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

Abstract

We propose a cosmological model in the framework of the Poincaré 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} $\mathcal{V}$ and the torsion {\it axial} vector $\mathcal{A}$ (including a $\mathcal{V}\mathcal{A}$ 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.

Latex computerscript, 25 pages; mistakes corrected, references added, notation and title slightly changed; accepted by Phys. Rev. D

References in corpus (11)

• Torsion Cosmology and the Accelerating Universe
• Canonical Gravity with Fermions
• Cosmological dynamics with propagating Lorentz connection modes of spin zero
• Quadratic metric-affine gravity
• Regular accelerating Universe without dark energy
• PP-waves with torsion and metric-affine gravity
• Einstein-Cartan formulation of Chern-Simons Lorentz-violating Gravity
• Dynamic Scalar Torsion and an Oscillating Universe
• Particles as Wilson lines of gravitational field
• Linear connections with propagating spin-3 field in gravity
• Gravity from a fermionic condensate of a gauge theory

Cited by in corpus (22)

• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• The particle spectrum of parity-violating Poincaré gravitational theory
• Addressing $H_0$ tension with emergent dark radiation in unitary gravity
• Einstein-Cartan gravity, matter, and scale-invariant generalization
• Generalized plane waves in Poincaré gauge theory of gravity
• Modified gravity: a unified approach to metric-affine models
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Exact Solutions in Poincaré Gauge Gravity Theory
• Generalized Birkhoff theorem in the Poincaré gauge gravity theory
• Cosmological Perturbation Theory in Metric-Affine Gravity
• Supercomputers against strong coupling in gravity with curvature and torsion
• Einstein-Proca theory from the Einstein-Cartan formulation
• Gravitational waves in metric-affine gravity theory
• Gravity waves in parity-violating Copernican Universes
• Mimetic-Metric-Torsion with induced Axial mode and Phantom barrier crossing
• Parity violation in Poincaré gauge gravity
• Geometric multipliers and partial teleparallelism in Poincaré gauge theory
• Optical cavity resonator in an expanding universe
• Cosmological Constant, Inflaton, and Dark Matter all Naturally Originated from Poincaré Gauge Gravity
• Thermodynamics of Kerr-AdS black holes in general Poincaré gauge theory
• Torsion and gravitational interaction in Riemann-Cartan space-time
• New effective theories of gravitation and their phenomenological consequences