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Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universethrough a bounce in the high energy region. We show that this is always true intachyon matter LQC. Different from the classical Friedman-Robertson-Walker(FRW) cosmology, the super inflation can appear in the tachyon matter LQC;furthermore, the inflation can be extended to the region where classicalinflation stops. Using numerical method, we give an evolution picture of thetachyon field with an exponential potential in the context of LQC. It indicatesthat the quantum dynamical solutions have the attractive behavior as theclassical solutions do. The whole evolution of the tachyon field is that in thedistant past, the tachyon field--being in the contracting cosmology--isaccelerates to climb up the potential hill with a negative velocity; then atthe boundary the tachyon field is bounced into an expanding universe withpositive velocity rolling down to the bottom of the potential. In the slow rolllimit, we compare the quantum inflation with the classical case in both ananalytic and numerical way.Comment: 8 pages, 3 figures, the version published in Phys.Rev.

Tachyon field in loop quantum cosmology: Inflation and evolution picture