  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.
