Auxiliary fields representation for modified gravity models
Abstract
We consider tensormultiscalar 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 GaussBonnet term and the square of the Weyl tensor. We present a simple procedure leading to an equivalent theory of a spacetime metric and four auxiliary scalars and especially discuss the calibration of a cosmological constant and the condition of the existence of de Sitterlike 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 Eddingtonlike 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 firstorder 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;
 Higherdimensional 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
 EPrint:
 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