# What is the error in the measured value of the Hubble Constant?

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## Solution 1

The Hubble constant, $H$, has been measured by many experiments. One of the most recently published measurement by the ESA Planck Surveyor indicates,

$$H\approx 2.20 \times 10^{-18} \pm \underbrace{2.50 \times 10^{-20}}_{\text{uncertainty}} \, \, \, \, \, \text{s}^{-1}$$

or equivalently in more common units (for the Hubble parameter),

$$H\approx 67.80 \pm 0.77 \, \, \frac{\text{km}}{\text{s}\,\text{Mpc}}.$$

## Solution 2

The paper Planck 2013 results. I. Overview of products and scientific results , dated 6/5/2014 reports at page 38

$$67 \pm 1.2$$ km/s per megaparsec.

It explains that other techniques have given higher values in conflict with this value.

"Riess et al. (2011) used Hubble Space Telescope observations of Cepheid variables in the host galaxies of eight SNe Ia to calibrate the supernova magnitude-redshift relation. Their ‘best estimate’ of the Hubble constant, from fitting the calibrated SNe magnitude-redshift relation is:

$$73.8 \pm 2.4$$ km/s per megaparsec.

A value from using "mid-infrared observations with the Spitzer Space Telescope to recalibrate secondary distance methods used in the HST Key Project" is also cited as:

$$74.3 \pm 1.5 \pm 2.1$$ km/s per megaparsec (the second uncertainty being systematic).

So the various techniques are not within the statistical uncertainty of each other

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### Chris Laforet

Updated on April 07, 2020

### Comments

• Chris Laforet over 3 years

I've found on the internet that the Hubble constant has been measured to be about $2.3\times 10^{-18} \, \mathrm{s}^{-1}$ Does anyone know what the current error bounds are on this value?

• John Rennie over 9 years
• Jim over 9 years
I think your order of magnitude for the uncertainty is a tad off
• David Z over 9 years
Yeah, maybe the uncertainty should be $\times 10^{-20}$? Also, could you link to your source? (Not that I don't believe you, but it'd be useful to provide an avenue for further reading, and make sure we don't duplicate results from the same source.)
• JamalS over 9 years
@DavidZ: Yes, thank you for spotting the typo! :) The resource is the same one mentioned afterwards by DavePhD, namely: arxiv.org/abs/1303.5062.
• rob over 9 years
Worth noting, perhaps, that for decades there was a cluster of Hubble constant measurements around 50 km/s/Mpc and another cluster of measurements around 100 km/s/Mpc; when it was discovered that the expansion of the universe was accelerating, the two camps suddenly agreed with each other.
• DavePhD over 5 years
@rob now the conflict is 67 versus 73 km/s/Mpc nature.com/articles/nphys4055 and arxiv.org/pdf/1801.01120.pdf
• rob over 5 years
More precisely, between $66.9\pm0.6$ and $73.2\pm1.7$ km/s/Mpc. It'd be fun to see a plot of the best measurements as a function of time. It's interesting that your 2014 answer includes both statistical and systematic uncertainty estimates The Reiss 2018 paper you linked to seems to be entirely about reducing the systematic uncertainty but, at least in the abstract, gives only a total uncertainty for $H_0$.
• rob over 5 years
Also, it's very interesting that the precision on both measurements has halved in the past four years. I would characterize your 2014 numbers as "not inconsistent with each other," even though the agreement is poor. The current disagreement is much more convincing.