# CMB tensions with low-redshift $H_0$ and $S_8$ measurements: impact of a redshift-dependent type-Ia supernovae intrinsic luminosity

## TL;DR

This study investigates the tensions between local and CMB measurements of $H_0$ and $S_8$, exploring how redshift-dependent supernovae luminosity and dynamic Dark Energy models can alleviate these discrepancies, but tensions persist with BAO data.

## Contribution

It introduces a model accounting for redshift-dependent supernovae luminosity and Dark Energy variations, assessing their impact on cosmological parameter tensions.

## Key findings

- Varying Dark Energy can reduce $H_0$ and $S_8$ tensions.
- Adding BAO data sustains the tensions despite systematic uncertainties.
- Systematic effects in BAO measurements may be key to resolving discrepancies.

## Abstract

With the recent increase in precision of our cosmological datasets, measurements of $\Lambda$CDM model parameter provided by high- and low-redshift observations started to be in tension, i.e., the obtained values of such parameters were shown to be significantly different in a statistical sense. In~this work we tackle the tension on the value of the Hubble parameter, $H_0$, and the weighted amplitude of matter fluctuations, $S_8$, obtained from local or low-redshift measurements and from cosmic microwave background (CMB) observations. We combine the main approaches previously used in the literature by extending the cosmological model and accounting for extra systematic uncertainties. With such analysis we aim at exploring non standard cosmological models, implying deviation from a cosmological constant driven acceleration of the Universe expansion, in the presence of additional uncertainties in measurements. In more detail, we reconstruct the Dark Energy equation of state as a function of redshift, while we study the impact of type-Ia supernovae (SNIa) redshift-dependent astrophysical systematic effects on these tensions. We consider a SNIa intrinsic luminosity dependence on redshift due to the star formation rate in its environment, or the metallicity of the progenitor. We find that the $H_0$ and $S_8$ tensions can be significantly alleviated, or~even removed, if we account for varying Dark Energy for SNIa and CMB data. However, the tensions remain when we add baryon acoustic oscillations (BAO) data into the analysis, even after the addition of extra SNIa systematic uncertainties. This points towards the need of either new physics beyond late-time Dark Energy, or other unaccounted systematic effects (particulary in BAO measurements), to fully solve the present tensions.