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Volume 13 | Issue 3 | Year 2026 | Article Id. IJAP-V13I3P103 | DOI : https://doi.org/10.14445/23500301/IJAP-V13I3P103

Analytical Study of Cosmic Expansion in a Parameterized Dark Energy Model

Doni Nurdiansyah

Received Revised Accepted Published
06 Sep 2026 09 Oct 2026 28 Oct 2026 13 Nov 2026

Citation :

Doni Nurdiansyah, "Analytical Study of Cosmic Expansion in a Parameterized Dark Energy Model," International Journal of Applied Physics, vol. 13, no. 3, pp. 23-35, 2026. Crossref, https://doi.org/10.14445/23500301/IJAP-V13I3P103

Abstract

The Chevallier–Polarski–Linder (CPL) equation of state, 𝑤(𝑎)=𝑤0+𝑤𝑎(1−𝑎), is the form through which DESI DR2 Baryon Acoustic Oscillation (BAO) data, combined with Cosmic Microwave Background (CMB) and Type Ia supernova (SN Ia) samples, express a preference for evolving dark energy. This study analyses the late-time expansion of a flat universe containing radiation, matter and CPL dark energy, and separates established relations from new results. The dark energy density, Hubble function, deceleration parameter, 𝑂𝑚 diagnostic and statefinder pair follow from standard relations and are collected only as a common basis. Three contributions go further. First, a pivot-based perturbative solution for the deceleration–acceleration transition redshift 𝑧𝑡 is derived; at second order it reproduces the exact root within 0.008 over −1≤𝑤0≤−0.6 and −1.5≤𝑤𝑎≤0, whereas the conventional first-order expansion about wCDM is in error by up to 0.29 at the DESI-like benchmarks. The solution shows that the earlier onset of acceleration is driven by the slope 𝑤𝑎, while the equation of state at the transition stays close to −1.09 for every benchmark. Second, the acoustic angular scale 𝜃∗ is evaluated: the sound horizon is unchanged to better than one part in 109, yet the comoving distance to last scattering shifts by up to 0.43%, so 𝜃∗ is preserved only if 𝐻0 decreases to 66.5–68.0 km s⁻¹ Mpc⁻¹ at fixed 𝛺𝑚ℎ2. Third, the closed-form jerk gives the condition 𝑤𝑎>−3𝑤0(1+𝑤0) for 𝑟0>1, which DESI-like parameters violate; this accounts for the gap between CPL values of 𝑟0 (from −0.82 to −0.06) and cosmographic reports of 𝑗0>1. For illustrative benchmarks, the dark energy density peaks 7–19% above its present value at 𝑧𝑐≈0.35–0.44, and 𝑧𝑡 lies between 0.74 and 0.78 once 𝛺𝑚0 and 𝐻0 take the values fitted jointly with (𝑤0,𝑤𝑎). Future re-deceleration is identified as a property of the linear form, not as a forecast.

Keywords

CPL parameterization, Dark energy, DESI, Deceleration parameter, Phantom crossing, Statefinder diagnostic, Transition redshift.

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