Evolution of gravitational perturbations in non-commutative inflation

Abstract

We consider the non-commutative inflation model in which it is the unconventionaldispersion relation for regular radiation which drives the accelerated expansion of space. Inthis model, we study the evolution of linear cosmological perturbations through thetransition between the phase of accelerated expansion and the regular radiation-dominatedphase of standard cosmology, a transition which is analogous to the reheating period inscalar field-driven models of inflation. If matter consists of only a single non-commutativeradiation fluid, then the curvature perturbations are constant on super-Hubble scales. Onthe other hand, if we include additional matter fields which oscillate during the transitionperiod, e.g. scalar moduli fields, then there can be parametric amplification of the amplitudeof the curvature perturbations. We demonstrate this explicitly by numerically solvingthe full system of perturbation equations in the case where matter consists ofboth the non-commutative radiation field and a light scalar field which undergoesoscillations. Our model is an example where the parametric resonance of the curvaturefluctuations is driven by the oscillations not of the inflaton field, but of the entropymode.