COSMOLOGICAL PERTURBATIONS IN THE INFLATIONARY UNIVERSE

Previously defined covariant and gauge-invariant perturbation variable s, representing, e.g., the fractional spatial energy density gradient on hypersurfaces of constant expansion, are used to simplify the linea r 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 ''ree ntry'' into the horizon and corresponding scalar field energy density perturbations at the first Hubble scale crossing during an early-de Si tter phase of a standard inflationary scenario.