  A gauge-independent, invariant theory of linear scalar perturbations of
inflation and gravitational fields has been created. This invariant theory
allows one to compare gauges used in the work of other researchers and to find
the unambiguous criteria to separate the physical and coordinate effects. It is
shown, in particular, that the so-called longitudial gauge, commonly used when
considering inflation instability, leads to a fundamental overestimation of the
effect because of non-physical perturbations of the proper time in the frame of
reference specified by this gauge. Back reaction theories employing this sort
of gauge [1] also involve coordinate effects. The invariant theory created here
shows that the classical Lifshitz (1946) [2] gauge does not lead to
non-physical perturbations of the proper time and can be used to analyze the
inflation regime and the back reaction of perturbations on this regime
properly. The first theory of back reaction on background of all types of
perturbations (scalar, vector and tensor) based on this gauge was published in
1975 [3] and has been applied recently to the inflation [4]. The investigation
of long-length perturbations, which characterize the stability of the
inflationary process, and quantum fluctuations, which form the
Harrison-Zel'dovich spectrum at the end of inflation, is performed in the
invariant form. The invariant theory proposed allows one to examine the effect
of quantum fluctuations on the inflationary stage when the periodic regime
changes to an aperiodic one. That only the invariant theory must be used to
analyze space experiments is one of the conclusions of the present work.
