# In the Realm of the Hubble tension $-$ a Review of Solutions

**Authors:** Eleonora Di Valentino, Olga Mena, Supriya Pan, Luca Visinelli, Weiqiang Yang, Alessandro Melchiorri, David F. Mota, Adam G. Riess, Joseph Silk  
**arXiv:** [2103.01183](https://arxiv.org/abs/2103.01183)  
**Date:** 2021-03-01  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2103.01183v1/

## Key points

- The $\Lambda$CDM model has been successful in explaining cosmological data
- Recent advancements in observations have revealed discrepancies among key cosmological parameters within this model
- One of the most significant tensions is the $4-6\sigma$ discrepancy between predictions of the Hubble constant ($H_0$) by early time probes and independent determinations of $H_0$ from local measurements
- Precision and consistency of data at both early and late times present challenges to finding a solution that can explain these observations
- Proposed theoretical solutions include new physics, unexpected large-scale structures, or unrelated errors
- Some models have shown success in improving fit to data through additional degrees of freedom, restoring agreement within $1-2\sigma$
- Reducing tension may come from changing $H_0$ or increasing its uncertainty due to degeneracy with additional physics
- Additional probes are needed to further investigate these discrepancies
- Potential solutions discussed include early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity
- No specific proposal stands out as highly likely or significantly better than others
- Continued research and exploration are needed to better understand this fundamental cosmological discrepancy.

## Summary

The $\Lambda$CDM model, which describes the expansion of the universe, has been successful in explaining a wide range of cosmological data. However, recent advancements in observations have revealed discrepancies among key cosmological parameters within this model. One of the most significant tensions is the $4-6\sigma$ discrepancy between predictions of the Hubble constant ($H_0$) by early time probes within the $\Lambda$CDM model and independent determinations of $H_0$ from local measurements. The precision and consistency of data at both early and late times present challenges to finding a solution that can explain these observations. This demands a hypothesis with enough rigor to account for multiple observations, whether it involves new physics, unexpected large-scale structures, or unrelated errors. In this review, a thorough examination of the problem is presented. It includes a discussion of recent estimates of the Hubble constant and an overview of proposed theoretical solutions. Some models presented in this review have shown formal success by improving the fit to the data through additional degrees of freedom. These models restore agreement within $1-2\sigma$ between various datasets such as {\it Planck} 2018 (using CMB power spectra data), Baryon Acoustic Oscillations (BAO), Pantheon Supernovae (SN) data, and R20 (the latest measurement by the SH0ES Team). It is important to note that reducing tension may not simply come from changing $H_0$, but also from increasing its uncertainty due to degeneracy with additional physics. This highlights the need for additional probes to further investigate these discrepancies. While no specific proposal stands out as highly likely or significantly better than others, several potential solutions are discussed in this review. These include models involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity. Until a better alternative emerges, these models provide the best options for addressing the Hubble tension. Overall, this review provides a comprehensive analysis of the Hubble tension problem and offers insights into potential theoretical solutions while emphasizing their limitations and uncertainties associated with them. The authors emphasize the need for continued research and exploration to better understand this fundamental cosmological discrepancy.