Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes. Analytic part

We propose a cosmological model in the framework of the Poincar\'e gauge theory of gravity (PG). The gravitational Lagrangian is quadratic in curvature and torsion. In our specific model, the Lagrangian contains (i) the curvature scalar $R$ and the curvature pseudo-scalar $X$ linearly and quadratically (including an $RX$ term) and (ii) pieces quadratic in the torsion {\it vector} $\cal V$ and the torsion {\it axial} vector $\cal A$ (including a ${\cal V}{\cal A}$ term). We show generally that in quadratic PG models we have nearly the same number of parity conserving terms (`world') and of parity violating terms (`shadow world'). This offers new perspectives in cosmology for the coupling of gravity to matter and antimatter. Our specific model generalizes the fairly realistic `torsion cosmologies' of Shie-Nester-Yo (2008) and Chen et al.\ (2009). With a Friedman type ansatz for an orthonormal coframe and a Lorentz connection, we derive the two field equations of PG in an explicit form and discuss their general structure in detail. In particular, the second field equation can be reduced to first order ordinary differential equations for the curvature pieces $R(t)$ and $X(t)$. Including these along with certain relations obtained from the first field equation and curvature definitions, we present a first order system of equations suitable for numerical evaluation. This is deferred to the second, numerical part of this paper.Comment: Latex computerscript, 25 pages; mistakes corrected, references added, notation and title slightly changed; accepted by Phys. Rev.

Beyond Einstein-Cartan gravity: Quadratic torsion and curvature invariants with even and odd parity including all boundary terms

Recently, gravitational gauge theories with torsion have been discussed by an increasing number of authors from a classical as well as from a quantum field theoretical point of view. The Einstein-Cartan(-Sciama-Kibble) Lagrangian has been enriched by the parity odd pseudoscalar curvature (Hojman, Mukku, and Sayed) and by torsion square and curvature square pieces, likewise of even and odd parity. (i) We show that the inverse of the so-called Barbero-Immirzi parameter multiplying the pseudoscalar curvature, because of the topological Nieh-Yan form, can only be appropriately discussed if torsion square pieces are included. (ii) The quadratic gauge Lagrangian with both parities, proposed by Obukhov et al. and Baekler et al., emerges also in the framework of Diakonov et al.(2011). We establish the exact relations between both approaches by applying the topological Euler and Pontryagin forms in a Riemann-Cartan space expressed for the first time in terms of irreducible pieces of the curvature tensor. (iii) Only in a Riemann-Cartan spacetime, that is, in a spacetime with torsion, parity violating terms can be brought into the gravitational Lagrangian in a straightforward and natural way. Accordingly, Riemann-Cartan spacetime is a natural habitat for chiral fermionic matter fields.Comment: 12 page latex, as version 2 an old file was submitted by mistake, this is now the real corrected fil

Volterra Distortions, Spinning Strings, and Cosmic Defects

Cosmic strings, as topological spacetime defects, show striking resemblance to defects in solid continua: distortions, which can be classified into disclinations and dislocations, are line-like defects characterized by a delta function-valued curvature and torsion distribution giving rise to rotational and translational holonomy. We exploit this analogy and investigate how distortions can be adapted in a systematic manner from solid state systems to Einstein-Cartan gravity. As distortions are efficiently described within the framework of a SO(3) {\rlap{\supset}\times}} T(3) gauge theory of solid continua with line defects, we are led in a straightforward way to a Poincar\'e gauge approach to gravity which is a natural framework for introducing the notion of distorted spacetimes. Constructing all ten possible distorted spacetimes, we recover, inter alia, the well-known exterior spacetime of a spin-polarized cosmic string as a special case of such a geometry. In a second step, we search for matter distributions which, in Einstein-Cartan gravity, act as sources of distorted spacetimes. The resulting solutions, appropriately matched to the distorted vacua, are cylindrically symmetric and are interpreted as spin-polarized cosmic strings and cosmic dislocations.Comment: 24 pages, LaTeX, 9 eps figures; remarks on energy conditions added, discussion extended, version to be published in Class. Quantum Gra

Levinson's theorem and scattering phase shift contributions to the partition function of interacting gases in two dimensions

We consider scattering state contributions to the partition function of a two-dimensional (2D) plasma in addition to the bound-state sum. A partition function continuity requirement is used to provide a statistical mechanical heuristic proof of Levinson's theorem in two dimensions. We show that a proper account of scattering eliminates singularities in thermodynamic properties of the nonideal 2D gas caused by the emergence of additional bound states as the strength of an attractive potential is increased. The bound-state contribution to the partition function of the 2D gas, with a weak short-range attraction between its particles, is found to vanish logarithmically as the binding energy decreases. A consistent treatment of bound and scattering states in a screened Coulomb potential allowed us to calculate the quantum-mechanical second virial coefficient of the dilute 2D electron-hole plasma and to establish the difference between the nearly ideal electron-hole gas in GaAs and the strongly correlated exciton/free-carrier plasma in wide-gap semiconductors such as ZnSe or GaN.Comment: 10 pages, 3 figures; new version corrects some minor typo

Ionization degree of the electron-hole plasma in semiconductor quantum wells

The degree of ionization of a nondegenerate two-dimensional electron-hole plasma is calculated using the modified law of mass action, which takes into account all bound and unbound states in a screened Coulomb potential. Application of the variable phase method to this potential allows us to treat scattering and bound states on the same footing. Inclusion of the scattering states leads to a strong deviation from the standard law of mass action. A qualitative difference between mid- and wide-gap semiconductors is demonstrated. For wide-gap semiconductors at room temperature, when the bare exciton binding energy is of the order of T, the equilibrium consists of an almost equal mixture of correlated electron-hole pairs and uncorrelated free carriers.Comment: 22 pages, 6 figure