Published July 9, 2026
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Structural Constraints on the Dark-Energy Equation-of-State Parameters in the Four-Sector FSC Cosmological Model: Analytic Proof of the Lower Bound on w₀ and Incompatibility with DESI 2025
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Abstract
We investigate the equation-of-state (EoS) parameters (w0,wa) of dark energy within
the Four-Sector FSC (Four-Sector Cosmological) framework, a cyclic cosmological
model in which the observable universe (Sector I), dark energy (Sector II), dark mat-
ter (Sector III), and a CPT-conjugate sector (Sector IV) exchange energy through
time-dependent transition rates ̃νk(τ). Using an extended suite of numerical ex-
periments (Models M6 through M8) combined with analytic estimation, we demon-
strate that the FSC four-sector ordinary differential equation (ODE) system imposes
a structural lower bound
w0 ≥ wmin0 ≈ −0.64,
independent of the functional form of ̃νk(τ), provided that the observed density
fractions (Ωb,ΩDM,ΩΛ) = (0.049, 0.268, 0.683) are satisfied. This bound is incom-
patible with the DESI 2025 best-fit value w0 = −0.838, establishing that the current
the Four-Sector FSC (Four-Sector Cosmological) framework, a cyclic cosmological
model in which the observable universe (Sector I), dark energy (Sector II), dark mat-
ter (Sector III), and a CPT-conjugate sector (Sector IV) exchange energy through
time-dependent transition rates ̃νk(τ). Using an extended suite of numerical ex-
periments (Models M6 through M8) combined with analytic estimation, we demon-
strate that the FSC four-sector ordinary differential equation (ODE) system imposes
a structural lower bound
w0 ≥ wmin0 ≈ −0.64,
independent of the functional form of ̃νk(τ), provided that the observed density
fractions (Ωb,ΩDM,ΩΛ) = (0.049, 0.268, 0.683) are satisfied. This bound is incom-
patible with the DESI 2025 best-fit value w0 = −0.838, establishing that the current
FSC ODE topology cannot reproduce the DESI result. We further show that the
spontaneous convergence β →0 observed in Model M8 is a numerical manifestation
of the underlying CPT symmetry of the FSC framework. Three minimal structural
modifications capable of resolving this tension are proposed, providing a roadmap
toward a next-generation FSC model (Paper I).
spontaneous convergence β →0 observed in Model M8 is a numerical manifestation
of the underlying CPT symmetry of the FSC framework. Three minimal structural
modifications capable of resolving this tension are proposed, providing a roadmap
toward a next-generation FSC model (Paper I).
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Additional details
Related works
- References
- Preprint: 10.5281/zenodo.21038702 (DOI)
- Preprint: 10.5281/zenodo.21094857 (DOI)
- Preprint: 10.5281/zenodo.21130308 (DOI)
- Preprint: 10.5281/zenodo.21206325 (DOI)
- Preprint: 10.5281/zenodo.21241760 (DOI)