Scalar field redefinition freedom in scalar-tensor gravity

Ott Vilson, University of Tartu, Estonia

Recent cosmological observations indicate that Einstein's general relativity does not give an adequate mathematical model of the Universe. Its possible modification amounts to introducing a single non-minimally coupled scalar field for describing the gravitational interaction in addition to the second order metric tensor. In this talk I argue that the scalar field can be arbitrarily redefined so that the structure of the corresponding action functional and equations of motion are preserved under that transformation even if the latter is singular at some value of the scalar field. The qualitative behaviour of solutions of linearized equations of the Friedmann cosmology which can describe cosmological observables is also preserved.