On the Hubble constant tension in the SNe Ia Pantheon sample (2103.02117v4)

Abstract: The Hubble constant ($H_0$) tension between Type Ia Supernovae (SNe Ia) and Planck measurements ranges from 4 to 6 $\sigma$. To investigate this tension, we estimate $H_{0}$ in the $\Lambda$CDM and $w_{0}w_{a}$CDM models by dividing the Pantheon sample, the largest compilation of SNe Ia, into 3, 4, 20 and 40 bins. We fit the extracted $H_{0}$ values with a function mimicking the redshift evolution: $g(z)={H_0}(z)=\tilde{H}0/(1+z)^\alpha$, where $\alpha$ indicates an evolutionary parameter and $\tilde{H}_0=H_0$ at $z=0$. We set the absolute magnitude of SNe Ia so that $H_0=73.5\,\, \textrm{km s}^{-1}\,\textrm{Mpc}^{-1}$, and we fix fiducial values for $\Omega{0m}^{\Lambda CDM}=0.298$ and $\Omega_{0m}^{w_{0}w_{a}CDM}=0.308$. We find that $H_0$ evolves with redshift, showing a slowly decreasing trend, with $\alpha$ coefficients consistent with zero only from 1.2 to 2.0 $\sigma$. Although the $\alpha$ coefficients are compatible with 0 in 3 $\sigma$, this however may affect cosmological results. We measure locally a variation of $H_0(z=0)-H_0(z=1)=0.4\, \textrm{km s}^{-1}\,\textrm{Mpc}^{-1}$ in 3 and 4 bins. Extrapolating ${H_0}(z)$ to $z=1100$, the redshift of the last scattering surface, we obtain values of $H_0$ compatible in 1 $\sigma$ with Planck measurements independently of cosmological models and number of bins we investigated. Thus, we have reduced the $H_0$ tension from $54\%$ to $72\%$ for the $\Lambda$CDM and $w_{0}w_{a}$CDM models, respectively. If the decreasing trend of $H_0(z)$ is real, it could be due to astrophysical selection effects or to modified gravity.

• The paper introduces a redshift-dependent model for H0 using binned Pantheon SNe Ia data, revealing a slight decrease in H0 as redshift increases.
• It finds that extrapolating H0 to z=1100 aligns with Planck measurements within 1σ, reducing the tension by up to 72% across tested models.
• The study suggests that astrophysical selection effects or new physics beyond ΛCDM may influence the H0 evolution, warranting further investigation into SNe Ia systematics.

Addressing the Hubble Constant Tension with the SNe Ia Pantheon Sample

The paper "On the Hubble Constant Tension in the SNe Ia Pantheon Sample" addresses the persistent discrepancy known as the Hubble Constant ($H_0$) tension, which arises from differing measurements of $H_0$ derived from local observations, such as Type Ia supernovae (SNe Ia), and those obtained from cosmic microwave background (CMB) radiation data, notably from Planck satellite measurements. The divergence between the local SNe Ia measurements and the Planck results is significant, ranging from 4 to 6 standard deviations ($\sigma$). The researchers in this paper explore this inconsistency by employing a detailed analysis of the Pantheon SNe Ia sample, the most extensive compilation of its type, to estimate $H_0$ using both the $\Lambda$CDM and $w_{0}w_{a}$CDM cosmological models.

The approach involves dividing the Pantheon sample into several redshift bins—specifically 3, 4, 20, and 40—and fitting the extracted $H_0$ values across these divisions using a model that accommodates redshift evolution: $g(z) = {H_0}(z) = \tilde{H}_0 / (1+z)^\alpha$. Here, $\alpha$ is a parameter describing potential evolutionary behavior, and $\tilde{H}_0$ represents the value of $H_0$ at redshift $z=0$. This methodological innovation enables the researchers to account for observed redshift trends in $H_0$ measurements, which traditionally assume constancy across the universe.

The findings indicate a slight redshift-dependent evolution of $H_0$, with coefficients $\alpha$ ranging from 1.2$\sigma$ to 2.0$\sigma$, thus not wholly consistent with zero. Such results suggest a slowly decreasing trend of $H_0$ as redshift increases. Most notably, when extrapolated to redshift $z=1100$, the epoch associated with the CMB's last scattering surface, the anticipated values of $H_0$ reconcile with Planck estimates within a margin of 1$\sigma$. This outcome implies a reduction in the $H_0$ tension, improving alignment between 54% and 72% across the number of bins and models considered.

One of the key implications of this research is the potential influence of astrophysical factors or extensions to the standard model of cosmology—such as modified gravity—on the perceived $H_0$ evolution. The observed trend might stem from underlying astrophysical selection effects, which could bias the supernova measurements, or perhaps even more intriguingly suggest new physics beyond the conventional $\Lambda$CDM model. Such findings prompt further investigation into unknown systematic effects within SNe Ia data or the need for alternative theoretical frameworks.

In summary, the investigation presents a plausible methodological approach to addressing the Hubble constant tension by considering the evolutionary behavior of $H_0$ with redshift. While the results do not completely resolve the tension, they provide a step towards understanding the factors influencing cosmological measurements and suggest future research directions, including more sophisticated treatments of SNe Ia systematics or novel theoretical perspectives in cosmology.