Archive for Cosmology

Hubble Tension: an “Alternative” View?

Posted in Bad Statistics, The Universe and Stuff with tags , , , , , on July 25, 2019 by telescoper

There was a new paper last week on the arXiv by Sunny Vagnozzi about the Hubble constant controversy (see this blog passim). I was going to refrain from commenting but I see that one of the bloggers I follow has posted about it so I guess a brief item would not be out of order.

Here is the abstract of the Vagnozzi paper:

I posted this picture last week which is relevant to the discussion:

The point is that if you allow the equation of state parameter w to vary from the value of w=-1 that it has in the standard cosmology then you get a better fit. However, it is one of the features of Bayesian inference that if you introduce a new free parameter then you have to assign a prior probability over the space of values that parameter could hold. That prior penalty is carried through to the posterior probability. Unless the new model fits observational data significantly better than the old one, this prior penalty will lead to the new model being disfavoured. This is the Bayesian statement of Ockham’s Razor.

The Vagnozzi paper represents a statement of this in the context of the Hubble tension. If a new floating parameter w is introduced the data prefer a value less than -1 (as demonstrated in the figure) but on posterior probability grounds the resulting model is less probable than the standard cosmology for the reason stated above. Vagnozzi then argues that if a new fixed value of, say, w = -1.3 is introduced then the resulting model is not penalized by having to spread the prior probability out over a range of values but puts all its prior eggs in one basket labelled w = -1.3.

This is of course true. The problem is that the value of w = -1.3 does not derive from any ab initio principle of physics but by a posteriori of the inference described above. It’s no surprise that you can get a better answer if you know what outcome you want. I find that I am very good at forecasting the football results if I make my predictions after watching Final Score

Indeed, many cosmologists think any value of w < -1 should be ruled out ab initio because they don’t make physical sense anyway.

 

 

 

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The Last Resting Place of the Hubble Parameter?

Posted in Uncategorized with tags , , , on July 22, 2019 by telescoper

Last week was rather busy on the blog, with a run of posts about the Hubble constant (or, more precisely, the  present value of the Hubble parameter) attracting the most traffic. Somehow during all the excitement I allowed myself to be persuaded to write a piece for RTÉ Brainstorm about this issue. My brief is to write a detailed account of the current controversy in language accessible to a lay reader in not more than 800 words. That’s quite a challenge. Better get on with it.

Perhaps after that I’ll be able to lay the Hubble parameter to rest, at least for a while:

The original photograph (and joke) may be found here.

New Publication at the Open Journal of Astrophysics!

Posted in Uncategorized with tags , , , , , , , on July 19, 2019 by telescoper

I was a bit busy yesterday doing a number of things, including publishing a new paper at The Open Journal of Astrophysics, but I didn’t get time to write a post about it until now. Anyway, here is how the new paper looks on the site:

The authors are Tom Kitching, Paniez Paykari and Mark Cropper of the Mullard Space Sciences Laboratory (of University College London) and Henk Hoekstra of Leiden Observatory.

You can find the accepted version on the arXiv here. This version was accepted after modifications requested by the referee and editor. Because this is an overlay journal the authors have to submit the accepted version to the arXiv (which we then check against the copy submitted to us) before publishing. We actually have a bunch of papers that we have accepted but are awaiting the appearance of the final version on the arXiv so we can validate it.

Anyway, this is another one for the `Cosmology and Nongalactic Astrophysics’ folder. We would be happy to get more submissions from other areas of astrophysics. Hint! Hint!

P.S. Just a reminder that we now have an Open Journal of Astrophysics Facebook page where you can follow updates from the Journal should you wish..

The Hubble Constant from the Tip of the Red Giant Branch

Posted in The Universe and Stuff with tags , , , , on July 16, 2019 by telescoper

At the risk of boring everyone again with Hubble constant news there’s yet another paper on the arXiv about the Hubble constant. This one is another `local’ measurement, in that it uses properties of nearby stars,  time based on a new calibration of the Red Giant Branch. This one is by Wendy Freedman et al. and its abstract reads:

We present a new and independent determination of the local value of the Hubble constant based on a calibration of the Tip of the Red Giant Branch (TRGB) applied to Type Ia supernovae (SNeIa). We find a value of Ho = 69.8 +/- 0.8 (+/-1.1\% stat) +/- 1.7 (+/-2.4\% sys) km/sec/Mpc. The TRGB method is both precise and accurate, and is parallel to, but independent of the Cepheid distance scale. Our value sits midway in the range defined by the current Hubble tension. It agrees at the 1.2-sigma level with that of the Planck 2018 estimate, and at the 1.7-sigma level with the SHoES measurement of Ho based on the Cepheid distance scale. The TRGB distances have been measured using deep Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) imaging of galaxy halos. The zero point of the TRGB calibration is set with a distance modulus to the Large Magellanic Cloud of 18.477 +/- 0.004 (stat) +/-0.020 (sys) mag, based on measurement of 20 late-type detached eclipsing binary (DEB) stars, combined with an HST parallax calibration of a 3.6 micron Cepheid Leavitt law based on Spitzer observations. We anchor the TRGB distances to galaxies that extend our measurement into the Hubble flow using the recently completed Carnegie Supernova Project I sample containing about 100 well-observed SNeIa. There are several advantages of halo TRGB distance measurements relative to Cepheid variables: these include low halo reddening, minimal effects of crowding or blending of the photometry, only a shallow (calibrated) sensitivity to metallicity in the I-band, and no need for multiple epochs of observations or concerns of different slopes with period. In addition, the host masses of our TRGB host-galaxy sample are higher on average than the Cepheid sample, better matching the range of host-galaxy masses in the CSP distant sample, and reducing potential systematic effects in the SNeIa measurements.

You can download a PDF of the paper here.

Note that the value obtained ising the TRGB here lies in between the two determinations using the cosmic microwave background and the Cepheid distance scale I discussed, for example, here. This is illustrated nicely by the following couple of Figures:

I know that this result – around 70 km s-1 Mpc-1 – has made some people a bit more relaxed about the apparent tension between the previous measurements, but what do you think? Here’s a poll so you can express your opinion.

My own opinion is that if there isn’t any tension at all at the one-sigma level then you should consider the possibility that you got sigma wrong!

Hubble’s Constant – A Postscript on w

Posted in The Universe and Stuff with tags , , , , , , , on July 15, 2019 by telescoper

Last week I posted about new paper on the arXiv (by Wong et al.) that adds further evidence to the argument about whether or not the standard cosmological model is consistent with different determinations of the Hubble Constant. You can download a PDF of the full paper here.

Reading the paper through over the weekend I was struck by Figure 6:

This shows the constraints on H0 and the parameter w which is used to describe the dark energy component. Bear in mind that these estimates of cosmological parameters actually involve the simultaneous estimation of several parameters, six in the case of the standard ΛCDM model. Incidentally, H0 is not one of the six basic parameters of the standard model – it is derived from the others – and some important cosmological observations are relatively insensitive to its value.

The parameter w is the equation of state parameter for the dark energy component so that the pressure p is related to the energy density ρc2 via p=wρc2. The fixed value w=-1 applies if the dark energy is of the form of a cosmological constant (or vacuum energy). I explained why here. Non-relativistic matter (dominated by rest-mass energy) has w=0 while ultra-relativistic matter has w=1/3.

Applying the cosmological version of the thermodynamic relation for adiabatic expansion  “dE=-pdV” one finds that ρ ∼ a-3(1+w) where a is the cosmic scale factor. Note that w=-1 gives a constant energy density as the Universe expands (the cosmological constant); w=0 gives ρ ∼ a-3, as expected for `ordinary’ matter.

As I already mentioned, in the standard cosmological model w is fixed at  w=-1 but if it is treated as a free parameter then it can be added to the usual six to produce the Figure shown above. I should add for Bayesians that this plot shows the posterior probability assuming a uniform prior on w.

What is striking is that the data seem to prefer a very low value of w. Indeed the peak of the likelihood (which determines the peak of the posterior probability if the prior is flat) appears to be off the bottom of the plot. It must be said that the size of the black contour lines (at one sigma and two sigma for dashed and solid lines respectively) suggests that these data aren’t really very informative; the case w=-1 is well within the 2σ contour. In other words, one might get a slightly better fit by allowing the equation of state parameter to float, but the quality of the fit might not improve sufficiently to justify the introduction of another parameter.

Nevertheless it is worth mentioning that if it did turn out, for example, that w=-2 that would imply ρ ∼ a+3, i.e. an energy density that increases steeply as a increases (i.e. as the Universe expands). That would be pretty wild!

On the other hand, there isn’t really any physical justification for cases with w<-1 (in terms of a plausible model) which, in turn, makes me doubt the reasonableness of imposing a flat prior. My own opinion is that if dark energy turns out not to be of the simple form of a cosmological constant then it is likely to be too complicated to be expressed in terms of a single number anyway.

 

Postscript to this postscript: take a look at this paper from 2002!

Hubble’s Constant – The Tension Mounts!

Posted in The Universe and Stuff with tags , , , , on July 12, 2019 by telescoper

There’s a new paper on the arXiv (by Wong et al.) that adds further evidence to the argument about whether or not the standard cosmological model is consistent with different determinations of the Hubble Constant. The abstract is here:

You can download a PDF of the full paper here.

You will that these measurements, based on observations of time delays in multiply imaged quasars that have been  gravitationally lensed, give higher values of the Hubble constant than determinations from, e.g., the Planck experiment.

Here’s a nice summary of the tension in pictorial form:

And here are some nice pictures of the lensed quasars involved in the latest paper:

 

It’s interesting that these determinations seem more consistent with local distance-scale approaches than with global cosmological measurements but the possibility remains of some unknown systematic.

Time, methinks, to resurrect my long-running poll on this!

Please feel free to vote. At the risk of inciting Mr Hine to clog up my filter with further gibberish,  you may also comment through the box below.

 

Cosmology with the Minimal Spanning Tree

Posted in The Universe and Stuff with tags , , , , , , on July 8, 2019 by telescoper

There’s a nice paper on the arXiv (by Naidoo et al) with the abstract:

The code mentioned at the end can be found here.

The appearance of this paper gives me an excuse to mention that I actually wrote a paper (with Russell Pearson) on the use of the Minimal (or Minimum) Spanning Tree (MST) to analyze galaxy clustering way back in 1995.

Here’s how we described the Minimal Spanning Tree in that old paper:

Strictly speaking , we used the Euclidean Minimum Spanning Tree in which the total length of the lines connecting a set of points in a tree is minimized. In general cases a weight can be assigned to each link that is not necessarily defined simply by the length. Here is visual illustration (which I think we drew by hand!)

You can think of the MST as a sort of pre-processing technique which accentuates linear features in a point process that might otherwise get lost in shot noise. Once one has a tree (pruned and/or separated as necessary) one can then extract various statistical properties in order to quantify the pattern present.

Way back in 1995 there were far fewer datasets available to which to apply this method and it didn’t catch on at the time. Now, with  ever-increasing availability of spectroscopic redshift surveys maybe its time has come at last! I look forward to playing with the Python code in due course!