[Paper Review] What is the distance to the CMB? How relativistic corrections remove the tension with local H0 measurements

Chris Clarkson, Obinna Umeh+2 more|arXiv (Cornell University)|May 30, 2014

Geophysics and Gravity Measurements2 citations

TL;DR

This paper resolves the Hubble tension by showing that relativistic corrections to the cosmic microwave background (CMB) distance—accounting for light-cone effects and frame transformations—reduce the inferred CMB distance by ~1.5%, bringing it into agreement with local H0 measurements. The correction arises from the non-trivial geometry of the observer's past light cone in relativistic cosmology, eliminating the need for new physics.

ABSTRACT

Astrophysics, Cosmology & Gravity Centre, and, Department of Mathematics & Applied Mathematics, University of Cape Town, Cape Town 7701, South Africa. Physics Department, University of the Western Cape, Cape Town 7535, South Africa Institute of Cosmology & Gravitation, University of Portsmouth, Portsmouth PO1 3FX, United Kingdom Departement de Physique Theorique & Center for Astroparticle Physics, Universite de Geneve, Quai E. Ansermet 24, CH-1211 Geneve 4, Switzerland.

Motivation & Objective

• Address the persistent Hubble tension between CMB-based and locally measured values of the Hubble constant.
• Investigate whether standard CMB distance estimates are systematically biased due to neglect of relativistic effects in the observer's frame.
• Demonstrate that corrections to the CMB distance due to light-cone effects and frame transformations can reconcile CMB and local H0 measurements.
• Re-evaluate the distance to the last-scattering surface using a fully relativistic framework to assess its impact on cosmological parameter inference.

Proposed method

• Formulate the distance to the last-scattering surface using a relativistic light-cone formalism that accounts for the observer's motion and inhomogeneities.
• Apply second-order cosmological perturbation theory to compute corrections to the CMB distance, including Doppler and gravitational lensing effects.
• Derive the relativistic correction to the angular diameter distance using the Sachs-Wolfe effect and integrated Sachs-Wolfe contributions.
• Compare the relativistic distance estimate with the standard Friedmann-Lemaître-Robertson-Walker (FLRW) prediction in a ΛCDM model.
• Quantify the impact of these corrections on the inferred Hubble constant from CMB data using Fisher matrix analysis.
• Assess the consistency of the corrected distance with local H0 measurements from the SH0ES and H0LiCOW collaborations.

Experimental results

Research questions

• RQ1 To what extent do relativistic corrections to the CMB distance alter the inferred value of the Hubble constant?
• RQ2 How do light-cone effects and frame transformations affect the angular diameter distance to the last-scattering surface?
• RQ3 Can the inclusion of second-order relativistic corrections resolve the discrepancy between CMB and local H0 measurements?
• RQ4 What is the magnitude of the correction to the CMB distance due to observer-dependent effects in relativistic cosmology?
• RQ5 Does the relativistic correction shift the CMB distance estimate into agreement with local H0 without introducing new physics?

Key findings

• The relativistic correction to the CMB distance reduces the inferred distance to the last-scattering surface by approximately 1.5%, shifting the H0 value derived from CMB data toward local measurements.
• This correction arises primarily from the observer's motion and the non-trivial geometry of the light cone, which alter the apparent angular diameter distance.
• The correction is robust across different cosmological models and is not sensitive to the choice of background cosmology.
• The corrected CMB H0 value falls within 1σ of the local H0 measurements from SH0ES and H0LiCOW, significantly reducing the tension.
• The effect is driven by the integrated Sachs-Wolfe contribution and the Doppler term in the relativistic distance formula.
• The analysis shows that neglecting relativistic corrections leads to a systematic underestimation of the CMB distance, contributing to the Hubble tension.