Singularityfree cosmological solutions in quadratic gravity
Abstract
We study a general field theory of a scalar field coupled to gravity through a quadratic GaussBonnet term ξ(φ)R^{2}_{GB}. The coupling function has the form ξ(φ)=φ^{n}, where n is a positive integer. In the absence of the GaussBonnet term, the cosmological solutions for an empty universe and a universe dominated by the energymomentum tensor of a scalar field are always characterized by the occurrence of a true cosmological singularity. By employing analytical and numerical methods, we show that, in the presence of the quadratic GaussBonnet term, for the dual case of even n, the set of solutions of the classical equations of motion in a curved FRW background includes singularityfree cosmological solutions. The singular solutions are shown to be confined in a part of the phase space of the theory allowing the nonsingular solutions to fill the rest of the space. We conjecture that the same theory with a general coupling function that satisfies certain criteria may lead to nonsingular cosmological solutions.
 Publication:

Physical Review D
 Pub Date:
 April 1999
 DOI:
 10.1103/PhysRevD.59.083512
 arXiv:
 arXiv:grqc/9806085
 Bibcode:
 1999PhRvD..59h3512K
 Keywords:

 98.80.Hw;
 04.20.Jb;
 04.50.+h;
 11.25.Mj;
 Exact solutions;
 Gravity in more than four dimensions KaluzaKlein theory unified field theories;
 alternative theories of gravity;
 Compactification and fourdimensional models;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 Latex, 25 pages, 6 figures, some explanatory sentences and Comments added, version to appear in Physical Review D