Cosmological perturbations in the inflationary Universe

Previously defined covariant and gauge-invariant perturbation variables, representing, e.g., the fractional spatial energy density gradient on hypersurfaces of constant expansion, are used to simplify the linear perturbation analysis of a classical scalar field. With the help of conserved quantities on large scales we establish an exact first-order relation between comoving fluid energy density perturbations at “reentry” into the horizon and corresponding scalar field energy density perturbations at the first Hubble scale crossing during an early de Sitter phase of a standard inflationary scenario.