**Authors:** W. D’Arcy Kenworthy, Dan Scolnic, and Adam Riess

**First Author’s Institution:** Johns Hopkins University

**Status:** Submitted to the Astrophysical Journal, open access on arXiV

### Why so tense?

Feeling a bit tense these days? So is the value of the Hubble constant. This parameter, written as H_{0}, governs the rate of expansion of the universe, caused by some unknown dark energy. Despite cosmologists’ best efforts at massaging out the knots, H_{0} has long suffered from a tension between competing measurements. Today’s paper uses more precise data to reevaluate one possible cause of this tension.

The Hubble constant is the proportionality factor between the distance of a galaxy and the speed it moves away from us; galaxies that are further away move away increasingly faster, as expected from the expansion of space. We measure H_{0} in units of km/s/Mpc, which I like to think of as the clogs of the unit world: clunky-looking but really quite sensible. It means that for every megaparsec (Mpc) further away you look, the galaxies there appear to speed away faster by H_{0} kilometers per second.

There are two main independent ways H_{0} has been measured: from the cosmic microwave background (CMB) and from the cosmic distance ladder. The former measurement was most recently made by the Planck satellite; for details, check out this astrobite. This gives a value of H_{0} = 67.4 ± 0.5 km/s/Mpc.

Figure 1: The cosmic distance ladder. We use stellar parallax, Cepheid variable stars and Type Ia supernovae (among others) as rungs along the ladder to measure distances to sources. (Figure from NASA/ESA)

For the latter measurement, we can just plot the speed of each galaxy as a function of its distance away from us. Fitting a line to this relation gives a value of H_{0} = 73.52 ± 1.62 km/s/Mpc. At first glance this isn’t too shabby, but looking closer, it disagrees with the CMB measurement by a quite-statistically-significant 3σ. Either there is some unknown physics at play, or at least one of our two methods is wrong.

### A void in the distance ladder

One place an issue could be hiding is in how we measure the distances to the galaxies, with what is known as the cosmic distance ladder, shown in Figure 1. The latest measurements are based on on Type Ia supernovae, which are fairly reliable standard candles. But to calibrate these distances, we need other more close-by candles, often Cepheid variable stars in local galaxies. You can guess where this is going: to calibrate the Cepheids, we have to keep stepping down the ladder. If any of these ladder rungs are “broken,” the more distant measurements will have a systematic offset.

Today’s paper considers what would happen if our distance measurements to nearby galaxies were off. This could be the case if the Milky Way were at the center of a local void (an under-density of galaxies), also known as a Hubble Bubble. This would cause the surrounding galaxies to be more strongly drawn towards higher-density regions, away from us. The extra pull would make the value for H_{0} that we measure locally higher than the true value; fixing this would bring it closer to the CMB measurement.

### A drop-off in the Hubble constant?

The authors use a sample of 1295 supernovae (SNe) covering a range of distances to probe the local structure with higher precision than has been done previously. They plot a modified Hubble diagram, known as a magnitude-redshift diagram (Figure 2), from which they calculate the value of H_{0}.

Figure 2: A Hubble diagram of the supernovae in today’s paper. Rather than the classic plot of galaxy velocity as a function of distance, with the slope of the points giving the value of the Hubble constant, this uses magnitude as a proxy for distance, and the x-axis is related to the velocity. The Hubble constant can be calculated from the x-intercept. (Figure 2 in the paper)

To investigate if there could be a void altering their measurement, they check how the Hubble constant changes with redshift. If there is a sharp drop-off in the value of H_{0}, that could suggest a void with an edge at that redshift. The authors measure this by splitting the SNe into two bins, above and below a given redshift z_{split}, and calculating the difference in H_{0} between these samples.

### Devoid of voids

The results of this are shown in Figure 3. The authors find that the biggest change is at z=0.023, but only to a significance of <2σ. This means that any inhomogeneities in the local density would have only a small effect on their measurement of the Hubble constant. All of the differences are much weaker than the offset needed to resolve the tension with CMB data, so voids clearly can’t explain the entire discrepancy.

Figure 3: The change in the value of the Hubble constant, as a function of the redshift of a potential void edge.The red crosses are voids predicted in previous works. The small changes disfavor the idea that a local void at any redshift has a significant effect on the Hubble constant. (Figure 6 in the paper)

To see if voids could still make some difference, the paper revisits two void models that have been predicted in previous works. They are at redshifts of z=0.05 (KBC) and z=0.07 (WS14), plotted as red crosses on Figure 3. They find that with their updated analysis, evidence for the voids evaporates: the changes in H_{0} at both of these redshifts disfavor the void models by 6.2σ and 4.5σ respectively.

While the paper only investigates a simple, sharp-edged void model, it makes a strong case that local voids aren’t significant to the measurement of the Hubble constant. Future SNe observations will allow us to probe other systematics that may be just the masseuse we need to relieve the Hubble tension.

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