Analytic solutions to Riemann-squared gravity with background isotropic torsion

Motivated by conventional gauge theories, we consider a theory of gravity in which the Einstein–Hilbert action is replaced by a term that is quadratic in the Riemann tensor. We focus on cosmological solutions to the field equations in flat, open and closed universes. The gravitational action is scale invariant, so the only matter source considered is radiation. The theory can also accommodate isotropic torsion and this generically removes singularities from the evolution equations. For general initial conditions the Hubble parameter H(t) is driven in a seemingly chaotic fashion by torsion to produce irregularly occuring inflationary regions. In the absence of torsion, the theory reproduces the standard cosmological solutions of a simple big bang model. A satisfying feature is that a cosmological constant arises naturally as a constant of integration, and does not have to be put into the Lagrangian by hand.