Hyperbolic Hybrid FRW Cosmology in Lyra Manifold

M. M.  Sancheti; S. S.  Wankhede

doi:Received: 22 May 2026; Received in revised form: 19 Jun 2026; Accepted: 21 Jun 2026; Available online: 25 Jun 2026

Indexing and Abstracting

Hyperbolic Hybrid FRW Cosmology in Lyra Manifold

M. M. Sancheti , S. S. Wankhede

International Journal of Chemistry, Mathematics And Physics(IJCMP), Vol-10,Issue-2, April - June 2026, Pages 36-51 , Received: 22 May 2026; Received in revised form: 19 Jun 2026; Accepted: 21 Jun 2026; Available online: 25 Jun 2026

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Article Info: 10.22161/ijcmp.10.2.4

Abstract:

In this paper, we investigate a new hyperbolic hybrid Friedmann–Robertson–Walker (FRW) cosmological model in the framework of Lyra geometry. To describe the cosmic expansion dynamics, we propose a hyperbolic hybrid Hubble flow of the form H(t)=αtanh(βt)+γ/(t+1), where α,β,γ>0 are model parameters, together with a decaying Lyra displacement vector field ϕ(t)=ϕ_0/(t+1), ϕ_0>0. Exact analytical solutions for the scale factor, deceleration parameter, energy density, pressure, equation of state parameter, jerk parameter, stability parameter, and energy conditions are obtained in closed form. The scale factor exhibits smooth, non-singular cosmic evolution, while the Hubble parameter remains positive throughout cosmic time, confirming continuous expansion of the universe. The deceleration parameter shows a transition from a mildly decelerated/early super-accelerated regime to a de-Sitter-type late-time attractor, q→-1. The equation of state parameter remains in the phantom dark energy region (ω<-1) throughout cosmic evolution and approaches the cosmological constant boundary ω→-1 from below at late cosmic times. The jerk parameter approaches unity, showing correspondence with the standard ΛCDM cosmology. The null and strong energy conditions remain violated throughout cosmic evolution, with the null energy condition asymptotically approaching zero from below. The stability parameter exhibits two narrow transitional regions, separating early-, intermediate-, and late-time regimes, and settles to a nearly constant value close to -1 at late cosmic times. The statefinder diagnostic pair (r,s) is also computed; the model traces a trajectory that passes through the ΛCDM fixed point (s,r)=(0,1) at intermediate times and asymptotically approaches it, while deviating from it at early times in a manner characteristic of phantom dark energy. The present work therefore provides a comparatively new, internally consistent analytical framework for studying accelerating, non-singular cosmology, higher-order cosmological diagnostics, and dark-energy-dominated cosmic evolution in the Lyra manifold.

Keywords:

Lyra Geometry; Hyperbolic Cosmology; Hybrid Hubble Parameter; Accelerated Expansion; Dark Energy; FRW Universe; Statefinder Diagnostic

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Hyperbolic Hybrid FRW Cosmology in Lyra Manifold

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