Cosmological Constraints on Minimal Cubic Galileon Models in Teleparallel Gravity

Technical Summary: Cosmological Constraints on Minimal Cubic Galileon Models in Teleparallel Gravity

Problem Statement
The standard $\Lambda$CDM cosmological model, while successful across multiple scales, faces significant challenges, including internal coherence issues regarding the cosmological constant, the lack of direct dark matter detection, and the statistical discrepancy known as the $H_0$ tension. This tension arises from the mismatch between late-time, model-independent measurements of the Hubble parameter and early-universe predictions derived from the $\Lambda$CDM framework. To address these issues, this work investigates alternative gravitational frameworks, specifically Teleparallel Gravity (TG), where gravity is mediated by torsion rather than curvature. The study focuses on Cubic Galileon models within this TG framework, which offer a mechanism for late-time cosmic acceleration without a cosmological constant through derivative self-interactions of a scalar field.

Methodology
The authors formulate a modified gravity action where the teleparallel equivalent of general relativity (TEGR) is extended by a function $f(T) = -T + \alpha(-T)^{b_1}$, coupled to a Cubic Galileon scalar field $\phi$. The model incorporates two distinct scalar-field potentials: a quadratic (power-law) potential $V(\phi) \propto \phi^2$ and an exponential potential $V(\phi) \propto e^{c_1\phi}$.

The study analyzes four specific scenarios by varying the treatment of the model parameter $b_1$ and the choice of potential:

1. Model I: Fixed $b_1 = 2$ with a quadratic potential.
2. Model II: Fixed $b_1 = 2$ with an exponential potential.
3. Model III: Free $b_1$ (constrained by data) with a quadratic potential.
4. Model IV: Free $b_1$ (constrained by data) with an exponential potential.

Observational constraints are derived using a Markov Chain Monte Carlo (MCMC) analysis combining four distinct datasets:

• Cosmic Chronometers (CC): 31 measurements of the Hubble parameter $H(z)$ via differential age evolution.
• Type Ia Supernovae (SNIa): The Pantheon+ (PN+) & SH0ES compilation, comprising 1701 events with Cepheid-based distance calibrations.
• Baryon Acoustic Oscillations (BAO): Data from multiple surveys (SDSS, 6dF, BOSS) covering a wide redshift range.

The analysis derives constraints on the Hubble constant ($H_0$), the present-day matter density parameter ($\Omega_{m,0}$), scalar field parameters, and the model parameter $b_1$. Model performance is evaluated against the standard $\Lambda$CDM model using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) to balance goodness-of-fit against model complexity.

Key Results

• Hubble Constant ($H_0$) Sensitivity: The inferred value of $H_0$ is highly sensitive to the dataset combination and the specific potential used.
  • Inclusion of the Pantheon+ & SH0ES data consistently shifts $H_0$ toward higher values (e.g., $\sim 72.9$ km s$^{-1}$ Mpc$^{-1}$ for quadratic potentials), aligning closer with local SH0ES measurements ($73.30 \pm 1.04$).
  • The addition of BAO data moderates these high values, pulling $H_0$ toward intermediate ranges (e.g., $\sim 68.9$ to $69.7$ km s$^{-1}$ Mpc$^{-1}$) and tightening constraints.
  • The free-$b_1$ quadratic potential model (Model III) with the full dataset yields $H_0 = 69.67^{+0.52}_{-0.76}$ km s$^{-1}$ Mpc$^{-1}$.
• Parameter Constraints:
  • The parameter $b_1$ remains poorly constrained in the quadratic potential case, with uncertainties large enough to include zero, suggesting current data do not strongly require a non-zero teleparallel deviation for this potential.
  • For the exponential potential, constraints on $b_1$ are tighter, particularly when BAO data are included.
  • The matter density parameter $\Omega_{m,0}$ shows model dependence, with the exponential potential favoring lower values ($\sim 0.20$) compared to the quadratic potential ($\sim 0.36$).
• Statistical Comparison:
  • AIC: When BAO data are included, the free-$b_1$ quadratic potential model (Model III) becomes the most competitive Galileon scenario, reducing $\chi^2_{min}$ by $\sim 6.55$ relative to $\Lambda$CDM. It achieves a $\Delta$AIC of $1.46$, indicating statistical support comparable to $\Lambda$CDM.
  • BIC: Despite the improved fit, the BIC criterion continues to favor the minimal $\Lambda$CDM model. The extended models incur a penalty for their larger parameter space, resulting in large positive $\Delta$BIC values (e.g., $\Delta$BIC $= 23.33$ for Model III), indicating that the improvement in goodness-of-fit is insufficient to justify the additional complexity.

Significance and Claims
The paper claims that teleparallel Cubic Galileon cosmologies remain phenomenologically viable candidates for describing the late-time expansion history of the universe. The study demonstrates that these models can accommodate the expansion history and produce a range of $H_0$ values depending on the potential and data combination, offering a potential pathway to address the $H_0$ tension.

However, the authors maintain a modest stance regarding the resolution of the tension. They conclude that while the free-$b_1$ quadratic potential model is competitive at the AIC level when BAO data are included, it is not statistically preferred over $\Lambda$CDM by the more conservative BIC criterion. Consequently, the analysis does not establish a decisive preference for Cubic Galileon teleparallel cosmology over the standard model. The authors note that a stronger claim regarding the resolution of the Hubble tension requires further consistency tests, specifically regarding perturbative stability and structure growth, which are left for future work.