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.
