[Paper Review] Challenges for $\Lambda$CDM: An update

Leandros Perivolaropoulos, Foteini Skara|arXiv (Cornell University)|May 12, 2021

Cosmology and Gravitation Theories8 citations

TL;DR

This 2022 review synthesizes growing tensions between the standard ΛCDM model and observational data, focusing on the Hubble tension (H₀ discrepancy), growth tension, CMB anomalies, cosmic dipoles, and small-scale issues like the core-cusp and missing satellite problems. It presents a unified assessment of 2σ or higher tensions across cosmological and astrophysical datasets, highlighting potential new physics beyond ΛCDM while referencing theoretical models that could resolve these discrepancies.

ABSTRACT

A number of challenges to the standard $\Lambda$CDM model have been emerging during the past few years as the accuracy of cosmological observations improves. In this review we discuss in a unified manner many existing signals in cosmological and astrophysical data that appear to be in some tension ($2\sigma$ or larger) with the standard $\Lambda$CDM model as specified by the Cosmological Principle, General Relativity and the Planck18 parameter values. In addition to the well-studied $5\sigma$ challenge of $\Lambda$CDM (the Hubble $H_0$ tension) and other well known tensions (the growth tension, and the lensing amplitude $A_L$ anomaly), we discuss a wide range of other less discussed less-standard signals which appear at a lower statistical significance level than the $H_0$ tension some of them known as 'curiosities' in the data) which may also constitute hints towards new physics. For example such signals include cosmic dipoles (the fine structure constant $\alpha$, velocity and quasar dipoles), CMB asymmetries, BAO Ly$\alpha$ tension, age of the Universe issues, the Lithium problem, small scale curiosities like the core-cusp and missing satellite problems, quasars Hubble diagram, oscillating short range gravity signals etc. The goal of this pedagogical review is to collectively present the current status (2022 update) of these signals and their level of significance, with emphasis on the Hubble tension and refer to recent resources where more details can be found for each signal. We also briefly discuss theoretical approaches that can potentially explain some of these signals.

Motivation & Objective

• To systematically review and unify the current status of cosmological tensions (2σ or higher) challenging the standard ΛCDM model as defined by the Cosmological Principle, General Relativity, and Planck 2018 parameters.
• To assess the statistical significance and consistency of lesser-known 'curiosities' in cosmological data, such as cosmic dipoles, CMB asymmetries, and oscillating gravity signals, alongside well-known tensions like the Hubble and lensing amplitude anomalies.
• To provide a critical overview of theoretical models that could resolve these tensions, including late-time modifications to H(z), early-time sound horizon deformations, and inhomogeneous/anisotropic extensions.
• To guide researchers toward recent, detailed resources for each tension signal, facilitating further investigation into potential new physics beyond ΛCDM.

Proposed method

• Systematic compilation and analysis of observational data from multiple probes: standard candles (e.g., Type Ia supernovae, Tully-Fisher), standard rulers (e.g., BAO, sound horizon), time-delay lenses, gravitational waves (standard sirens), masers, cosmic chronometers, and γ-ray attenuation.
• Use of Planck 2018 parameter values as the ΛCDM benchmark to quantify deviations in H₀, growth rate, lensing amplitude (Aₗ), and other parameters.
• Statistical evaluation of tensions using significance levels (e.g., 2σ, 5σ), including comparison of early- vs. late-time measurements and consistency checks across datasets.
• Inclusion of theoretical modeling for tension resolution: late-time H(z) modifications (e.g., early dark energy, interacting dark energy), inhomogeneous cosmologies, and modified gravity scenarios.
• Use of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric and Einstein’s field equations as the theoretical foundation, with perturbations and anisotropies analyzed within the framework of General Relativity.
• Categorization of anomalies into broad classes: Hubble tension, growth tension, CMB anomalies (e.g., hemispherical asymmetry, cold spot), cosmic dipoles (velocity, quasar, α), small-scale issues (core-cusp, missing satellites), and others (e.g., Lithium problem, quasar Hubble diagram).

Experimental results

Research questions

• RQ1 To what extent do current cosmological observations (e.g., H₀ measurements from local distance ladders vs. CMB extrapolations) indicate a 5σ tension with ΛCDM?
• RQ2 How do lesser-known anomalies—such as cosmic dipoles in the fine-structure constant, quasars, or velocity—challenge the isotropy and homogeneity assumptions of the Cosmological Principle?
• RQ3 What is the statistical significance and consistency of CMB anomalies (e.g., quadrupole-octopole alignment, lack of large-scale correlations) across multiple datasets and analysis methods?
• RQ4 To what degree do small-scale astrophysical observations (e.g., rotation curves, dwarf galaxy counts) contradict ΛCDM predictions, and can these be quantified as 'curiosities' or 'problems'?
• RQ5 Which theoretical models (e.g., early dark energy, interacting dark sectors, inhomogeneous models) offer viable explanations for multiple observed tensions simultaneously?

Key findings

• The Hubble tension remains the most significant challenge, with local measurements of H₀ (e.g., from the SH0ES collaboration) yielding values ~73 km s⁻¹ Mpc⁻¹, while Planck 2018 extrapolations give ~67 km s⁻¹ Mpc⁻¹, resulting in a 5σ discrepancy.
• The growth tension is evident in the discrepancy between observed large-scale structure growth (from weak lensing and redshift-space distortions) and predictions from ΛCDM using Planck parameters, with significance levels around 2–3σ.
• CMB anomalies include a 2.5σ preference for a closed universe when comparing CMB data with BAO measurements, and a 3σ anomaly in the integrated Sachs-Wolfe effect, suggesting possible deviations from statistical isotropy.
• Cosmic dipoles—such as the velocity dipole, quasar dipole, and fine-structure constant α dipole—show evidence of anisotropy at ~2–3σ, challenging the isotropy of the cosmological principle.
• Small-scale curiosities such as the core-cusp problem (dark matter cores too large in simulations vs. observations) and the missing satellite problem (fewer dwarf galaxies than predicted) remain unresolved, with the 'Too Big To Fail' problem indicating a 3σ tension in subhalo mass functions.
• The Lithium problem persists, with observed primordial lithium-7 abundance in metal-poor stars being ~2–3σ lower than ΛCDM predictions from Big Bang nucleosynthesis, suggesting possible new physics in early universe processes.