# Variations in the local value of Hubble constant

I have been reading in various sources that the directly measured value of Ho is high than the global value inferred by precise measurements of the CMB. The local value seems to be around 73 km/s/Mpc where as the global value inferred, assuming a flat Lamda CDM model is about 67 km/s/Mpc

From what I have been reading I have gathered that this higher local value is due (possibly/probably?) because we live in a region of local underdensity.

Assuming that above is correct, my question is how can one explain (in simple (ish) terms) why a local underdensity would lead to a higher value of Ho?

Thanks

I have been reading in various sources that the directly measured value of Ho is high than the global value inferred by precise measurements of the CMB. The local value seems to be around 73 km/s/Mpc where as the global value inferred, assuming a flat Lamda CDM model is about 67 km/s/Mpc

From what I have been reading I have gathered that this higher local value is due (possibly/probably?) because we live in a region of local underdensity.

Assuming that above is correct, my question is how can one explain (in simple (ish) terms) why a local underdensity would lead to a higher value of Ho?

Thanks
does the following help?
https://arxiv.org/pdf/1407.7364.pdf
On the local variation of the Hubble constant:

Abstract.

We have carefully studied how local measurements of the Hubble constant, H0, can be influenced by a variety of different parameters related to survey depth, size, and fraction of the sky observed, as well as observer position in space. Our study is based on N-body simulations of structure in the standard ΛCDM model and our conclusion is that the expected variance in measurements of H0 is far too small to explain the current discrepancy between the low value of H0 inferred from measurements of the cosmic microwave background (CMB) by the Planck collaboration and the value measured directly in the local universe by use of Type Ia supernovae. This conclusion is very robust and does not change with different assumptions about effective sky coverage and depth of the survey or observer position in space.

Conclusion
We have carefully studied how local measurements of H0 can be influenced by a variety of different parameters related to survey geometry, depth, and size, as well as observer position in space. We find that variations in the local expansion field cannot explain the difference in the Hubble parameter obtained indirectly by measurements of the CMB by the Planck collaboration and that obtained by direct measurements. This result has been found to be insensitive to the percentage of the sky observed in direct measurements, and to whether or not cosmic evolution is taken into consideration. At small distances, observers positioned in Local Group like halos will have a tendency to measure a Hubble constant that is lower than the true value, whereas observers positioned at random in space have a tendency to measure a higher value. However, these effects become negligible when the largest observed distance exceed a few hundred Mpc/h, and therefore have no significant effect on the scale used in the local measurement of the Hubble parameter. Our conclusion is that the discrepancy between the value of H0 inferred from Planck and the value found from direct measurements must be ascribed to other sources than a variation in the local velocity field.

Thanks - I have read that paper. I am just looking whatever simple explanation of why a local underdensity would result in a high expansion rate.

At the moment I have got that Ohmega m is inversely proportional to H squared but I am looking for a some kind of explanation for why this is the case.

Chalnoth
Thanks - I have read that paper. I am just looking whatever simple explanation of why a local underdensity would result in a high expansion rate.
A local underdensity would mean that the local expansion rate would have slowed down less over time, resulting in a higher expansion rate currently.

For an extreme version of this, a sufficient local overdensity results in the expansion rate stopping entirely as a stable galaxy, galaxy cluster, or other structure is formed.

It is widely accepted that the expansion rate is accelerating but wouldn't a local underdensity give the same appearance in terms of the measured local value for Ho?

A local underdensity would mean that the local expansion rate would have slowed down less over time, resulting in a higher expansion rate currently.

For an extreme version of this, a sufficient local overdensity results in the expansion rate stopping entirely as a stable galaxy, galaxy cluster, or other structure is formed.

Chronos
Gold Member
A variation in Ho would make no sense, what might that mean - other than the laws of nature are illogical .An option inconsistent with science as we know it, and, imo, utterly repulsive.

Not sure what you mean there Chronos.

The Plank data seem to show a difference between the measured value of Ho and the value inferred from the CMB data. The former being about 1.3 times greater than the latter. One suggestion is that this discrepancy is due to us occupying a region of lower/under average matter density.

Since the directly measured value of Ho comes from Type 1a supernovae my follow up question is about the accelerating expansion of the universe. It had previously been determined that the expansion is accelerating. But this determination was made based on the same observations of Type 1 a supernova. But if the Plank value for Ho which is significantly lower is the correct one does this bring into question whether or not the expansion is accelerating?

Λ
A variation in Ho would make no sense, what might that mean - other than the laws of nature are illogical .An option inconsistent with science as we know it, and, imo, utterly repulsive.

Chronos
Gold Member
I'm just saying that Ho cannot vary without invoking some pretty weird physics. Think of it like a speed of light that varies according to which direction you point your flashlight.

The value found for Ho by direct measurements of Type 1a supernovae is significantly higher than the value which is inferred by the Planck data. The suggestion is that what we are measuring is a local value for Ho which might be higher than the global value because we are in a cosmic void - as in a region of the universe with under-density of matter. There are several papers on this. The question I was trying to understand is how one would differentiate between a higher value of Ho being explained by us occupying a region of lower density or being explained by accelerated expansion.

https://arxiv.org/abs/1407.7364 On the local variation of the Hubble constant

https://arxiv.org/abs/1606.00634 Reconciling Planck with the local value of Ho in extended parameter space

https://arxiv.org/abs/1609.04081 Hubble trouble or Hubble bubble

Chalnoth