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The effective gravitational Lagrangian and the energy-momentum tensor in the inflationary universe. (English) Zbl 0593.53045

Summary: The inflationary model proposed by Guth is based on non-classical behaviour of the energy-momentum tensor. We try to evaluate the corrections to the usual linear relation between the scalar curvature and the trace of the energy-momentum tensor, \(R\sim T\), replacing the usual Einstein-Hilbert Lagrangian R by an unknown function f(R) and imposing the inflationary solution upon the scale factor a(t) of the Robertson- Walker metric. Solving for f(R) enables us to evaluate the corrections to the relation \(R\sim T\), which may be developed in powers of R or T at will.

MSC:

53B50 Applications of local differential geometry to the sciences
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C99 General relativity
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