Qualitative study of Lyra cosmologies with spatial curvature

Exact solution to the geodesic equations in spherically symmetric space-time

“…We conclude with a few remarks: (i) In the present work, the equations for the geodesic in spherically symmetric space-time obtained by Nolan [8] have been completely solved. This will lead to a better understanding of the physical situation regarding singularities inside spherically symmetric black holes [9][10][11][12][13][14][15], in the realm of astrophysics [16][17][18][19] as well as cosmology [20][21][22][23][24].…”

Lyra cosmologies with the dynamical system perspective

“…The existence of fixed points in this dynamical system formulation is governed by the model paramater γ. This system does not illustrate the cosmological phase dominated by radiation prior to the dark matter dominated era of the Universe evolution [36]. This issue presents a limitation of the Lyra model in spatially curved spacetime.…”

“…In other words, for the present cosmic dynamical system formulation using new dynamical variables, we inquire whether (or not), the Lyra geometry model in the FRW framework will admit the 'realistic' universe solutions having radiation, dark matter and dark energy dominated evolution phases? For the affirmative answer to this question, we may have explicit examples (with present study and of [36]) in literature that the dynamical systems of the gravity theories may yield different cosmological dynamics subjected to the defined dynamical variables. The dynamical system method is an interesting tool to understand the qualitative dynamics of gravity theories in a manner which does not depend on the choice of initial conditions.…”

“…These Lyra models offer explanations for the late-time accelerating universe. The bouncing models in the Lyra's framework may yield non-singular universe evolution by overcoming the initial singularity of General relativity [36][37][38]. The traversable wormholes satisfying energy conditions may exist in the Lyra model framework, subjected to the suitable displacement vector field [39].…”

“…The model yields early deceleration phase of matter dominated era transiting into the dark energy dominated era due to the consequence of variable Λ term and scalar field [24,25]. The spatially curved FRW universe studied with the kinetic and potential-like variables (yielded by the linear combinations of the energy density and pressure) would give rise to the fixed point corresponding to the phases governed by the stiff fluid, dark matter and dark energy [36]. The existence of fixed points in this dynamical system formulation is governed by the model paramater γ.…”