We consider a Lagrangian to describe gravity using a nonlinear term depending on the Gauss-Bonnet topological invariant. We examine the conditions for a bouncing and the existence of an ulterior accelerated phase of t...We consider a Lagrangian to describe gravity using a nonlinear term depending on the Gauss-Bonnet topological invariant. We examine the conditions for a bouncing and the existence of an ulterior accelerated phase of the universe. The original concept of Einstein's first paper on cosmology was to modify the equations that control the gravitational metric. Based on this, several authors have proposed different formalisms to modify general relativity. Herein, a function of the topological invariant is used in a homogeneous and isotropic cosmological model. First, a case with the topological invariant as a constant is thoroughly examined, yielding specific constraints on the evolution of the Hubble parameter. Subsequently, we study a function of the topological invariant squared. In an empty space-time scenario, the term that modifies Einstein's equations functions as an effective geometrical density, and we map regions in the phase space in which the effective pressure is positive or negative. This results in non-trivial integral solutions such as cyclic stages of acceleration and deceleration of the scale factor in the model, among other behaviors. We add cosmic dust to the system, and for certain classes of solutions, we observe that the minimum positive value of the Hubble parameter is limited by the cosmic dust matter density. If this matter density reaches zero, the minimum value of the Hubble parameter also reaches zero.展开更多
文摘We consider a Lagrangian to describe gravity using a nonlinear term depending on the Gauss-Bonnet topological invariant. We examine the conditions for a bouncing and the existence of an ulterior accelerated phase of the universe. The original concept of Einstein's first paper on cosmology was to modify the equations that control the gravitational metric. Based on this, several authors have proposed different formalisms to modify general relativity. Herein, a function of the topological invariant is used in a homogeneous and isotropic cosmological model. First, a case with the topological invariant as a constant is thoroughly examined, yielding specific constraints on the evolution of the Hubble parameter. Subsequently, we study a function of the topological invariant squared. In an empty space-time scenario, the term that modifies Einstein's equations functions as an effective geometrical density, and we map regions in the phase space in which the effective pressure is positive or negative. This results in non-trivial integral solutions such as cyclic stages of acceleration and deceleration of the scale factor in the model, among other behaviors. We add cosmic dust to the system, and for certain classes of solutions, we observe that the minimum positive value of the Hubble parameter is limited by the cosmic dust matter density. If this matter density reaches zero, the minimum value of the Hubble parameter also reaches zero.
