[Paper Review] What is the Standard Cosmological Model?

Eric V. Linder|arXiv (Cornell University)|May 6, 2021

Cosmology and Gravitation Theories33 references4 citations

TL;DR

This paper re-evaluates the standard cosmological model by emphasizing its deep, multi-layered foundations across global geometry, cosmic history, and matter content. It argues that apparent tensions—like the H₀ and σ₈ discrepancies—may stem from narrow interpretations rather than fundamental flaws, advocating for a holistic 'All Cosmology, All the Time' approach using cross-probes like gravitational wave standard sirens and matter growth to test general relativity and detect deviations consistently.

ABSTRACT

Reports of "cosmology in crisis" are in vogue, but as Mark Twain said, "the report of my death was an exaggeration". We explore what we might actually mean by the standard cosmological model, how tensions - or their apparent resolutions - might arise from too narrow a view, and why looking at the big picture is so essential. This is based on the seminar "All Cosmology, All the Time".

Motivation & Objective

• To clarify what constitutes the standard cosmological model across multiple conceptual levels: global geometry, cosmic history, and matter content.
• To challenge the narrative of a 'crisis' in cosmology by showing that apparent tensions may arise from incomplete or narrow interpretations of data.
• To advocate for a comprehensive approach—'All Cosmology, All the Time'—that integrates all robust observations across redshifts to test model consistency.
• To develop and promote a new statistical test, $ D_G(a) $, to cross-check general relativity using gravitational wave and electromagnetic distance probes against matter growth.
• To demonstrate that deviations from the standard model, if any, must be consistent across multiple probes to avoid epicyclic reasoning and systematic errors.

Proposed method

• Defining the standard cosmological model through three conceptual levels: Level 1 (global properties: homogeneity, isotropy, Robertson-Walker metric), Level 2 (cosmic history: radiation, matter, and dark energy eras), and Level 3 (observed components: CMB, large-scale structure, neutrinos, gravitational waves).
• Using the $ D_G(a) $ statistic to compare gravitational wave luminosity distance ($ d_{L,GW} $) and matter growth rate ($ f ilde{\sigma}_8 $), with $ D_G(a) = \frac{[d_{L,GW}/d_{L}^{\rm GR}](a)}{[f\tilde{\sigma}_8^{\rm MG}/f\tilde{\sigma}_8^{\rm GR}](a)} $, where deviations from unity indicate modified gravity or systematics.
• Analyzing how gravitational wave propagation depends on both expansion history $ H(z) $ and the running of the Planck mass $ \alpha_M(z) $, while light propagation depends only on $ H(z) $, enabling cross-checks.
• Applying the principle of consistency checks: if one probe shows a deviation, the model must predict a specific redshift-dependent behavior in others, avoiding ad hoc fixes.
• Highlighting the role of future data—especially from standard sirens and deep redshift surveys—in testing the model’s robustness across all layers.
• Using theoretical frameworks such as modified gravity (MG) models with variable $ G_{\rm eff}(z) $ and $ M_{\rm Pl}^2(z) $ to predict distinct $ D_G(a) $ shapes, enabling model discrimination.

Experimental results

Research questions

• RQ1 What defines the standard cosmological model across different conceptual levels—global geometry, cosmic history, and observed matter content?
• RQ2 Why do apparent tensions (e.g., H₀ and σ₈) persist, and could they stem from incomplete or narrow interpretations rather than fundamental model failure?
• RQ3 How can gravitational wave standard sirens provide a new, independent test of the connection between cosmic expansion and structure growth?
• RQ4 What is the predictive power of the $ D_G(a) $ statistic in distinguishing between general relativity and modified gravity models?
• RQ5 Can a consistent, multi-probe approach prevent the need for epicyclic adjustments and systematics in resolving cosmological tensions?

Key findings

• The standard cosmological model rests on deeply rooted foundations—homogeneity, isotropy, and the Robertson-Walker metric—that are robust and unlikely to be overturned by current tensions.
• The $ D_G(a) $ statistic provides a model-independent consistency test: in general relativity, $ D_G(a) = 1 $ for all redshifts; deviations indicate modified gravity or systematics.
• Gravitational wave distances depend on both $ H(z) $ and $ \alpha_M(z) $, while electromagnetic distances depend only on $ H(z) $, enabling a direct cross-check of gravity’s behavior.
• A deviation in $ d_{L,GW} $ relative to $ d_{L,EM} $ would signal a breakdown of general relativity or unaccounted systematics, with $ D_G(a) $ quantifying the redshift dependence of such deviations.
• The $ D_G(a) $ curve shape is distinct for different gravity models, allowing clear discrimination between theories, even if amplitudes scale with $ G_{\rm eff}(z=0) $.
• The paper concludes that apparent tensions may not reflect a crisis in the standard model, but rather a need for broader, more consistent data integration—'All Cosmology, All the Time'—to avoid epicyclic reasoning.