A Consistency Criterion for Reconstructive Cosmological Models

Reconstructive methods are widely used in modified gravity cosmology to avoid the difficulty of finding exact analytical solutions. These methods, however, contain an implicit assumption. The kinematic ansatz for the Hubble parameter and the dynamic equations of motion determine the transition to accelerated expansion through independent procedures. There is no guarantee that these two approaches yield consistent results. In this work, we introduce the phase coherence criterion, defined as Δz=∣zq−zω∣\Delta z = |z_q - z_{\omega}|Δz=∣zq​−zω​∣. Here, zqz_qzq​ is obtained from the kinematic condition q(zq)=0q(z_q) = 0q(zq​)=0, and zωz_{\omega}zω​ is obtained from the dynamic condition ωdyn(zω)=−1/3\omega_{\mathrm{dyn}}(z_{\omega}) = -1/3ωdyn​(zω​)=−1/3 on the equation of state. We demonstrate the criterion on the generalized Einstein–scalar–Gauss–Bonnet model using three independent observational datasets. These are Cosmic Chronometers, BAO from SDSS and DESI, and Pantheon+ with SH0ES calibration. The exact analytical solution obtained via Noether symmetry yields Δz∼10−3\Delta z \sim 10^{-3}Δz∼10−3 across all datasets. This value is two orders of magnitude below the observational threshold derived from Pantheon+ precision. In contrast, the hybrid reconstructive ansatz produces Δz≈0.69\Delta z \approx 0.69Δz≈0.69. This exceeds the threshold by a factor of five. The criterion is straightforward to evaluate and requires no new observational data. It is compatible with any modified gravity theory that admits an effective fluid interpretation within the flat FLRW framework.