The effective gravitational Lagrangian and the energy-momentum tensor in the inflationary universe

The inflationary model proposed by Guth [1981, Phys.Rev. D 23, 347] is based on non-classical behaviour of the energy-momentum tensor. The authors try to evaluate the corrections to the usual linear relation between the scalar curvature and the trace of the energy-momentum tensor, R approx. = T, replacing the usual Einstein-Hilbert Lagrangian R by an unknown function f(R) and imposing the inflationary solution upon the scale factor α(t) of the Robertson-Walker metric. Solving for f(R) enables one to evaluate the corrections to the relation R approx. = T, which may be developed in powers of R or T at will. (author)