Variational derivatives of arbitrarily high order and multi-inflation cosmological models

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Abstract
For the Lagrangian L=F(R, Square Operator R, . . ., Square Operator kR) square root -g the author deduces the field equation and discusses its relation to Einstein's theory with many scalar fields. It turns out that they are conformally equivalent. The masses of the scalar fields can be calculated from the linearised field equation of L. For F=R Square Operator kR, the trace of the field equation is a divergence for the dimension n=2k+4 only, i.e., in the scale-invariant case. The author deduces the condition which must be fulfilled that an inflationary (de Sitter) cosmological model is a solution of the field equation. He discusses the appearance of many inflationary phases of cosmic evolution.

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