This plot is Figure 1 from Di Valentino [2011.00246] A combined analysis of the $H_0$ late time direct measurements and the impact on the Dark Energy sector:

Slide from Adam Riess talk on 22-Feb-2021 using the above Di Valentino plot:

Below is a plot of the H₀ measurement data as of July 2019 and is taken from the paper Tensions between the Early and the Late Universe. This paper is a summary review of a KITP-UCSB workshop convened to bring together both experimental and theoretical researchers in the field to review and assess the current state of affairs and identify promising next steps at resolution of this issue.

New developments since this post was originally created:

• Videos of two presentations at the KITP-UCSB conference Tensions between the Early and the Late Universe in mid-July 2019: (1) Lloyd Knox presentation: Sounds Discordant, and (2) Vivian Poulin presentation: Early Dark Energy.
• Also see Sunny Vagnozzi's comments at the end of this post.
• See this later post on the impact of EDE models on large-scale structure observables: [2003-07355] Early Dark Energy Does Not Restore Cosmological Concordance. This paper was rebutted in [2009.10740] Early dark energy is not excluded by current large-scale structure data and the authors of this new paper “suggest that EDE still provides a potential resolution to the Hubble tension and that it is worthwhile to test the predictions of EDE with future data-sets and further study its theoretical possibilities.” ___
  

This is about two recent papers with the premise that H₀ tension resolution could come from new physics at early times before recombination.

The first paper, Sounds Discordant: Classical Distance Ladder & ΛCDM-based Determinations of the Cosmological Sound Horizon [arxiv:1811.00537] is based on looking at the tension in terms of the sound horizon r_s. They cite several advantages of doing so: (1) “added insensitivity to extreme changes in the cosmology at z < 0.1, since one does not need to extrapolate to z = 0”, (2) “the ΛCDM predictions for the sound horizon are more robust than those for H₀”, (3) “as with the inverse distance ladder, this approach clarifies that reconciliation can not be delivered by altering cosmology at z < 1”, (4) “it serves to clarify that the reconciliation of distance ladder, BAO, and CMB observations via a cosmological solution is likely to include a change to the cosmological model in the two decades of scale factor evolution prior to recombination”, and (5) “σ(r_s)/r_s from CMB data, assuming ΛCDM, is four times smaller than the σ(H₀)/H₀ from the same data and assumed model.”

Virtual Particles: PhysicsForums series | Matt Strassler article | reddit post |

Planck Length: PhysicsForums article

Cosmology: Sean Carroll on True Facts About Cosmology (or, Misconceptions Skewered) | Inflationary Misconceptions and the Basics of Cosmological Horizons | Inflation Balloon Analogy Misconceptions | Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe, by Davis and Lineweaver |

Quantum Mechanics: reddit thread

Statistics: Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations

Slides from talk by Chris Tully at the Opening New Windows to the Universe forum at Brookhaven National Labs on 2021-11-03: PTOLEMY: Relic Neutrino Detection New developments since this post was originally created: Cosmologist Sunny Vagnozzi shares some updated info on the PTOLEMY project status in a short thread here. He also mentions that he is collaborating on a paper about PTOLEMY with Stefano Gariazzo that will soon (as of March 2020) be posted on the arXiv. -—

This is about paper 1902.05508, posted to the arXiv on 2/14/2019.

I was mostly unfamiliar with this groundbreaking project so this new paper provided a reading-up opportunity, leading to these general overview notes. I added the bolding for emphasis.

The PTOLEMY project¹ aims to directly detect relic neutrinos from the cosmic neutrino background (CNB or CνB), along with a impressive broader set of capabilities or opportunities^2a. The project is described as the “the first of its kind and the only one^2b conceived that can look directly at the image of the Universe encoded in neutrino background produced in the first second after the Big Bang”.³ (pg2) Achieving the project's goal “would profoundly confront and extend the sensitivity of precision cosmology data.”(pg5) This paper addresses the theoretical aspects of the project, its physics goals, and an outline of the project's scope of work to be done in the next three years. An earlier paper 1808.01892 gives more details on three phases of the project: proof-of-principle demonstrator, scalable prototype realization and tests, and full detector construction.

The technology is based on neutrino capture on beta decaying nuclei (NCB)⁵, with tritium (³H) determined as the best choice. The capture results in a tiny boost of energy to the electrons emitted in tritium decay, so there'll be a peak in the electron spectrum above the β-decay endpoint⁴. The planned target is ∼100g of tritium atomically bound to a radio-pure graphene substrate (they refer to it as “tritiated graphene”). They expect ∼10 CνB capture events per year, depending on the mass hierarchy and the Dirac versus Majorana nature of the neutrinos; the rate is half as large for non-relativistic Dirac neutrinos^2a. The anticipated energy resolution is ∼0.05eV, “an order of magnitude beyond the original target and the highest resolution of any calorimeter.” [source]

The graphic below is from Planck 2013 results. XVI. Cosmological parameters, Table 1 on page 6.