Initial condition of scalar perturbation in inflation

We show that the physics of pre-inflation produces an effect on the power spectrum of curvature perturbations. Namely, based on the physical conditions before inflation, the possibility exists that the initial state of scalar perturbations is not only the Bunch–Davies state, but also a more general state (a squeezed state). A formula for the power spectrum of curvature perturbations having any initial conditions in inflation is obtained. For example, the derived formula for the power spectrum is calculated using simple toy cosmological models. When there exists a radiation-dominated period before inflation, the behaviour of the scalar perturbation is revealed not to vary greatly; however, from large scales to small scales, the power spectrum of the curvature perturbations oscillates around the normal value. In addition, when inflation has a large break and the breaking time is a radiation-dominated period, a large enhancement is revealed to occur which depends on the length of the breaking time.