  The gauge-independent invariant approach to investigation of the linear
scalar perturbations of inflaton and gravitational fields is developed in
self-consistent way. This approach allows to compare various gauges used by
other researchers and to find unambiguous selection criteria of physical and
coordinate effects. We have shown that the so-called longitudinal gauge
commonly used for studying the gravitational instability leads to
overestimation of physical effects due to the presence of nonphysical proper
time perturbations. Equation of invariant dynamics (EID) is derived. The
general long-wave solution of EID for an arbitrary potential U(phi) has been
obtained. We have also found analytical solutions for all wave lengths at all
stages of the universe evolution in the framework of simplest potential
U(phi)=m^2*phi^2/2. We have constructed the analytical expressions for the
energy density perturbations spectrum Delta(k,t) at all possible k and t.
Amplitude of the long-wave spectrum in the case of the transition from short
waves to long ones occurs at the inflationary stage is almost flat, i.e. has
the Harrison-Zeldovich form, for arbitrary potential U(phi).
