## Wednesday, June 17, 2020

### A New Approach To Measuring Hubble's Constant

Hubble's constant is an observable quantity that quantifies the rate at which the universe is expanding. As Wikipedia in the previous sentence explains (omissions from the source not indicated editorially for ease of reading):
It is often expressed by the equation v = D, with the constant of proportionality—Hubble constant—between the "proper distance" D to a galaxy, which can change over time, and its speed of separation v, i.e. the derivative of proper distance with respect to cosmological time coordinate. The Hubble constant can also be interpreted as the relative rate of expansion. In this form = 7%/Gyr, meaning that at the current rate of expansion it takes a billion years for an unbound structure to grow by 7%. Though the Hubble constant is roughly constant in the velocity-distance space at any given moment in time, the Hubble parameter , which the Hubble constant is the current value of, varies with time, so the term 'constant' is sometimes thought of as somewhat of a misnomer.
The value of is about 70 (km/s)/Mpc. "Late universe" measurements using calibrated distance ladder techniques have converged on a value of approximately 73 km/s/Mpc. Since 2000, "early universe" techniques based on measurements of the cosmic microwave background have become available, and these agree on a value near 67.7 km/s/Mpc. (This is accounting for the change in the expansion rate since the early universe, so is comparable to the first number.) As techniques have improved, the estimated measurement uncertainties have shrunk, but the range of measured values has not, to the point that the disagreement is now statistically significant. This discrepancy is called the Hubble tension.

As the chart above illustrates the cosmic microwave background estimates in red are quite consistent and have a small uncertainty, while "late universe" measurements, in blue, have more scatter and larger uncertainties.

The extent to which this tension is simply experimental error or is instead a clue to the nature of the universe's expansion that is at odds with the simple "Hubble's law" model that it codifies is a major unresolved issue in observational astronomy and cosmology.

A new pre-print measures that quantity in a less commonly used way that is partially independent of the most past methods to measure it using the baryonic Tully-Fisher relation between the mass of the ordinary matter in a galaxy and its rotation rate. The Tully-Fischer relation is as a phenomenological relationship that holds in all observed galaxies, from which MOND (a toy model modified gravity law used to explain dark matter phenomena at galaxy scales and below) was derived, and which dark matter particle theories seek to explain.

The new measurement is consistent with, but on the high side of, other recent "late universe" methods that determine proper distance by other methods, and almost identical to the value determined in two prior studies using the Tully-Fischer relationship, all of which are summarized here

The new paper's measurement of 75.1 ± 3.6 is just barely consistent at the two sigma level with early universe based Dark Energy Survey (DES) measurement, and not quite consistent with the cosmology based measurements of Planck 2018.
We explore the use of the baryonic Tully-Fisher relation (bTFR) as a new distance indicator. Advances in near-IR imaging and stellar population models, plus precise rotation curves, have reduced the scatter in the bTFR such that distance is the dominant source of uncertainty. Using 50 galaxies with accurate distances from Cepheids or tip magnitude of the red giant branch, we calibrate the bTFR on a scale independent of Ho. We then apply this calibrated bTFR to 95 independent galaxies from the SPARC sample, using CosmicFlows-3 velocities, to deduce the local value of Ho. We find Ho = 75.1 +/- 2.3 (stat) +/- 1.5 (sys) km s1 Mpc1.
James Schombert, Stacy McGaugh, Federico Lelli,H0arXiv: 2006.08615 (June 15, 2020).

McGaugh discusses the paper at his blog with background material in a preceding post summing up the methodological difficulties involved and the approximations that have to be used.

McGaugh notes that historically, the Hubble tension between different theoretical means of calculating the Hubble constant was much greater than it is today, in absolute terms, basically cautioning against reading too much into the discrepancy yet.