[Paper Review] Running Hubble constant from the SNe Ia Pantheon sample?

Tiziano Schiavone, Giovanni Montani+4 more|arXiv (Cornell University)|May 14, 2022

Gamma-ray bursts and supernovae7 citations

TL;DR

This paper investigates the Hubble constant tension using the Pantheon SNe Ia sample by performing a redshift-binned analysis to test for a running Hubble constant. It finds a slow, statistically consistent-with-no-evolution decrease in $H_0(z)$ with redshift, described by $H_0(z) = \tilde{H}_0(1+z)^{-\alpha}$ with $\alpha \sim 10^{-2}$, and shows that extrapolating this evolution to $z=1100$ yields $H_0$ values consistent with Planck CMB measurements within 1$\sigma$, suggesting a potential resolution to the tension via modified gravity models.

ABSTRACT

The mismatch between different independent measurements of the expansion rate of the Universe is known as the Hubble constant ($H_0$) tension, and it is a serious and pressing problem in cosmology. We investigate this tension considering the dataset from the Pantheon sample, a collection of 1048 Type Ia Supernovae (SNe Ia) with a redshift range $0

Motivation & Objective

• To investigate whether the Hubble constant tension originates in late-time cosmological data by analyzing the Pantheon SNe Ia sample.
• To test if $H_0$ evolves with redshift in the $0 < z < 2.26$ range using binned analysis.
• To explore whether a running $H_0(z)$ can reconcile local SNe Ia measurements with early-universe CMB data from Planck.
• To model the observed $H_0(z)$ evolution within $f(R)$ modified gravity theories and derive the corresponding scalar field potential in the Jordan frame.

Proposed method

• Performing a redshift-binned analysis of the Pantheon SNe Ia dataset, dividing the sample into three and four equally populated redshift bins.
• Using Markov Chain Monte Carlo (MCMC) methods to estimate $H_0$ in each bin under both $\Lambda$CDM and $w_0w_a$CDM cosmological models.
• Fitting the observed $H_0$ values with the parametric function $H_0(z) = \tilde{H}_0(1+z)^{-\alpha}$ to model a running Hubble constant.
• Deriving the scalar field potential $V(\phi)$ in the Jordan frame from the $f(R)$-gravity formalism, assuming a dynamical $H_0(z)$.
• Constructing the $f(R)$ function from the scalar potential using the relation $f(R) = R\phi(R) - V(\phi(R))$, and expanding it in powers of $\alpha$.
• Extrapolating the $H_0(z)$ fit to $z=1100$ to compare with Planck CMB measurements of $H_0$.

Experimental results

Research questions

• RQ1 Does the Hubble constant exhibit a redshift-dependent evolution in the Pantheon SNe Ia sample?
• RQ2 Can a running $H_0(z)$ model reconcile local SNe Ia measurements with early-universe CMB data from Planck?
• RQ3 What is the theoretical interpretation of the observed $H_0(z)$ evolution in terms of modified gravity, specifically $f(R)$ gravity?
• RQ4 What form does the scalar field potential take in the Jordan frame that reproduces the observed $H_0(z)$ evolution?
• RQ5 How do the inferred $f(R)$ gravity models deviate from General Relativity, and what is the significance of the $\alpha$ parameter?

Key findings

• The binned analysis reveals a decreasing trend of $H_0$ with redshift, well-described by $H_0(z) = \tilde{H}_0(1+z)^{-\alpha}$ with $\alpha \sim 10^{-2}$.
• The observed $\alpha$ value is consistent with no evolution at the 1.2$\sigma$ to 2.0$\sigma$ confidence level, indicating a weak but non-zero running.
• Extrapolating the $H_0(z)$ fit to the last scattering surface at $z=1100$ yields $H_0$ values consistent with Planck CMB measurements within 1$\sigma$.
• The inferred scalar field potential in the Jordan frame is $V(\phi) = 3m^2\left[1 - \left(\frac{\phi}{\phi_0}\right)^{\frac{3-2\alpha}{3}}\right]$, with $m^2 = \tilde{H}_0^2 \Omega_{0m}$.
• The corresponding $f(R)$ function deviates from General Relativity at first order in $\alpha$, with $f(R) \approx R - 6m^2\frac{1-\Omega_{0m}}{\Omega_{0m}} + \frac{2}{3}\alpha\left[R\ln\left(-\frac{R}{m^2}\right) - (1+\ln 18)R + 18m^2\frac{1-\Omega_{0m}}{\Omega_{0m}}\right]$.
• The results suggest that the $H_0$ tension may stem from a hidden astrophysical or cosmological evolution not accounted for in standard $\Lambda$CDM, possibly resolved by $f(R)$ gravity with a specific scalar potential.