained in three and four dimensions, we argue that it is the mass dimension two condensate $⟨A_{\min }^2⟩$ which probably explains our findings.

We study muonium-antimuonium conversion and ${\mu }^{+}{e}^{-}\to {\mu }^{-}{e}^{+}$ scattering within two different lepton-flavor-violating models with heavy neutrinos: model I is a typical seesaw that violates lepton number as well as flavor; model II has a neutrino mass texture where lepton number is conserved. We look for the largest possible amplitudes of these processes that are consistent with current bounds. We find that model I has very limited chance of providing an observable signal, except if a finely tuned condition in parameter space occurs. Model II, on the other hand, requires no fine tuning and could cause larger effects. However, the maximum amplitude provided by this model is still 2 orders of magnitude below the sensitivity of current experiments: one predicts an effective coupling $G_{M\overline{M}}$ up to ${10}^{-4}{G}_F$ for heavy neutrino masses near 10 TeV. We have also clarified some discrepancies in previous literature on this subject.

Quantum fluctuations of the electromagnetic field produced by an elementary particle are investigated. Using the Schwinger-Keldysh formalism, it is found that the two-point correlation function of the Coulomb potential has a nonvanishing value already at zeroth order in the Planck constant. It is proved that to this order, the correlation function is gauge independent and has a well-defined coincidence limit. In this limit, the leading term in the long-range expansion of the correlation function is calculated explicitly. Furthermore, the spectrum of the electromagnetic fluctuations is investigated. It is found, in particular, that in a wide range of practically important frequencies, the spectral density of the electromagnetic field fluctuations exhibits an inverse frequency dependence. It is shown also that in the case of a macroscopic body, the ${\hslash }^0$ part of the correlation function is suppressed by a factor $1/N$, where $N$ is the number of particles in the body. Relation of the obtained results to the problem of measurability of the electromagnetic field is mentioned.

The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted coproduct. This allows for the definition of conformal symmetry in a noncommutative background geometry. The twisted coproduct is reviewed for the Poincaré algebra and the construction is then extended to the full conformal algebra. The case of Moyal-type noncommutativity of the coordinates is considered. It is demonstrated that conformal invariance need not be viewed as incompatible with noncommutative geometry; the noncommutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincaré algebra.

We calculate exactly the functional determinant for fermions in fundamental representation of $SU(2)$ in the background of periodic instanton with nontrivial value of the Polyakov line at spatial infinity. The determinant depends on the value of the holonomy $\mathrm{v}$, the temperature, and the parameter $r_{12}$, which at large values can be treated as separation between the Bogomol’nyi-Prasad-Sommerfield monopoles monopoles (or dyons) which constitute the periodic instanton. We find a compact expression for small and large $r_{12}$ and compute the determinant numerically for arbitrary $r_{12}$ and $\mathrm{v}$.

We give an analytic demonstration that the $3+1$-dimensional large $N$ $SU(N)$ pure Yang-Mills theory, compactified on a small $S^3$ so that the coupling constant at the compactification scale is very small, has a first order deconfinement transition as a function of temperature. We do this by explicitly computing the relevant terms in the canonical partition function up to three-loop order; this is necessary because the leading (one-loop) result for the phase transition is precisely on the border line between a first order and a second order transition. Since numerical work strongly suggests that the infinite-volume large $N$ theory also has a first order deconfinement transition, we conjecture that the phase structure is independent of the size of the $S^3$. To deal with divergences in our calculations, we are led to introduce a novel method of regularization useful for non-Abelian gauge theory on $S^3$.

We derive the perturbation equations for relativistic stars in scalar-tensor theories of gravity and study the corresponding oscillation spectrum. We show that the frequency of the emitted gravitational waves is shifted proportionally to the scalar field strength. Scalar waves which might be produced from such oscillations can be a unique probe for the theory, but their detectability is questionable if the radiated energy is small. However, we show that there is no need for a direct observation of scalar waves: The shift in the gravitational wave spectrum could unambiguously signal the presence of a scalar field.

Ever since Karl Schwarzschild’s 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star—a static spherically symmetric blob of fluid with position-independent density—the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.

The dark energy transition between quintessence ($w>-1$) and phantom ($w<-1$) regimes (the crossing of the cosmological constant boundary) is studied using the dark energy equation of state. Models characterized by this type of transition are explicitly constructed and their equation of state is found to be implicitly defined. The behavior of the more general models with the implicitly defined equation of state, obtained by the generalization of the explicitly constructed models, is studied to gain insight into the necessary conditions for the occurrence of the transition, as well as to investigate the mechanism behind the transition. It is found that the parameters of the generalized models need to satisfy special conditions for the transition to happen and that the mechanism behind the transition is the cancellation of the contribution of the cosmological constant boundary. The aspects of the behavior of the generalized models which are not related to the transition are briefly discussed and the role of the implicitly defined dark energy equation of state in the description of the dark energy evolution is emphasized.

We introduce a simple parametrization of the dark energy equation of state, $\omega$, which is motivated from theory and recent experimental data. The theory is related to the tracker solution to alleviate the fine-tuning problem. Recent experimental data indicates that the present value of $\omega$ is close to $-1$. We analyze the evolution of $\omega$ from the separation of CMB peaks and the time variation of the fine structure constant, $\alpha$. We find that $-1.00\le {\omega }^{(0)}\le -{0.971}_{-0.027}^{+0.017}$ and ${1.76}_{-0.42}^{+0.29}\times {10}^{-4}\le (d\omega /dz{)}_{z=0}\le {0.041}_{-0.037}^{+0.016}$ at 95% confidence level.

Weak-lensing distortions of the cosmic-microwave-background (CMB) temperature and polarization patterns can reveal important clues to the intervening large-scale structure. The effect of lensing is to deflect the primary temperature and polarization signal to slightly different locations on the sky. Deflections due to density fluctuations, gradient-type for the gradient of the projected gravitational potential, give a direct measure of the mass distribution. Curl-type deflections can be induced by, for example, a primordial background of gravitational waves from inflation or by second-order effects related to lensing by density perturbations. Whereas gradient-type deflections are expected to dominate, we show that curl-type deflections can provide a useful test of systematics and serve to indicate the presence of confusing secondary and foreground non-Gaussian signals.

I present the two-loop self-energy functions for scalar bosons in a general renormalizable theory, within the approximation that vector bosons are treated as massless or equivalently that gauge symmetries are unbroken. This enables the computation of the two-loop physical pole masses of scalar particles in that approximation. The calculations are done simultaneously in the mass-independent $\overline{\mathrm{MS}}$, $\overline{\mathrm{DR}}$, and ${\overline{\mathrm{DR}}}^{\prime }$ renormalization schemes, and with arbitrary covariant gauge fixing. As an example, I present the two-loop supersymmetric quantum chromodynamics corrections to squark masses, which can increase the known one-loop results by of order 1%. More generally, it is now straightforward to implement all two-loop sfermion pole mass computations in supersymmetry using the results given here, neglecting only the electroweak vector boson masses compared to the superpartner masses in the two-loop parts.

Electroweak radiative corrections can be evaluated in the Sudakov approximation, a systematic high-energy expansion known to be relevant for the analysis of future collider experiments in the TeV energy range. In the minimal supersymmetric standard model and at next-to-leading order, Sudakov electroweak corrections satisfy remarkable relations at the one-loop level. Explicit computations in component fields are available for various different $2\to 2$ processes relevant for linear collider or CERN LHC physics. The Sudakov corrections turn out to be equal or closely related in several classes of processes differing by the replacement of certain final or initial states with their superpartners. This fact suggests that supersymmetry is partially restored at high energy. We analyze the supersymmetric structure of such relations by computing the Sudakov corrections in the framework of superfield perturbation theory. As a simple application, we derive in full details an extended complete set of supersymmetric relations among different processes related by supersymmetry to the fundamental fermion pair production process $e^{+}{e}^{-}\to f\overline{f}$.

We explore the Higgs sector of the Minimal Left-Right (LR) Model based on the gauge group $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}$ with explicit $CP$ violation in the Higgs potential. Since flavour-changing neutral current experiments and the small scale of neutrino masses both place stringent constraints on the Higgs potential, we seek to determine whether minima of the Higgs potential exist that are consistent with current experimental bounds. We focus on the case in which the right-handed symmetry-breaking scale is only moderately large, of order 15–50 TeV. Unlike the case in which the Higgs potential is $CP$-invariant, the $CP$ noninvariant case does yield viable scenarios, although these require a small amount of fine-tuning. We consider a LR model supplemented by an additional $U(1)$ horizontal symmetry, which results in a Higgs sector consistent with current experimental constraints and a realistic spectrum of neutrino masses.

We compute the cross section for pair production of charged Higgs bosons at the LHC and compare the three production mechanisms. The bottom-parton scattering process is computed to next-to-leading order (NLO), and the validity of the bottom-parton approach is established in detail. The light-flavor Drell-Yan cross section is evaluated at NLO as well. The gluon-fusion process through a one-loop amplitude is then compared with these two results. We show how a complete sample of events could look, in terms of total cross sections and distributions of the heavy final states.

String theories in principle address the origin and values of the quark and lepton masses. Perhaps the small values of neutrino masses could be explained generically in string theory even if it is more difficult to calculate individual values, or perhaps some string constructions could be favored by generating small neutrino masses. We examine this issue in the context of the well-known three-family standard-like $Z_3$ heterotic orbifolds, where the theory is well enough known to construct the corresponding operators allowed by string selection rules, and analyze the D- and F-flatness conditions. Surprisingly, we find that a simple seesaw mechanism does not arise. It is not clear whether this is a property of this construction, or of orbifolds more generally, or of string theory itself. Extended seesaw mechanisms may be allowed; more analysis will be needed to settle that issue. We briefly speculate on their form if allowed and on the possibility of alternatives, such as small Dirac masses and triplet seesaws. The smallness of neutrino masses may be a powerful probe of string constructions in general. We also find further evidence that there are only 20 inequivalent models in this class, which affects the counting of string vacua.

We compute the inclusive and differential cross sections for the associated production of a top quark along with a charged Higgs boson at hadron colliders to next-to-leading order (NLO) in perturbative quantum chromodynamics (QCD) and in supersymmetric QCD. For small Higgs boson masses we include top-quark pair production diagrams with subsequent top-quark decay into a bottom quark and a charged Higgs boson. We compare the NLO differential cross sections obtained in the bottom parton picture with those for the gluon-initiated production process and find good agreement. The effects of supersymmetric loop contributions are explored. Only the corrections to the Yukawa coupling are sizable in the potential discovery region at the CERN Large Hadron Collider (LHC). All expressions and numerical results are fully differential, permitting selections on the momenta of both the top quark and the charged Higgs boson.

We numerically investigate the transition of the static quark-antiquark string into a static-light meson-antimeson system. Improving noise reduction techniques, we are able to resolve the signature of string breaking dynamics for $n_f=2$ lattice QCD at zero temperature. This result can be related to properties of quarkonium systems. We also study short-distance interactions between two static-light mesons.