Cosmological constraints on the big bang quantum cosmology model

The big bang quantum cosmology model introduces the trace $J$ of the Schouten tensor as a form of dynamic dark energy. Together with cold dark matter, these components form the so-called $J$CDM cosmology model, proposed by M.H.P.M. van Putten (J. High Energy Astrophys., 45, 2025, 194), which offers a potential resolution to the Hubble tension. We derive the constraints on the $J$CDM cosmology model, utilizing early- and late-time cosmological data including cosmic microwave background (CMB), baryon acoustic oscillations (BAO) released by the Dark Energy Spectroscopic Instrument (DESI), cosmic chronometers (CC), and type Ia supernovae (SNIa). For a flat universe, the $J$CDM model yields $H_0 = 66.95 \pm 0.51 \, \rm{km~s^{-1}~Mpc^{-1}}$ and $\Omega_m = 0.3419 \pm 0.0065$, results that are consistent with early-universe observations but exhibit a higher $\Omega_m$ compared to the $\Lambda$CDM model. In the case of a non-flat universe, $J$CDM favors a slightly curved geometry with $\Omega_k = 0.0154 \pm 0.0027$, leading to $H_0 = 69.13 \pm 0.56 \, \rm {km~s^{-1}~Mpc^{-1}}$ and $\Omega_m = 0.3477 \pm 0.0074$. The increase in $H_0$ in the non-flat scenario suggests a geometric degeneracy between spatial curvature and $H_0$. We also investigate the internal inconsistencies present in DESI data and evaluate their impacts on cosmological parameter constraints. Our analysis shows that while the $J$CDM model, which is constructed from first principles without free parameters beyond those of $\Lambda$CDM, agrees excellently with late-time cosmology, it struggles to simultaneously match early-universe observations in a fully self-consistent manner.