  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.
