Auxiliary fields representation for modified gravity models
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 R and □R, 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.
- Publication:
-
Physical Review D
- Pub Date:
- April 2011
- DOI:
- 10.1103/PhysRevD.83.084028
- arXiv:
- arXiv:1101.5028
- Bibcode:
- 2011PhRvD..83h4028R
- Keywords:
-
- 04.50.-h;
- 04.50.Kd;
- 98.80.-k;
- 98.80.Jk;
- Higher-dimensional gravity and other theories of gravity;
- Modified theories of gravity;
- Cosmology;
- Mathematical and relativistic aspects of cosmology;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- 83D05;
- 83F05
- E-Print:
- Added a few comments on quantum properties and a new section about quantum UV completion of the classically equivalent theories, plus corresponding references. Fits the manuscript accepted for publication in Physical Review D. 29 pages, no figures