  It is shown that a first-order relativistic perturbation theory for the open,
flat or closed Friedmann-Lemaitre-Robertson-Walker universe admits one, and
only one, gauge-invariant quantity which describes the perturbation to the
energy density and which becomes equal to the usual Newtonian energy density in
the non-relativistic limit. The same holds true for the perturbation to the
particle number density. These facts exclude all definitions of gauge-invariant
quantities used to describe density perturbations in former theories. Using
these two new quantities, a manifestly covariant and gauge-invariant
cosmological perturbation theory, adapted to non-barotropic equations of state
for the pressure, has been developed. The new theory is valid for all scales
since metric gradients do not occur in the final evolution equations. The new
theory has an exact non-relativistic limit with a time-independent Newtonian
potential. The usual Newtonian perturbation theory is inadequate to study the
evolution of density perturbations. In the radiation-dominated era,
perturbations in the particle number density are gravitationally coupled to
perturbations in the total energy density, irrespective of the nature of the
particles. This implies that structure formation can commence only after
decoupling of matter and radiation. After decoupling of matter and radiation
density perturbations evolve diabatically, i.e., they exchange heat with their
environment. This heat loss of a perturbation may enhance the growth rate of
its mass sufficiently to explain stellar formation in the early universe, a
phenomenon not understood, as yet, without the additional assumption of the
existence of Cold Dark Matter. This theoretical observation is the main result
of this article.
