Cosmology Intertwined III: $f σ_8$ and $S_8$ (2008.11285v4)

Abstract: The standard $\Lambda$ Cold Dark Matter cosmological model provides a wonderful fit to current cosmological data, but a few tensions and anomalies became statistically significant with the latest data analyses. While these anomalies could be due to the presence of systematic errors in the experiments, they could also indicate the need for new physics beyond the standard model. In this Letter of Interest we focus on the tension of the Planck data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). We list a few interesting models for solving this tension, and we discuss the importance of trying to fit with a single model a full array of data and not just one parameter at a time.

• The paper demonstrates that ΛCDM exhibits significant S8 tension, with Planck data suggesting higher values than those from weak lensing surveys.
• The study finds that resolving the H0 discrepancy often exacerbates the σ8 inconsistency, highlighting a complex interplay in cosmic observations.
• The work underscores the need for comprehensive multi-dataset analyses and future surveys like Euclid and DESI to refine cosmological models.

An Analytical Examination of the $f \sigma_8$ and $S_8$ Tensions in Cosmology

The paper under discussion scrutinizes the notable tensions within the standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmological model, specifically focusing on the tensions related to the parameters $f \sigma_8$ and $S_8$. These parameters are integral to understanding the universe's structure formation and matter density, offering insights into potential deviations from the traditional cosmological model.

At the core of the paper lies the $S_8$ tension, which is highlighted as a significant discrepancy between values inferred from the Planck satellite's measurements of CMB anisotropies and those obtained from weak lensing surveys and redshift space distortion studies (RSD). The Planck data suggest a high $S_8$ value of 0.834 with a 68% confidence interval, while weak lensing surveys such as KiDS-450 report significantly lower values, approximating $0.745$ to $0.766$, with tensions reaching up to the $3.4\sigma$ level when different datasets are combined. This inconsistency suggests either a need for improved experimental methodologies or the possible indication of new physics beyond $\Lambda$CDM.

The document also addresses the "conjoined history problem" that links this $S_8$ tension with the well-documented Hubble constant ($H_0$) discrepancy. Attempts to resolve one tension often exacerbate the other. For instance, models that resolve the $H_0$ tension by modifying late-time cosmic geometry typically result in higher $\sigma_8$ values, conflicting with other observational data. This interdependency emphasizes the requirement for comprehensive analyses spanning multiple datasets rather than addressing individual parameters in isolation.

A thorough exploration of potential solutions is presented, including alternative cosmological models such as axion monodromy inflation, modified gravity, running vacuum models, and more speculative constructions including interacting dark energy or decaying dark matter. Despite extensive research, no single model presently reconciles all available cosmological observations, underscoring the challenges posed by these tensions.

The paper concludes by discussing the anticipated advancements in observational capabilities that will further elucidate these issues. Upcoming projects like Euclid, DESI, and advanced 21 cm experiments (e.g., CHIME, HIRAX) promise to refine measurements of cosmic expansion and structure growth with unprecedented accuracy. These endeavors will either clarify systematic errors in current data or solidify these tensions, guiding theoretical innovations beyond the conventional cosmological paradigm.

The discussions in this paper provide a critical assessment of the challenges facing cosmologists in fine-tuning the $\Lambda$CDM model to align with emerging empirical evidence. The implications extend toward a deeper understanding of cosmic evolution, with future observations likely playing a pivotal role in confirming or refuting proposed extensions to our current understanding of the universe.