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

Abstract: The $\Lambda$CDM model provides a good fit to a large span of cosmological data but harbors areas of phenomenology. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the $4-6\sigma$ disagreement between predictions of the Hubble constant $H_0$ by early time probes with $\Lambda$CDM model, and a number of late time, model-independent determinations of $H_0$ from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demand a hypothesis with enough rigor to explain multiple observations--whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. We present a thorough review of the problem, including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions. Some of the models presented are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within $1-2\sigma$ between {\it Planck} 2018, using CMB power spectra data, BAO, Pantheon SN data, and R20, the latest SH0ES Team measurement of the Hubble constant ($H_0 = 73.2 \pm 1.3{\rm\,km\,s^{-1}\,Mpc^{-1}}$ at 68\% confidence level). Reduced tension might not simply come from a change in $H_0$ but also from an increase in its uncertainty due to degeneracy with additional physics, pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.[Abridged]

• The paper systematically reviews multiple models that attempt to resolve the Hubble tension by altering early Universe dynamics and dark energy behavior.
• It categorizes proposals into early dark energy, late dark energy, extra relativistic degrees, interacting models, modified gravity, unified cosmologies, and alternative recombination scenarios.
• The review underscores the importance of multi-probe observational tests and robust theoretical frameworks to refine our understanding of cosmic expansion.

Analysis of Proposed Solutions to the Hubble Tension

The paper "In the Realm of the Hubble tension - a Review of Solutions" provides an exhaustive review of the various models and hypotheses that have been put forward to address the discrepancy between the value of the Hubble constant $H_0$ derived from early Universe observations, such as those conducted by the Planck satellite, and local measurements obtained through distance ladder techniques. This discrepancy, often referred to as the "Hubble tension," is one of the prominent challenges in modern cosmology, with implications for our understanding of dark energy, dark matter, and the overall dynamics of the Universe.

Overview of Proposed Models

The authors categorize the solutions into distinct groups, underlying the complexity and wide-reaching implications of the problem:

1. Early Dark Energy: These models propose a modification in the Universe's expansion history before recombination, often introducing a new scalar field or energy component that can reconcile the CMB-derived $H_0$ with local measurements by altering the sound horizon. For example, effective models involving Ultra-Light Axions and Anharmonic Oscillations show promise in adjusting early Universe dynamics.
2. Late Dark Energy: This category explores modifications to the dark energy equation of state that change the late-time expansion rate. These models are intriguing as they could provide an innovative approach to fit both the local distance ladder and early Universe observations into a coherent framework, albeit at the risk of complicating the agreement with BAO and other datasets.
3. Models with Extra Relativistic Degrees of Freedom: By introducing additional, non-standard components to the radiation content, encapsulated by a change in $N_{\rm eff}$, these models attempt to mitigate the tension. Sterile neutrinos and thermal axions are often considered here, adjusting the expansion dynamics at recombination.
4. Interacting Models: These theories propose non-standard interactions between dark matter and dark energy, or other particles, which adjust the expansion history and potentially alleviate the $H_0$ tension. Interactions could theoretically provide the necessary changes in cosmological evolution without necessitating exotic new physics.
5. Modified Gravity: Approaches in this category reconsider the foundations of gravitational interactions in cosmology. By extending general relativity or considering alternative models, such as $f(R)$ gravity or scalar-tensor theories, these solutions challenge conventional gravitational paradigms and offer a rich field for resolving tensions.
6. Unified Cosmologies and Inflationary Models: These proposals integrate aspects of dark matter and dark energy into a single framework or modify inflationary premises to yield a consistent $H_0$ across datasets.
7. Modified Recombination Histories: Small-scale, high-density inhomogeneities or variations in fundamental constants during recombination are explored as potential resolutions, given their capacity to affect the deduced value of the Hubble constant.
8. Physical Phenomena and Alternative Proposals: These encompass diverse theories, including those inspired by critical phenomena or alterations in cosmic inhomogeneities, which could account for observational discrepancies through unconventional yet physically motivated mechanisms.

Implications and Future Directions

The myriad solutions indicate the breadth and depth of theoretical ingenuity aimed at resolving the Hubble tension. However, none provide a definitive answer, highlighting both the potential and the challenges of extending beyond $\Lambda$CDM. Certain models, especially those involving new physics in the early Universe or modifications of dark energy, stand out in their potential but demand rigorous scrutiny against a wide array of cosmological probes to ensure consistency and empirical validation.

Looking ahead, advancements in both observation (e.g., new CMB measurements, gravitational wave astronomy) and theory are essential. Collaboration between these domains promises to either uncover new physics or pinpoint systematic errors underlying current discrepancies. The path forward is as much about refining observational techniques and reducing error margins as it is about developing innovative theoretical constructs that robustly describe the Universe's intricate tapestry.

This thorough examination of possible resolutions to the Hubble tension serves as a pivotal reference for astrophysicists and cosmologists invested in mapping the future of the discipline. By meticulously categorizing and evaluating extant models, the paper encourages further exploration and refinement in pursuit of a reconciled cosmological model.