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Poincar\`e gauge theory (PGT) is an alternative gravity theory, whichattempts to bring the gravity into the gauge-theoretic frame, where theLagrangian is quadratic in torsion and curvature. Recently, the cosmologicalmodels with torsion based on this theory have drawn many attentions, which tryto explain the cosmic acceleration in a new way. Among these PGT cosmologicalmodels, the one with only even parity dynamical modes -- SNY model, for itsrealistic meaning, is very attractive. In this paper, we first analyze thepast-time cosmic evolution of SNY model analytically. And based on theseresults we fit this model to the most comprehensive SNeIa data (Union 2) andthus find the best-fit values of model parameters and initial conditions, whoserelated $\chi^{2}$ value is consistent with the one from $\Lambda$CMD at the1$\sigma$ level. Also by the $\chi^{2}$ estimate, we provide certainconstraints on these parameters. Using these best-fit values for the Union 2SNeIa dataset, we are able to predict the evolution of our real universe overthe late time. From this prediction, we know the fate of our universe that itwould expand forever, slowly asymptotically to a halt, which is in accordancewith the earlier works.

Torsion Cosmology of Poincar\'e gauge theory and the constraints of its parameters via SNeIa data