Poincaré 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 both curvature and torsion. In our specific model, the Lagrangian contains (i) the curvature scalar R and the curvature pseudoscalar X linearly and quadratically (including an RX term) and (ii) pieces quadratic in the torsion vector V and the torsion axial vector A (including a V 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 RðtÞ and XðtÞ. 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.

Generalized plane waves in Poincaré gauge theory of gravity

“…Recently, however, there has been a growing interest for the extended class of models with a general Lagrangian that includes both parity even and parity odd quadratic terms, see for instance [18][19][20][21][22][23]. An important difference between these two classes of PGT models is manifest in their particle spectra.…”

Inflation by spin and torsion in the Poincaré gauge theory of gravity

“…Consequently, the effects of spin tensor in the large-scale dynamics of the universe will only be relevant at the very early times. However, one should note that due to the fundamental difference between the field equations of PGT and their general relativistic counterparts, torsion can also effects the late-time dynamics of the universe, as has been shown in [5,8,23,24] One of the most important tests for any inflationary model is its ability to generate nearly scale-invariant spectrum of scalar perturbations at the end of inflation. The scalar spectral index is given by [27] …”

“…Here we show that in PGT using the Lagrangian in the form of (11), the effects of spin and torsion cause the Universe to enter an inflationary epoch with a wide range of parameters. Also, using the assumption of vanishing spin tensor at late times, it has been shown that Poincaré gauge theory of gravity is also able to explain present time accelerated expansion of the universe [5,8,[23][24][25].…”

“…However cosmological implications of also including the parity violating terms have been studied in [5,6]. Field equations are obtained by variation of Lagrangian with respect to dynamical variables, tetrad field and spin connection (or equivalently curvature and torsion).…”

Cosmology in Poincaré gauge gravity with a pseudoscalar torsion

“…We focus on the case including a pseudoscalar scalar torsion function f as suggested by Baekler, Hehl and Nester [98]. The gravitational field equation and the two-family cosmological equations has been obtained in ref.…”