Abstract: We investigate an anisotropic Bianchi type I cosmological model in General Relativity, employing a nonlinear cubic equation of state p=λρ3+μρ2-ρ
together with a hyperbolic Hubble flow parametrization Ht=αtanhβt
. Exact analytical expressions are obtained for the scale factor, directional scale factors, Hubble parameter, deceleration, jerk and statefinder parameters, energy density, an effective pressure and equation of state, expansion and shear scalars, the anisotropy ratio σ2/θ2
, a sound-speed (stability) parameter, the null and strong energy conditions, the Omz
diagnostic, and – derived directly and independently of λ,μ
from the field equations – the true anisotropic skewness parameters γt
and δt
.
The model is exactly isotropic at t=0
(σ2=0
); γ
and δ
are formally singular there only because the normalizing energy density ρ
vanishes, while the underlying anisotropic stresses remain finite. As cosmic time increases, σ2
, γ , and δ all relax toward small, non-zero constants, so the universe evolves toward a state of permanent, bounded (“frozen”) anisotropy rather than isotropizing – a result stated sharply via the exactly constant anisotropy ratio σ2/θ2≈1.11×10-3
, which depends only on the anisotropy exponents m,n
. The deceleration parameter satisfies qt<-1
for all t>0
(kinematic super-acceleration, H>0
, despite ωt≥-1
), diverging as t→0+
and approaching the de Sitter value q=-1
only as t→∞
; the corresponding jerk parameter jt
and statefinder pair r,s
approach the Λ
CDM fixed point r,s=1,0
from the quintessence-like quadrant as t→∞ .
For the adopted parameters (λ=0.02, μ=0.1
, chosen to satisfy the causality bound 3λρ∞2+2μρ∞≤2
), the effective equation-of-state parameter ωt
interpolates monotonically from the de Sitter value ω=-1
at t=0 to a mild quintessence value ω≈-0.20
at late times, the null energy condition holds throughout, the strong energy condition is violated only in a brief early window (t≲2.1
) and is restored thereafter, and the sound speed satisfies cs2≤1
for all t
. Phantom behaviour (ω<-1
) is not realized for λ,μ>0
and would require λ<0
or μ<0
.
The model thus provides a causally consistent, exactly solvable framework for an anisotropic universe that begins isotropic, passes through a transient dark-energy-like phase, and settles into a permanently and mildly anisotropic, quintessence-dominated late-time state.
Keywords: Bianchi type I cosmology; Anisotropic dark energy; Cubic equation of state; Exact solutions; State finder and Om(z) diagnostics; Quintessence.
Title: Hyperbolic Reconstruction of an Anisotropic Bianchi Type-I Cosmology with a Cubic Dark Energy Fluid
Author: M. M. Sancheti, S. S. Wankhede
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
Vol. 14, Issue 1, April 2026 - September 2026
Page No: 64-75
Research Publish Journals
Website: www.researchpublish.com
Published Date: 17-June-2026
