# Why do we continue to find a discrepancy in the Hubble Constant?

After taking a look at some recent papers (examples below) that attempt to derive the value of the Hubble Constant, they all conclude with dramatically different values (speaking in context). Why is this? Each of the techniques seems sufficiently rigorous and equally well rooted in understood physics. Is this simply some form of error or is it due to some yet-to-be-discovered physics?

Papers:

I do understand that this is a hot topic right now in cosmology, however I just don't yet understand why we're having trouble with getting our measured values of the Hubble Constant to converge.

• Why haven't you put any error bars on these values? Without error bars any comparison is utterly meaningless. Oct 14 '18 at 18:54
• And the new measurement from the DES group "First Cosmological Results using Type Ia Supernovae from the Dark Energy Survey: Measurement of the Hubble" Constant" (arXiv:1811.02376v1) offers H_0=67.77+/-1.30 Nov 7 '18 at 14:15

To make a long story short, the measurements from Planck and the Hubble Space Telescope disagree, and the reason behind this isn't known.

First, let's look at the values with the uncertainties. We then have three different results that are, perhaps, not as inconsistent as they originally seemed:

• $$70.0^{+12.0}_{-8.0}\text{ km s}^{-1}\text{ Mpc}^{-1}$$ from LIGO.
• $$67.8\pm0.9\text{ km s}^{-1}\text{ Mpc}^{-1}$$ from Planck.
• $$73.48\pm1.66\text{ km s}^{-1}\text{ Mpc}^{-1}$$ from Hubble Space Telescope (HST) observations.

The LIGO measurement is consistent with the others, as the authors happily note in their conclusions. However, there is a discrepancy between the results from Planck and the results from the HST. This isn't a new problem; the Hubble group previously determined a value for the Hubble constant of $$73.24\pm1.24\text{ km s}^{-1}\text{ Mpc}^{-1}$$ in 2016. The uncertainties in the measurements describe one standard deviation; it doesn't mean that all values beyond the interval of the measurement plus or minus one standard deviation are impossible.

Now, the difference between Planck results and the 2016 HST data is $$3.4\sigma$$, which is a lot. The group came up with several explanations for the discrepancy:

• Systematic errors in the data collection, including in the use of the Cepheid variables used for the measurements.
• Small-scale variations in the Hubble constant, which appear unlikely to have propagated through the data.
• Systematic errors in the Planck results.
• Corrections needed to the $$\Lambda$$CDM model of cosmology, used by Planck.

In the 2018 paper, the authors note that the conflict with the Planck data is even stronger - $$3.7\sigma$$ (and we're now getting results that say it could be $$4.4\sigma$$; I should check those out). They haven't been able to point a figure at any single problem that could be behind the discrepancy; they do optimistically say that it could be the sign of new physics.

• Why do you refer to lambda CDM only with respect to Planck? Are the Hubble results independent of a cosmological model. If the Hubble results are more straightforward this discrepancy seems interesting. Apr 11 '18 at 15:17

While the Hubble constant describes the current expansion rate of the Universe, it should also be seen as a parameter (among others) of a given cosmological model (e.g., Lambda-CDM).

All methods to measure the Hubble constant are more or less indirect in some way, and they rely on very different assumptions. For example, the emission of the Cosmic Microwave Background (CMB) observed by Planck happened in the early Universe, when the expansion rate was very different from its current value. Therefore, a "measurement" of the Hubble constant from the Planck papers is only possible within a very specific cosmological model, that describes how this CMB would look today. If something is wrong with this model, the Hubble constant computed from Planck data would no longer correspond to the current expansion rate of the Universe, and so disagree with more local "measurements". In this context, local means closer to the current moment in the expansion history.

This is why "having trouble with measuring the Hubble constant" is one symptom of "learning about the cosmological model". The community broadly agrees that we don't know yet what causes the inconsistencies when Lambda-CDM is assumed. As the tension becomes more significant, it could be some form of unknown systematic error (observational or more theoretical), or it could be that Lambda-CDM is an inaccurate description of our Universe.

The Hubble constant discrepancy with Planck lambda CDM results has been reconciled by the Quantum Mass-Energy theory (QME)= 67.76 (km/s)/Mpc ... See research paper QME Theory Universal Hubble Constant Ho = 67.76 (km/s)/Mpc Allows Full Reconciliation of Space Telescopes with Satellites Results.

Abstract:

By applying the principles of Quantum Mass-Energy (QME) theory, the vastly different Hubble constant (Ho) values from various sources such as satellite measurements, space telescope observations, QME theory, LIGO, BOA, WMAP, and sky surveys are scientifically reconciled into a single true universal value of Ho(Universal)=67.76 (km/s)/Mpc.

• Please summarise the "explanation". Oct 14 '18 at 18:55
• From the "journal's own web page: "The General Science Journal is a non-peer-reviewed electronic journal that allows all scientific opinions to be aired". i.e. not peer reviewed and mostly full of nonsense. Sample title: "Theory of Objective Motions - Einstein was wrong" Oct 14 '18 at 19:02