Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

TL;DR

This white paper surveys the H0 and S8 tensions as a compass pointing beyond ΛCDM, outlining a coordinated strategy to test early- and late-time new physics, non-FLRW geometries, and modified gravity. It emphasizes Bayesian model comparison, joint multi-probe analyses, and robust handling of systematics to determine whether tensions arise from data issues or point to a deeper cosmological framework. The report catalogs a broad landscape of proposed solutions—from Early Dark Energy and extra relativistic species to running vacuum and Horndeski-type theories—along with the challenges posed by large-scale anomalies and the age of the universe. It argues for a data-driven, model-agnostic approach initially (reconstructions, EFT formulations, and scale-aware analyses), followed by targeted theoretical models with concrete, falsifiable predictions to be tested by next-generation CMB, galaxy surveys, gravitational-wave, and 21 cm experiments. The optimistic outlook is that upcoming facilities (CMB-S4, LSST, Euclid, Roman, SKA, LISA, etc.) will either relieve tensions or reveal new physics, guiding the next standard cosmology beyond ΛCDM.

Abstract

In this paper we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant $H_0$, the $σ_8$--$S_8$ tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the $5.0\,σ$ tension between the {\it Planck} CMB estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the {\it Planck} CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density $Ω_m$, and the amplitude or rate of the growth of structure ($σ_8,fσ_8$). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the $H_0$--$S_8$ tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals.[Abridged]

Figures (26)

• Figure 2: 68% CL constraint on $H_0$ from different cosmological probes (based on Refs. DiValentino:2021izsPerivolaropoulos:2021jda).
• Figure 3: 1, 2 and 3 times the standard deviation $\left\langle \delta_{H}^2 \right\rangle_R^{1/2}$ as a function of redshift $z$ and scale $R(z)$. The dashed line marks the redshift $z=0.023$. The Hubble constant is estimated by SH0ES in the redshift range $0.023<z<0.15$. Plot from Ref. Camarena:2018nbr.
• Figure 4: Constraints on $S_8$ and its corresponding 68% error (updated from Ref. Perivolaropoulos:2021jda). We show the nominal reported values by each study, which may differ in their definition of the constraints. The definition $S_8= \sigma_8 (\Omega_{\rm m}/0.3)^\alpha$ with $\alpha=1/2$ has been uniformly used for all points. In those cases where $\alpha \neq 1/2$ has been used in some references, the value of $S_8$ with $\alpha =1/2$ was recalculated (along with the uncertainties) using the constraints on $\sigma_8$ and $\Omega_{\rm m}$ shown in those references, assuming their errors are Gaussian. This concerns only 5 CC points where the published value of $\alpha$ was different from $1/2$ and the difference from the published $S_8$ (with different $\alpha$) is very small. The rest of the points are taken directly from the published values.
• Figure 5: Tensor-to-scalar ratio $r$ versus spectral index $n_s$, for the $\Lambda$CDM model (blue) and for the NEDE model (gold). To get the NEDE model constraint, we approximate the $\Lambda$CDM contour as a bivariate Gaussian, and substitute the mean and error on $n_s$ by the ones got in the NEDE model. This approximate procedure reproduces well a full analysis Ye:2021nej. The round dots are predictions of potentials $\sim \phi^p$ with $0.1 \leq p \leq 0.5$. The square dots are the predictions of the Starobinsky $R^2$ inflation Starobinsky:1980te. This figure is from DAmico:2021zdd.
• Figure 6: Evolution of $\sigma_{8M} (z)$ for clustering and homogeneous DE models. For all models, $w_0=-1$, $\Omega_m=0.315$, and $\sigma_{8\Lambda}=0.811$ have been used to normalize $\sigma_{8M} (z)$ at $z_{\rm rec}$.