[Paper Review] Constraints on $f(T)$ Cosmology with Pantheon+

Rebecca Briffa, Celia Escamilla‐Rivera+2 more|arXiv (Cornell University)|Mar 24, 2023

Cosmology and Gravitation Theories4 citations

TL;DR

This study constrains $f(T)$ gravity models using the new Pantheon+ and SH0ES supernova data sets, finding that these models yield higher Hubble constant values ($H_0 \approx 73.2$--$73.4\,\text{km\,s}^{-1}\text{Mpc}^{-1}$) consistent with late-time measurements, thereby alleviating the $H_0$ tension. The results show tighter constraints and reduced parameter degeneracies when combining Pantheon+ with cosmic chronometers and baryonic acoustic oscillation data.

ABSTRACT

$f(T)$ cosmology has shown promise in explaining aspects of cosmic evolution. In this work, we analyze constraints on leading models of $f(T)$ gravity in the context of the recently released Pantheon+ data set, together with comparisons with previous releases. We also consider other late-time data sets including cosmic chronometers and baryonic acoustic oscillation data. Our main result is that we find that the different $f(T)$ models under investigation connect to a variety of Hubble constant, which may help alleviate the cosmic tension on this parameter.

Motivation & Objective

• To investigate whether $f(T)$ gravity models can alleviate the $H_0$ tension observed in late-time and early-time cosmological measurements.
• To compare constraints from the new Pantheon+ and SH0ES supernova data sets with previous Pantheon data and other late-time probes.
• To assess the impact of combining cosmic chronometers and baryonic acoustic oscillation data on parameter degeneracies and $H_0$ values in $f(T)$ gravity models.
• To evaluate the performance of leading $f(T)$ gravity models in light of updated observational data, particularly in the context of the $H_0$ tension.

Proposed method

• Performing Markov Chain Monte Carlo (MCMC) analyses to constrain parameters of $f(T)$ gravity models using the Pantheon+ and SH0ES supernova data sets.
• Incorporating additional late-time data sets: cosmic chronometers (CC) and baryonic acoustic oscillations (BAO) to improve parameter constraints.
• Comparing results from the Pantheon+ and SH0ES data set with those from the earlier Pantheon data set to assess improvements in statistical precision.
• Using the $\Lambda$CDM model as a benchmark to evaluate the performance and consistency of $f(T)$ models across different data combinations.
• Analyzing posterior distributions and confidence contours to quantify parameter degeneracies and shifts in $H_0$ values across models and data sets.
• Evaluating the significance of $H_0$ deviations from Planck 2018 (P18) results in units of $\sigma$ to assess tension alleviation.

Figure 1: Confidence contours and posteriors for $f_{1}$ CDM for the parameters $H_{0}$ , $\Omega_{m,0}$ and $p_{1}$ . The blue and green contours represent data set combinations that include PN data set, while the red and purple contours show combinations that also include the $\mathrm{PN}^{+}\,\&\

Experimental results

Research questions

• RQ1 Do $f(T)$ gravity models produce $H_0$ values consistent with late-time measurements from SH0ES and Pantheon+?
• RQ2 How do the constraints on $f(T)$ gravity parameters improve when using the higher-statistics Pantheon+ data set compared to the original Pantheon release?
• RQ3 To what extent do the inclusion of cosmic chronometers and baryonic acoustic oscillation data reduce parameter degeneracies in $f(T)$ models?
• RQ4 Can $f(T)$ gravity models reconcile the $H_0$ tension without requiring new physics beyond modified gravity?
• RQ5 How do the posterior distributions and $H_0$ values in $f(T)$ models compare to those in the $\Lambda$CDM model under the same data combinations?

Key findings

• The Pantheon+ and SH0ES data set yields higher $H_0$ values in $f(T)$ models, with $H_0 \approx 73.2$--$73.4\,\text{km\,s}^{-1}\text{Mpc}^{-1}$, aligning with late-time measurements and reducing the $H_0$ tension.
• The inclusion of cosmic chronometers and baryonic acoustic oscillation data significantly reduces parameter degeneracies, particularly between $H_0$ and $p_i$ parameters.
• The $\mathrm{PN}^+\&\text{SH0ES}$ data set produces tighter constraints on model parameters compared to the original Pantheon data set.
• The $f(T)$ models considered show a strong anti-correlation between $H_0$ and $p_i$ when BAO data is included, indicating improved sensitivity to model structure.
• The $\Lambda$CDM model constrained with $\mathrm{PN}^+\&\text{SH0ES}$ yields $H_0 = 73.4 \pm 1.1\,\text{km\,s}^{-1}\text{Mpc}^{-1}$, closer to SH0ES than to early-universe estimates.
• All $f(T)$ models tested produce $H_0$ values within $1\sigma$ of the SH0ES measurement, suggesting potential alleviation of the $H_0$ tension.

Figure 2: Confidence contours and posteriors for $f_{2}$ CDM for the parameters $H_{0}$ , $\Omega_{m,0}$ and $\frac{1}{p_{2}}$ . The blue and green contours represent data set combinations that include PN data set, while the red and purple contours show combinations that also include the $\mathrm{PN