Cooper pairing and finite-size effects in a NJL-type four-fermion model

Starting from a NJL-type model with N fermion species fermion and difermion condensates and their associated phase structures are considered at nonzero chemical potential $\mu$ and zero temperature in spaces with nontrivial topology of the form $S^1\otimes S^1\otimes S^1$ and $R^2\otimes S^1$. Special attention is devoted to the generation of the superconducting phase. In particular, for the cases of antiperiodic and periodic boundary conditions we have found that the critical curve of the phase transitions between the chiral symmetry breaking and superconducting phases as well as the corresponding condensates and particle densities strongly oscillate vs $\lambda\sim 1/L$, where $L$ is the length of the circumference $S^1$. Moreover, it is shown that at some finite values of $L$ the superconducting phase transition is shifted to smaller values both of $\mu$ and particle density in comparison with the case of $L=\infty$.Comment: 13 pages, 13 figures; minor changes; new references added; version accepted to PR

Cosmic Microwave Background Polarization

Cosmic microwave background (CMB) anisotropy is our richest source of cosmological information; the standard cosmological model was largely established thanks to study of the temperature anisotropies. By the end of the decade, the Planck satellite will close this important chapter and move us deeper into the new frontier of polarization measurements. Numerous ground--based and balloon--borne experiments are already forging into this new territory. Besides providing new and independent information on the primordial density perturbations and cosmological parameters, polarization measurements offer the potential to detect primordial gravity waves, constrain dark energy and measure the neutrino mass scale. A vigorous experimental program is underway worldwide and heading towards a new satellite mission dedicated to CMB polarization.Comment: Review given at TAUP 2005; References added; Additional reference

Skewness in the Cosmic Microwave Background Anisotropy from Inflationary Gravity Wave Background

In the context of inflationary scenarios, the observed large angle anisotropy of the Cosmic Microwave Background (CMB) temperature is believed to probe the primordial metric perturbations from inflation. Although the perturbations from inflation are expected to be gaussian random fields, there remains the possibility that nonlinear processes at later epochs induce ``secondary'' non-gaussian features in the corresponding CMB anisotropy maps. The non-gaussianity induced by nonlinear gravitational instability of scalar (density) perturbations has been investigated in existing literature. In this paper, we highlight another source of non-gaussianity arising out of higher order scattering of CMB photons off the metric perturbations. We provide a simple and elegant formalism for deriving the CMB temperature fluctuations arising due to the Sachs-Wolfe effect beyond the linear order. In particular, we derive the expression for the second order CMB temperature fluctuations. The multiple scattering effect pointed out in this paper leads to the possibility that tensor metric perturbation, i.e., gravity waves (GW) which do not exhibit gravitational instability can still contribute to the skewness in the CMB anisotropy maps. We find that in a flat $\Omega =1$ universe, the skewness in CMB contributed by gravity waves via multiple scattering effect is comparable to that from the gravitational instability of scalar perturbations for equal contribution of the gravity waves and scalar perturbations to the total rms CMB anisotropy. The secondary skewness is found to be smaller than the cosmic variance leading to the conclusion that inflationary scenarios do predict that the observed CMB anisotropy should be statistically consistent with a gaussian random distribution.Comment: 10 pages, Latex (uses revtex), 1 postscript figure included. Accepted for publication in Physical Review

Inertial mechanism: dynamical mass as a source of particle creation

A kinetic theory of vacuum particle creation under the action of an inertial mechanism is constructed within a nonpertrubative dynamical approach. At the semi-phenomenological level, the inertial mechanism corresponds to quantum field theory with a time-dependent mass. At the microscopic level, such a dependence may be caused by different reasons: The non-stationary Higgs mechanism, the influence of a mean field or condensate, the presence of the conformal multiplier in the scalar-tensor gravitation theory etc. In what follows, a kinetic theory in the collisionless approximation is developed for scalar, spinor and massive vector fields in the framework of the oscillator representation, which is an effective tool for transition to the quasiparticle description and for derivation of non-Markovian kinetic equations. Properties of these equations and relevant observables (particle number and energy densities, pressure) are studied. The developed theory is applied here to describe the vacuum matter creation in conformal cosmological models and discuss the problem of the observed number density of photons in the cosmic microwave background radiation. As other example, the self-consistent evolution of scalar fields with non-monotonic self-interaction potentials (the W-potential and Witten - Di Vecchia - Veneziano model) is considered. In particular, conditions for appearance of tachyonic modes and a problem of the relevant definition of a vacuum state are considered.Comment: 51 pages, 18 figures, submitted to PEPAN (JINR, Dubna); v2: added reference

Natural Inflation: Particle Physics Models, Power Law Spectra for Large Scale Structure, and Constraints from COBE

A pseudo-Nambu-Goldstone boson, with a potential of the form $V(\phi) = \Lambda^4[1 \pm \cos(\phi/f)], naturally gives rise to inflation if$f \sim M_{Pl}$and$\Lambda \sim M_{GUT}$. We show how this can arise in technicolor-like and superstring models, and work out an explicit string example in the context of multiple gaugino condensation models. We study the cosmology of this model in detail, and find that sufficient reheating to ensure that baryogenesis can take place requires$f > 0.3 M_{Pl}$. The primordial density fluctuation spectrum generated is a non-scale-invariant power law,$P(k) \propto k^{n_s}$, with$n_s \simeq 1 - (M^2_{Pl}/8\pi f^2)$, leading to more power on large length scales than the$n_s = 1$Harrison-Zeldovich spectrum. The standard CDM model with$0 \la n_s \la 0.6-0.7$could in principle explain the large-scale clustering observed in the APM and IRAS galaxy surveys as well as large-scale flows, but the COBE microwave anisotropy implies such low amplitudes (or high bias factors,$b>2$) for these CDM models that galaxy formation occurs too late to be viable; combining COBE with sufficiently early galaxy formation or the large-scale flows leads to$n_s >0.6$, or$f > 0.3 M_{Pl}$as well. For extended and power law inflation models, this constraint is even tighter,$n_s > 0.7$; combined with other bounds on large bubbles in extended inflation, this leaves little room for most extended models.Comment: 42 pages, (12 figures not included but available from the authors

Pion condensation of quark matter in the static Einstein universe

In the framework of an extended Nambu--Jona-Lasinio model we are studying pion condensation in quark matter with an asymmetric isospin composition in a gravitational field of the static Einstein universe at finite temperature and chemical potential. This particular choice of the gravitational field configuration enables us to investigate phase transitions of the system with exact consideration of the role of this field in the formation of quark and pion condensates and to point out its influence on the phase portraits. We demonstrate the effect of oscillations of the thermodynamic quantities as functions of the curvature and also refer to a certain similarity between the behavior of these quantities as functions of curvature and finite temperature. Finally, the role of quantum fluctuations for spontaneous symmetry breaking in the case of a finite volume of the universe is shortly discussed.Comment: RevTex4; 15 pages, 10 figure