Ive been off and on watching for papers researching the hubble contention between early and late time measurements. Figured I would share this interesting article here.

https://arxiv.org/abs/2408.06153

One of the factors involved being Leavitts law

https://www.astro.gsu.edu/lab/website/4LeavittLab-1.pdf

The main point however is the paper expresses no new physics is required and supports the need for tighter constraints on luminosity to distance relations including tighter calibrations.

Last link above is just a quick overview of the law.

Below is a more recent calibration papers.

https://arxiv.org/abs/2509.16331

A simplistic way of describing the law is The longer the period of the star, the higher its absolute luminosity. Local cephieds however are used to calibrate this law however as distance increases other factors may become involved hence the last link is further studies increasing calibration constraints

Edited January 22Jan 22 by Mordred

On the early time measurements ie measurements using the CMB in regards to improved calibration. The process involves calibrating the Baryon acoustic oscillations (BAO)

https://arxiv.org/pdf/2405.20306

This paper includes references to the Hubble tension.

For reference here are the 2024 DESI constraints.

https://www.osti.gov/servlets/purl/3011043

Many of the regular forums members have often seen me refer to the equations of state and how matter, radiation evolve over time and seen me post a key formula to determine Hubble rate in the past compared to Hubble rate today as a function of redshift.

https://www.osti.gov/servlets/purl/3011043

See equation 2.2 of article.

this post I show how equation 2.2 comes about in the key equations and includes the look back time adjustment based on the same procedure.

Edited January 22Jan 22 by Mordred