Cosmological signatures of time-asymmetric gravity

We develop the model proposed by Cort\^es, Gomes & Smolin, to predict cosmological signatures of time-asymmetric extensions of general relativity they proposed recently. Within this class of models the equation of motion of chiral fermions is modified by a torsion term. This term leads to a dispersion law for neutrinos that associates a new time-varying energy with each particle. We find a new neutrino contribution to the Friedmann equation resulting from the torsion term in the Ashtekar connection. In this note we explore the phenomenology of this term and observational consequences for cosmological evolution. We show that constraints on the critical energy density will ordinarily render this term unobservably small, a maximum of order $10^{-25}$ of the neutrino energy density today. However, if the time-asymmetric dark energy is tuned to cancel the cosmological constant, the torsion effect may be a dark matter candidate.