Cosmological study of autonomous dynamical systems in modified Tele-Parallel gravity

Abstract

Cosmological approaches of autonomous dynamical system in the framework of f (T ) gravity are investigated in this paper. Our methods applied to flat Friedmann-Robertson-Walker equations in f (T ) gravity, consist to extract dynamical systems whose time-dependence is contained in a single parameter m depending on the Hubble rate of Universe and its second derivative. In our attempt to investigate the autonomous aspect of the dynamical systems reconstructed in both vacuum and nonvacuum f (T ) gravities, two values of the parameter m have been considered for our present analysis. In the so-called quasi-de Sitter inflationary era (m ≃ 0), the corresponding autonomous dynamical systems provide stable de Sitter attractors and unstable de Sitter fixed points. Especially in the vacuum f (T ) gravity, the approximate form of the f (T ) gravity near the stable and the unstable de Sitter fixed points has been performed. The matter dominated era case (m = − 9 2 ) leads to unstable fixed points confirming matter dominated era or not, and stable attractor fixed point describing dark energy dominated era. Another subtlety around the stable fixed point obtained at matter dominated case in the non-vacuum f (T ) gravity is when the dark energy dominated era is reached, at the same time, the radiation perfect fluid dominated succumbs.

Reconstruction Method in <i>F(G)</i> Gravity: Stability Study and Inflationary Survey

“…The actor of this exit is the scalar field because in their previous analysis [50] without scalar field, the obtained de Sitter solution is eternally stable. This last result is confirmed in ( ) f T theory by [51]. On can conclude from these last approach that the instability in a dynamical evolution is a source of graceful exit.…”

Teleparallel Gravity: From Theory to Cosmology

“…For the remaining works [1080,956,957,451,744,483], instead of a 1 dimensional system, a larger autonomous system is constructed which allows for a more general investigation of non-de Sitter critical points. Of note, two notable approaches were employed.…”

“…Finally, in the second consideration examined in Ref. [483], the phase-space variables The critical points along with their stability and cosmological description for an arbitrary f (T ) model based on the analysis carried out in Ref. [744].…”

Cosmological dynamics of dark energy in scalar-torsion $$f(T,\phi )$$ gravity

“…The modified gravity extension of the teleparallel equivalent of general relativity, or teleparallel gravity [58][59][60][61][62][63][64][65][66][67][68][69][70] for short, namely, f (T ) gravity [76,77] has been proposed as a good alternative to the curvature-based modified gravity theories like f (R) gravity [71][72][73][74][75], to explain the current accelerated expansion of the Universe, and its cosmological dynamics has been studied in detail in Refs. [134][135][136][137]. However, as it has been shown in Refs.…”

“…These consequences, namely, the existence of new dark energy attractors and new scaling solutions, are originated by the addition of the scalar field φ non-minimally coupled to the non-linear function G(T ) ∼ T 1+s . Furthermore, these solutions are not present neither in pure f (T ) gravity [134][135][136][137] nor in non-minimally coupled scalar field models with a linear coupling to torsion (s = 0), the so-called teleparallel dark energy model [113,115,116]. In fact, the new dark energy attractors are the fixed points j and k, that are field dominated solutions, and the fixed point l which is a de Sitter solution.…”