Curved space quantum scalar field theory with accompanying metric fluctuations

We show that, in the analysis of quantum-field theory in curved space, taking the simultaneously excited metric fluctuations into account is not only quite feasible but also the results can be regarded as more self-consistent. Although the resulting equations become necessarily somewhat involved, certain simplifications occur such that the analysis becomes simpler and even general solutions are available. We present a minimally coupled scalar field theory in a flat Friedmann-Lema\^tre-Robertson-Walker background metric. By a "proper" choice of gauge fixing, we are able to produce the same results derived from quantum-field theory in curved space neglecting the metric perturbations in exponential and power-law expansion stages, now supported by the background scalar field. We also show that in the large scale the general integral form solution can be derived for an arbitrary scalar field potential (this is generally possible in any other gauge analysis). The uniform-curvature gauge allows the simplest analysis. Based on these results we are able to provide a firm basis for previous naive calculations of density perturbations generated during inflation. The quantum generation process is treated with full account of the accompanying metric fluctuations, and the analysis is simplified in a coherent manner.