Thermodynamical properties of metric fluctuations during inflation

During inflation vacuum fluctuations on scales smaller than the Hubble radius are magnified into classical perturbations of the scalar field on super Hubble scales. The primordial perturbations arise solely from the zero-point fluctuations of the quantized fields. Although the region which ultimately expanded to become the observed universe may have contained excitations above the vacuum, these excitations would not have any significant effect on the present state of the universe because a sufficiently large amount of the inflation would have redshifted these excitations to inmeasurably long wavelengths [1]. Hence, the density perturbations should be responsible for the large scale structure formation in the universe [3]. The scalar perturbations of the metric are related to density perturbations. These are the spin-zero projections of the graviton, which only exist in nonvacuum cosmologies. The issue of gauge invariance becomes critical when attempt to analyze how the scalar metric perturbations produced in the very early universe influence a globally flat isotropic and homogeneous universe on super Hubble scales. This allows us to formulate the problem of the evolution for the amplitude of scalar metric perturbations around the FriedmannRobertson-Walker (FRW) universe in a coordinate-independent manner at every moment in time [4]. Since the results do not depend on the gauge, the perturbed globally flat FRW metric is well described by