Abstract
We consider tensor-multiscalar representations for several types of modified gravity actions. The first example is the theory with the action representing an arbitrary smooth function of the scalar curvature and , the integrand of the Gauss-Bonnet term and the square of the Weyl tensor. We present a simple procedure leading to an equivalent theory of a space-time metric and four auxiliary scalars and especially discuss the calibration of a cosmological constant and the condition of the existence of de Sitter-like solutions in the case of an empty universe. The condition for obtaining a smaller number of independent scalar fields is derived. The second example is the Eddington-like gravity action. In this case we show, in particular, the equivalence of the theory to general relativity with the cosmological constant term, with or without use of the first-order formalism, and also discuss some possible generalizations.
- Received 21 January 2011
DOI:https://doi.org/10.1103/PhysRevD.83.084028
© 2011 American Physical Society