In order to avoid having to make a start on examination marking I was having a trawl through the arXiv this morning when I found an interesting paper by Stephens & Gleiser called An Informational Approach to Cosmological Parameter Estimation. The abstract is:

I haven’t had time to go through the manuscript in detail but while it doesn’t seem to say very much of a specific nature about the Hubble constant tension issue, it does introduce an approach which is new to me. The Jensen-Shannon Divergence is a variation on the familiar Kullback-Leibler Divergence.

Anyway, I’d be interested in comments on this from experts!

I wasn’t able to get to the Ordinary Meeting of the Royal Astronomical Society on Friday 11th January as I was otherwise engaged. In case you didn’t know, these meetings happen on the second Friday of every month and consist of short talks, longer set-piece prize lectures and Society business. The January meeting is when the annual awards are announced, so I missed the 2019 crop of medals and other prizes. When I got to the Athenaeum for dinner I was delighted to be informed that one of these – the prestigious Eddington Medal – had been awarded to my erstwhile Cardiff colleague Bernard Schutz (with whom I worked in the Data Innovation Research Institute and the School of Physics & Astronomy).

Here is a short video of the man himself talking about the work that led to this award:

I report here how gravitational wave observations can be used to determine the Hubble constant, H 0. The nearly monochromatic gravitational waves emitted by the decaying orbit of an ultra–compact, two–neutron–star binary system just before the stars coalesce are very likely to be detected by the kilometre–sized interferometric gravitational wave antennas now being designed1–4. The signal is easily identified and contains enough information to determine the absolute distance to the binary, independently of any assumptions about the masses of the stars. Ten events out to 100 Mpc may suffice to measure the Hubble constant to 3% accuracy.

In this paper, Bernard points out that a binary coalescence — such as the merger of two neutron stars — is a self calibrating `standard candle’, which means that it is possible to infer directly the distance without using the cosmic distance ladder. The key insight is that the rate at which the binary’s frequency changes is directly related to the amplitude of the gravitational waves it produces, i.e. how `loud’ the GW signal is. Just as the observed brightness of a star depends on both its intrinsic luminosity and how far away it is, the strength of the gravitational waves received at LIGO depends on both the intrinsic loudness of the source and how far away it is. By observing the waves with detectors like LIGO and Virgo, we can determine both the intrinsic loudness of the gravitational waves as well as their loudness at the Earth. This allows us to directly determine distance to the source.

It may have taken 31 years to get a measurement, but hopefully it won’t be long before there are enough detections to provide greater precision – and hopefully accuracy! – than the current methods can manage!

Congratulations to Bernard on his thoroughly well-deserved Eddington Medal!

Just a quick post to point out the exciting news that this week a clutch of papers on cosmology using Type 1a Supernovae have been released by the Dark Energy Survey team. Naturally, all of them are on the arXiv. You can also read them here. For convenience I’ve provided links below to arXiv versions through their titles:

Here’s a plot showing some of the cosmological constraints:

The parameter plotted on the vertical axis is the dark energy equation of state parameter, w, and w=-1 corresponds to a cosmological constant.

For those of youparticularly interested in the Hubble constant, the headline value from Paper 6 is H_{0} = 67.77 +/- 1.30 km s^{-1} Mpc^{-1}. This closer to the value obtained from Planck and in tension with other values as I’ve blogged about before, and gives me an excuse to continue my online poll:

My correspondent also alleges that in writing this blog I am doing the Devil’s work. That may be the case, of course, but I can’t help thinking that there must be more effective ways for him to get his work done. Either that or he’s remarkably unambitious.

Anyway, to satisfy my correspondent here is one for the problems folder:

Using the information provided in Isaiah Chapter 40 verse 22, show that the value of the Hubble constant is precisely 70.98047 km s^{-1} Mpc^{-1}.

You may quote the relevant biblical verse without proof. In the King James version it reads:

40.22. It is he that sitteth upon the circle of the earth, and the inhabitants thereof are as grasshoppers; that stretcheth out the heavens as a curtain, and spreadeth them out as a tent to dwell in.

By the way, please note that the inverse of the Hubble constant has dimensions of time, not distance.

Answers into my spam folder please (via the comments box).

While I am on the subject of Hubble, I will mention the news that the Hubble Space Telescope is having a few technical problems as a result of a failure of one of its gyros. In fact a few days ago it went into `safe mode’ to help engineers diagnose and fix the problem, during which time no observations are being taken. I’m told by people who know about such things that the spacecraft can actually operate on only one gyro if necessary, using information from other systems for attitude control, so this problem is not going to be terminal, but it will slow down the pointing quite a bit thus make it less efficient. With a bit of luck HST will be back in operation soon.

Here are two interesting plots that I got via Renée Hložek on Twitter from the recent swathe of papers from Planck The first shows the `tension’ between Planck’s parameter estimates `direct’ measurements of the Hubble Constant (as exemplified by Riess et al. 2018); see my recent post for a discussion of the latter. Planck actually produces joint estimates for a set of half-a-dozen basic parameters from which estimates of others, including the Hubble constant, can be derived. The plot below shows the two-dimensional region that is allowed by Planck if both the Hubble constant (H_{0}) and the matter density parameter (Ω_{M}) are allowed to vary within the limits allowed by various observations. The tightest contours come from Planck but other cosmological probes provide useful constraints that are looser but consistent; `BAO’ refers to `Baryon Acoustic Oscillations‘, and `Pantheon’ is a sample of Type Ia supernovae.

You can see that the Planck measurements (blue) mean that a high value of the Hubble constant requires a low matter density but the allowed contour does not really overlap with the grey shaded horizontal regions. For those of you who like such things, the discrepancy is about 3.5σ..

Another plot you might find interesting is this one:

The solid line shows how the Hubble `constant’ varies with redshift in the standard cosmological model; H_{0} is the present value of a redshift-dependent parameter H(z) that measures the rate at which the Universe is expanding. You will see that the Hubble parameter is larger at high redshift, but decreases as the expansion of the Universe slows down, until a redshift of around 0.5 and then it increases, indicating that the expansion of the Universe is accelerating. Direct determinations of the expansion rate at high redshift are difficult, hence the large error bars, but the important feature is the gap between the direct determination at z=0 and what the standard model predicts. If the Riess et al. 2018 measurements are right, the expansion of the Universe seems to have been accelerating more rapidly than the standard model predicts.

So after that little update here’s a little poll I’ve been running for a while on whether people think this apparent discrepancy is serious or not. I’m interested to see whether these latest findings change the voting!

Last week when I wrote about the 2nd Data Release from Gaia, somebody emailed me to ask whether the new results said anything about the cosmological distance ladder and hence the Hubble Constant. As far as I could see, no scientific papers were released on this topic at the time and I thought there probably wasn’t anything definitive at this stage. However, it turns out that there is a paper now, by Riess et al., which focuses on the likely impact of Gaia on the Cepheid distance scale. Here is the abstract:

We present HST photometry of a selected sample of 50 long-period, low-extinction Milky Way Cepheids measured on the same WFC3 F555W, F814W, and F160W-band photometric system as extragalactic Cepheids in SN Ia hosts. These bright Cepheids were observed with the WFC3 spatial scanning mode in the optical and near-infrared to mitigate saturation and reduce pixel-to-pixel calibration errors to reach a mean photometric error of 5 millimags per observation. We use the new Gaia DR2 parallaxes and HST photometry to simultaneously constrain the cosmic distance scale and to measure the DR2 parallax zeropoint offset appropriate for Cepheids. We find a value for the zeropoint offset of -46 +/- 13 muas or +/- 6 muas for a fixed distance scale, higher than found from quasars, as expected, for these brighter and redder sources. The precision of the distance scale from DR2 has been reduced by a factor of 2.5 due to the need to independently determine the parallax offset. The best fit distance scale is 1.006 +/- 0.033, relative to the scale from Riess et al 2016 with H0=73.24 km/s/Mpc used to predict the parallaxes photometrically, and is inconsistent with the scale needed to match the Planck 2016 CMB data combined with LCDM at the 2.9 sigma confidence level (99.6%). At 96.5% confidence we find that the formal DR2 errors may be underestimated as indicated. We identify additional error associated with the use of augmented Cepheid samples utilizing ground-based photometry and discuss their likely origins. Including the DR2 parallaxes with all prior distance ladder data raises the current tension between the late and early Universe route to the Hubble constant to 3.8 sigma (99.99 %). With the final expected precision from Gaia, the sample of 50 Cepheids with HST photometry will limit to 0.5% the contribution of the first rung of the distance ladder to the uncertainty in the Hubble constant.

So, nothing definitive yet but potentially very interesting in the future and this group, led by Adam Riess, is now claiming a 3.8σ tension between measurements of the Hubble constant from cosmic microwave background measurements and from traditional `distance ladder’ approaches, though to my mind this is based on some rather subjective judgements.

The appearance of that paper reminded me that I forgot to post about a paper by Bernal & Peacock that appeared a couple of months ago. Here is the abstract of that one:

When combining data sets to perform parameter inference, the results will be unreliable if there are unknown systematics in data or models. Here we introduce a flexible methodology, BACCUS: BAyesian Conservative Constraints and Unknown Systematics, which deals in a conservative way with the problem of data combination, for any degree of tension between experiments. We introduce hyperparameters that describe a bias in each model parameter for each class of experiments. A conservative posterior for the model parameters is then obtained by marginalization both over these unknown shifts and over the width of their prior. We contrast this approach with an existing hyperparameter method in which each individual likelihood is scaled, comparing the performance of each approach and their combination in application to some idealized models. Using only these rescaling hyperparameters is not a suitable approach for the current observational situation, in which internal null tests of the errors are passed, and yet different experiments prefer models that are in poor agreement. The possible existence of large shift systematics cannot be constrained with a small number of data sets, leading to extended tails on the conservative posterior distributions. We illustrate our method with the case of the H_{0} tension between results from the cosmic distance ladder and physical measurements that rely on the standard cosmological model.

This paper addresses the long-running issue of apparent tension in different measurements of the Hubble constant that I’ve blogged about before (e.g. here) by putting the treatment of possible systematic errors into a more rigorus and consistent (i.e. Bayesian) form. It says what I think most people in the community privately think about this issue, i.e. that it’s probably down to some sort of unidentified systematic rather than exotic physics.

The title of the paper includes the phrase `Conservative Cosmology’, but I think that’s a bit of a misnomer. I think `Sensible Cosmology’. Current events suggest `conservative’ and `sensible’ have opposite meanings. You can find a popular account of it here, from which I have stolen this illustration of the tension:

A chart showing the two differing results for the Hubble constant – The expansion rate of the universe (in km/s/Mpc) Result 1: 67.8 ± 0.9 Cosmic microwave background Result 2: 73.52 ± 1.62 Cosmic distance ladder

Anyway, I have a poll that has been going on for some time about whether this tension is anything to be excited about, so why not use this opportunity cast your vote?

One of the topics that is bubbling away on the back burner of cosmology is the possible tension between cosmological parameters, especially relating to the determination of the Hubble constant (H_{0}) by Planck and by “traditional” methods based on the cosmological distance ladder; see here for an overview of the latter.

Before getting to the point I should explain that Planck does not determine H_{0} directly, as it is not one of the six numbers used to specify the minimal model used to fit the data. These parameters do include information about H_{0}, however, so it is possible to extract a value from the data indirectly. In other words it is a derived parameter:

The above summary shows that values of the Hubble constant obtained in this way lie around the 67 to 68 km/s/Mpc mark, with small changes if other measures are included. According to the very latest Planck paper on cosmological parameter estimates the headline determination is H_{0} = (67.8 +/- 0.9) km/s/Mpc.

About 18 months I blogged about a “direct” determination of the Hubble constant by Riess et al. using Hubble Space Telescope data quotes a headline value of (73.24+/-1.74) km/sec/Mpc, hinting at a discrepancy somewhere around the 3 sigma level depending on precisely which determination you use. A news item on the BBC hot off the press reports that a more recent analysis by the same group is stubbornly sitting around the same value of the Hubble constant, with a slight smaller error so that the discrepancy is now about 3.4σ. On the other hand, the history of this type of study provides grounds for caution because the systematic errors have often turned out to be much larger and more uncertain than the statistical errors…

Nevertheless, I think it’s fair to say that there isn’t a consensus as to how seriously to take this apparent “tension”. I certainly can’t see anything wrong with the Riess et al. result, and the lead author is a Nobel prize-winner, but I’m also impressed by the stunning success of the minimal LCDM model at accounting for such a huge data set with a small set of free parameters.

If one does take this tension seriously it can be resolved by adding an extra parameter to the model or by allowing one of the fixed properties of the LCDM model to vary to fit the data. Bayesian model selection analysis however tends to reject such models on the grounds of Ockham’s Razor. In other words the price you pay for introducing an extra free parameter exceeds the benefit in improved goodness of fit. GAIA may shortly reveal whether or not there are problems with the local stellar distance scale, which may reveal the source of any discrepancy. For the time being, however, I think it’s interesting but nothing to get too excited about. I’m not saying that I hope this tension will just go away. I think it will be very interesting if it turns out to be real. I just think the evidence at the moment isn’t convincing me that there’s something beyond the standard cosmological model. I may well turn out to be wrong.

Anyway, since polls seem to be quite popular these days, so let me resurrect this old one and see if opinions have changed!

The views presented here are personal and not necessarily those of my employer (or anyone else for that matter).
Feel free to comment on any of the posts on this blog but comments may be moderated; anonymous comments and any considered by me to be abusive will not be accepted. I do not necessarily endorse, support, sanction, encourage, verify or agree with the opinions or statements of any information or other content in the comments on this site and do not in any way guarantee their accuracy or reliability.

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