Phase space of modified Gauss-Bonnet gravity

Area of Science:

• Cosmology and Gravitational Physics
• Theoretical Physics

Background:

• Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes are fundamental to modern cosmology.
• Gauss-Bonnet gravity offers an extension to Einstein's general relativity, incorporating higher-order curvature terms.

Purpose of the Study:

• To investigate the dynamical evolution of non-vacuum FLRW spacetimes within Gauss-Bonnet gravity.
• To identify conditions leading to cosmic acceleration and analyze the phase space of these theories.

Main Methods:

• Development and application of a novel method to explore the phase space of Gauss-Bonnet gravity models.
• Analysis of dynamical equations to derive general conditions for specific cosmological behaviors.

Main Results:

• Demonstrated the transition from decelerating to accelerating expansion in various Gauss-Bonnet gravity models.
• Identified general conditions on the gravitational action that ensure accelerated expansion.
• Revealed the existence of finite-time singularities as attractors for specific initial conditions, analogous to f(R) gravity.

Conclusions:

• The presence of finite-time singularities in Gauss-Bonnet gravity is attributed to the fourth-order derivative terms in the field equations.
• Gauss-Bonnet gravity provides a framework for exploring diverse cosmological evolutions, including accelerated expansion.
• The study highlights the importance of higher-order gravity theories in understanding cosmic dynamics and potential instabilities.