Large-scale energy-density perturbations and inflation

A first-order differential equation is given for large-scale energy-density perturbations in a Friedmann universe, which expresses the fact that each region of spacetime evolves like a separate Friedmann universe with small spatial curvature (the average curvature is taken to vanish). Using it perturbations generated in an inflationary era are evolved to the present (for sufficiently large scales) with essentially no assumption about intervening eras. The field fluctuations are shown to be essentially quantum mechanical until a few Hubble times after the scale leaves the horizon during the de Sitter era, but probably classical at later times. Full comparison with earlier work is made.