Cosmological constraints on the big bang quantum cosmology model

1. Problem Statement

The standard $\Lambda$CDM cosmological model, while successful in describing the Cosmic Microwave Background (CMB), faces significant challenges, most notably the Hubble tension. This is the discrepancy between the Hubble constant ($H_0$) inferred from early-universe CMB data ($H_0 \approx 67.36$ km s$^{-1}$ Mpc$^{-1}$) and direct late-universe measurements via the local distance ladder ($H_0 \approx 73.04$ km s$^{-1}$ Mpc$^{-1}$). Additionally, there are tensions regarding the amplitude of matter clustering ($S_8$) and the static nature of the cosmological constant ($\Lambda$).

The JCDM model (proposed by M.H.P.M. van Putten) offers a potential resolution by introducing dynamic dark energy derived from first principles of quantum cosmology. In this model, dark energy is not a static constant but a relic of the Big Bang, characterized by the trace $J$ of the Schouten tensor. The model predicts a specific scaling relation $H_0 = \sqrt{6/5} H_{\Lambda}^0$, theoretically yielding a higher $H_0$ ($\approx 74.9$ km s$^{-1}$ Mpc$^{-1}$) to resolve the tension. However, previous estimates lacked rigorous statistical constraints and did not fully account for parameter correlations or internal inconsistencies in recent datasets.

2. Methodology

The authors performed a comprehensive statistical analysis to constrain the JCDM model parameters using a Markov Chain Monte Carlo (MCMC) approach.

• Datasets:
  • DESI DR1 (Dark Energy Spectroscopic Instrument): Baryon Acoustic Oscillation (BAO) data across multiple redshift bins (Bright Galaxy, Luminous Red Galaxy, Emission Line Galaxy, Quasar, and Lyman-$\alpha$ Forest samples).
  • CMB (Planck 2018): Used as distance priors (acoustic scale $l_A$, shift parameter $R$, and baryon density $\Omega_b h^2$) rather than full power spectrum analysis to reduce computational cost while maintaining robustness.
  • Cosmic Chronometers (CC): 31 data points measuring the Hubble expansion rate $H(z)$ directly from galaxy ages.
  • Type Ia Supernovae (SNIa): The Pantheon+ compilation (1048 supernovae) spanning $0.01 < z < 2.3$.
• Model Framework:
  • The JCDM model modifies the Friedmann equation, introducing a dynamic dark energy density scaling with the Hubble parameter $H(z)$.
  • The analysis was conducted under two geometric assumptions: Flat Universe ($\Omega_k = 0$) and Non-Flat Universe ($\Omega_k \neq 0$).
• Key Variables:
  • Parameters constrained: Matter density ($\Omega_m$), Hubble constant ($H_0$), curvature density ($\Omega_k$), and baryon density ($\Omega_b h^2$).
  • Acoustic Horizon ($r_d$) Treatment: The study compared two scenarios for the sound horizon at the drag epoch:
    1. "Unfixed" case: $r_d$ calculated dynamically from model parameters using Eq. (7).
    2. "Fixed" case: $r_d$ fixed to the Planck-derived prior ($147.09 \pm 0.26$ Mpc).
• Internal Consistency Check: A specific focus was placed on the DESI LRG sample at $z_{eff} = 0.51$, which previously showed an anomalously high matter density ($\Omega_m \approx 0.67$) inconsistent with other probes. The authors performed analyses both including and excluding this specific data point to assess its impact.

3. Key Contributions

• Rigorous MCMC Constraints: Provided the first comprehensive MCMC constraints on the JCDM model using the full DESI DR1 dataset combined with CMB, CC, and SNIa, moving beyond simple point estimates.
• Sensitivity to $r_d$ Priors: Demonstrated that JCDM constraints are highly sensitive to the specification of the sound horizon ($r_d$). The choice between a model-derived $r_d$ and a Planck-prior $r_d$ leads to significant shifts in $H_0$ and $\Omega_m$.
• DESI Data Anomaly Investigation: Systematically evaluated the impact of the $z_{eff}=0.51$ LRG outlier. The study found that while $\Lambda$CDM is robust against this outlier, JCDM is highly sensitive, suggesting the model relies on this specific data point to maintain consistency with other constraints.
• Geometric Degeneracy: Identified a strong geometric degeneracy between spatial curvature ($\Omega_k$) and $H_0$ in the non-flat JCDM scenario, where a curved geometry allows for a higher $H_0$.

4. Key Results

A. Flat Universe Constraints:

• Unfixed $r_d$ (Model-derived):
  • $H_0 = 66.95 \pm 0.51$ km s$^{-1}$ Mpc$^{-1}$
  • $\Omega_m = 0.3419 \pm 0.0065$
  • Observation: The $H_0$ is significantly lower than the theoretical JCDM prediction ($\sim 74.9$) and the local distance ladder value ($\sim 73$). It aligns with early-universe CMB values but fails to resolve the Hubble tension.
• Fixed $r_d$ (Planck Prior):
  • $H_0 = 65.40 \pm 0.52$ km s$^{-1}$ Mpc$^{-1}$
  • $\Omega_m = 0.3640 \pm 0.0073$
  • Observation: Fixing $r_d$ further lowers $H_0$ and increases $\Omega_m$, creating a tension with late-time observations.

B. Non-Flat Universe Constraints:

• Unfixed $r_d$:
  • Favors a positively curved universe: $\Omega_k = 0.0154 \pm 0.0027$ (deviation from flatness $>5\sigma$).
  • $H_0 = 69.13 \pm 0.56$ km s$^{-1}$ Mpc$^{-1}$
  • $\Omega_m = 0.3477 \pm 0.0074$
  • Observation: The non-flat geometry allows for a higher $H_0$ (closer to local measurements) but requires significant positive curvature.

C. Impact of the $z_{eff}=0.51$ DESI Data Point:

• $\Lambda$CDM: Removing the $z=0.51$ point has a negligible effect on parameters, confirming the model's robustness.
• JCDM: Removing this point causes a significant shift:
  • In the non-flat case, $H_0$ drops from $69.13$ to $67.51$ km s$^{-1}$ Mpc$^{-1}$.
  • $\Omega_k$ decreases from $0.0154$ to $0.0096$.
  • This indicates JCDM relies heavily on the high-matter-density signal from the $z=0.51$ LRG sample to sustain its preferred curvature and $H_0$ values.

D. Comparison with $\Lambda$CDM:

• JCDM consistently yields a higher matter density ($\Omega_m \approx 0.34-0.36$) compared to $\Lambda$CDM ($\Omega_m \approx 0.30$) across all datasets.
• While JCDM fits late-time data (local distance ladder) well in its original formulation, the current analysis shows it struggles to simultaneously satisfy early-universe CMB constraints without introducing new tensions (e.g., requiring non-flat geometry or specific data outliers).

5. Significance and Conclusion

The paper concludes that the JCDM model, while theoretically elegant and capable of explaining high $H_0$ values via first principles, does not currently provide a fully self-consistent resolution to the Hubble tension when constrained by the full suite of modern cosmological data.

• Complementary Success: The study suggests a "complementary" success: $\Lambda$CDM aligns well with early-universe (CMB) constraints, whereas JCDM aligns better with late-time (local distance ladder) observations but fails to bridge the gap without tension.
• Data Dependence: The model's viability is highly sensitive to the treatment of the sound horizon ($r_d$) and specific DESI data points. The internal inconsistencies in DESI data (specifically the $z=0.51$ LRG sample) significantly bias the JCDM constraints.
• Future Outlook: The authors emphasize that while JCDM offers a promising alternative to the cosmological constant, further observational tests and a better understanding of systematic errors in BAO reconstruction are required to determine if the model can be reconciled with both early and late-universe physics. The current results suggest that JCDM may not be the ultimate solution to the Hubble tension in its present form.