# LQG Legend Writes Paper Claiming GR Explains Dark Matter Phenomena

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On page 5 in https://arxiv.org/pdf/2301.10861.pdf Deur mentiones zL = 1728, whereby "zL is the redshift at the time of last rescattering". How does this make sense remembering the temperatures 3000 K at last scattering and ~ 2.7 K today?
Could you spell out a bit more what contradiction or issue you're seeing? I'm not doubting that there might be one, but I'm not following your reasoning.

Mentor
Could you spell out a bit more what contradiction or issue you're seeing?
I suspect it's the redshift value at last scattering; the usual value given is about 1100, not 1728.

hesar and ohwilleke
Gold Member
Could you spell out a bit more what contradiction or issue you're seeing? I'm not doubting that there might be one, but I'm not following your reasoning.
In addition to @PeterDonis: redshift of last scattering 1728 would mean, that the plasma temperature then were about 4712 K instead of 3000 K as usually assumed. Cooling happens inverse to expansion.

I think if Deur's field self-interaction replaces $\Lambda$ then one would expect that his model yields the same relative increase of the scale factor till today as the L-CDM model does.

ohwilleke
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one would expect that his model yields the same relative increase of the scale factor till today as the L-CDM model does
The relationship between redshift and scale factor, and between redshift and CMB temperature, is not model dependent; it's a general property of any FRW solution. So I would agree that we should not expect anything in Deur's proposed model to change those relationships.

hesar, ohwilleke and timmdeeg
Gold Member
In addition to @PeterDonis: redshift of last scattering 1728 would mean, that the plasma temperature then were about 4712 K instead of 3000 K as usually assumed. Cooling happens inverse to expansion.

I think if Deur's field self-interaction replaces $\Lambda$ then one would expect that his model yields the same relative increase of the scale factor till today as the L-CDM model does.
Thanks for clearing that up. Redshift of last scattering is not one of those number I have stored away in the quick reference table in my head. Good point.

timmdeeg
Why do they use the term 'last rescattering', though? Is that something different than last scattering, or just a mannerism?

Come to think of it, probably recombination and last scattering jumbled together.

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Gold Member
Why do they use the term 'last rescattering', though? Is that something different than last scattering, or just a mannerism?

Come to think of it, probably recombination and last scattering jumbled together.
I think last scattering, recombination and decoupling have all the same meaning, the short period where the universe changed from opaque to transparent. See also here post #3:

https://www.physicsforums.com/threa...diation-temperature-at-recombination.1049591/

ohwilleke
Yes, they do. It's 'rescattering' I've never seen before.

timmdeeg, ohwilleke and PeterDonis
Gold Member
Indeed, one "last rescattering", two "last scattering", a bit weird, but seems to mean the same. I don't understand "re" anyway.

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Mentor
I don't understand "re" anyway, because at least to my knowledge there wasn't any scattering before that time.
Yes, there was: the term "last scattering" is used precisely because that's when the scattering that had been going on until then, because the matter in the universe was plasma (electrons and ions), stopped, because the matter in the universe became neutral atoms.

hesar, Davephaelon, ohwilleke and 1 other person
Gold Member
Yes, there was: the term "last scattering" is used precisely because that's when the scattering that had been going on until then, because the matter in the universe was plasma (electrons and ions), stopped, because the matter in the universe became neutral atoms.
Yes, thanks. I've recognized that and deleted this sentence before I've seen your answer.

ohwilleke
Gold Member
There is another issue with that new paper Hubble Tension and Gravitational Self-Interaction which is unclear for me.

They mention the current values:

The discrepancy presently reaches a 5σ significance: the combined high-z measurements yield 67.28 ± 0.60 km/s/Mpc while the combined low-z measurements yield H0 = 73.04 ± 1.04 km/s/Mpc [8].

But they don't mention the values which according to their model match well without tension.

How to interpret this statement:

Finally, we verify that with the constrained parameters, the GR-SI fit reproduces better the CMB power spectrum with the low-z value of H0 than with the high-z H0 determination. We also find that if H0 is left a free parameter, its best fit value agrees with the low-z determination rather than the high-z one. This indicates an absence of Hubble tension in the GR-SI model.

Does this mean that their GR-SI fit yields the low-z value ~ 73 of the Hubble constant also for the early (high-z) universe? But they don't mention that explicitly somewhere.

Any ideas?

Gold Member
There is another issue with that new paper Hubble Tension and Gravitational Self-Interaction which is unclear for me.

They mention the current values:

The discrepancy presently reaches a 5σ significance: the combined high-z measurements yield 67.28 ± 0.60 km/s/Mpc while the combined low-z measurements yield H0 = 73.04 ± 1.04 km/s/Mpc [8].

But they don't mention the values which according to their model match well without tension.

How to interpret this statement:

Finally, we verify that with the constrained parameters, the GR-SI fit reproduces better the CMB power spectrum with the low-z value of H0 than with the high-z H0 determination. We also find that if H0 is left a free parameter, its best fit value agrees with the low-z determination rather than the high-z one. This indicates an absence of Hubble tension in the GR-SI model.

Does this mean that their GR-SI fit yields the low-z value ~ 73 of the Hubble constant also for the early (high-z) universe? But they don't mention that explicitly somewhere.

Any ideas?
In their model they aren't really predicting a Hubble constant, which, of course, isn't a constant in their model anyway. They are using the Hubble constant measurements as inputs to fit their depletion function, rather than as outputs predicted from some other inputs.

Their depletion function, a bit like the proportions of ordinary matter, dark matter, and dark energy in LCDM, isn't something that one can determine with all parameters set with precision from first principles. It is a summary description of the way a big complex system of the structure of the universe at various points in time evolved that has some free parameters to match to observations. The evolution and impacts of their depletion function, however, once you fix the parameters, can be determined more precisely.

What they are saying is that you can adjust the parameters in their model such that it is consistent with both low-z and high-z values of the Hubble "constant" thereby alleviating the tension. Hence, from their perspective, you can use the Hubble constant measurement to calibrate their deletion function's free parameters.
we verify that with the constrained parameters, the GR-SI fit reproduces better the CMB power spectrum with the low-z value of H0 than with the high-z H0 determination
This is neither here nor there, since the Hubble constant isn't a constant in their model.

It is an observation which is a bit surprising. But no really big conclusions are drawn from it. It is just mentioned.

It is surprising because you would think that the high-z Hubble constant measurement ought to produce the best CMB fit since the CMB arises at high-z.

But, it doesn't necessarily mean much.

The determination of the high-z Hubble constant value in LCDM is an output that is derived (solely) from the input of the CMB fit. This Hubble constant determination from the CMB fit is model dependent. So, it isn't necessarily that crazy that in a different model, the CMB fit would imply a modestly different inferred Hubble constant value.

Comparing Hubble constant values in a GR-SI model isn't truly an apples to apples comparison with the Hubble constant in the LCDM model. The models assign different meaning to what observations of the Hubble constant at a particular point in time mean, even though the observational measurement at a point in time is the same. And, there is no way to directly measure the Hubble constant at the time of the CMB imprint apart from looking at the CMB to determine if the Hubble constant inferred in LCDM from the CMB fit is consistent with other ways of observing it in that era.

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Davephaelon and timmdeeg
Gold Member
In their model they aren't really predicting a Hubble constant, which, of course, isn't a constant in their model anyway. They are using the Hubble constant measurements as inputs to fit their depletion function, rather than as outputs predicted from some other inputs.
A Hubble constant can be determined model dependent by observation. I have no clue how their "GR-SI fit" works but if they say it " ... reproduces the CMB power spectrum with the low-z value ..." doesn't seem to include a calculation of the Hubble constant. Perhaps implicitly?

I have been thinking differently. Supposed their fit includes the matter density at certain times then it should be possible the obtain the values of the corresponding Hubble constants.

Focusing at the time of the CMB makes it quite easy. Then in their model the universe is isotropic, so no field self-interaction and thus the depletion function D(z) has the value one, FIG. 1. So neglecting the K-term H² is proportional to the baryonic matter density ##\rho##, resulting from the CMB data, whereas in the L-CDM model ##\rho## includes Dark Matter.
It should be possible to calculate the Hubble constant at low-z as ##\rho## goes with 1/a³ using D(z) and their CMB redshift.

That's just my reasoning, no guarantee for correctness.

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ohwilleke
I'm slightly suspicious of their use of the value of the high redshift around 67.28 ± 0.60 in their model, because the original calculations of the Hubble constant of the Planck data measurements are based upon FLRW and Lambda; if one gets rid of FLRW and Lambda and tries to recalculate the Hubble constant from Planck data with a different model, wouldn't one get a different Hubble constant than 67.28 ± 0.60?

Unless I am reading the article wrong and they are saying that they did recalculate the Hubble constant from Planck data and ended up getting the low redshift around 73.04 ± 1.04 in their model.

ohwilleke
Gold Member
I'm slightly suspicious of their use of the value of the high redshift around 67.28 ± 0.60 in their model, because the original calculations of the Hubble constant of the Planck data measurements are based upon FLRW and Lambda; if one gets rid of FLRW and Lambda and tries to recalculate the Hubble constant from Planck data with a different model, wouldn't one get a different Hubble constant than 67.28 ± 0.60?
I think this is a good question. In general their model is based on the assumption that the universe is anisotropic with the exception of the early universe as shown in Fig. 1 in Hubble Tension and Gravitational Self-Interaction, where the Depletion function has the value 1 for z > 10. So that's in accordance with the L-CDM model but the matter density ##\rho## isn't. Their matter density is purely baryonic whereas the L-CDM matter density includes Dark Matter in addition.

At that time neglecting ##\Lambda## we obtain

So the deviating values of the matter densities should produce deviating values of the Hubble constant, if I see it correctly.

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ohwilleke
Gold Member
He comes at it by analogy to QCD which is, of course, formulated as a quantum theory. And, the logic of why it should have that effect is a lot more obvious when formulated in quantum form and in a way that can exploit known analogies in QCD.

But, fundamentally, the self-interaction that matters is already present in classical GR. It is just a lot harder to see when you try to work directly with Einstein's field equations, in which, of course, the gravitational field isn't on the right hand side in the stress-energy tensor, but instead appears on the left hand side as the non-linearity in the gravitational field part.
In this paper

On the Invention of Dark Matter and Dark Energy Craig Mackay, Institute of Astronomy, Cambridge, UK.*

the author argues with the Einstein-Hilbert Lagrangian (page 6), whereby the nonlinearities take the self-interaction into account.

The polynomial comes from expanding gµν around the constant metric ηµν , with the gravitational field φµν = gµν - ηµν . The square brackets indicate sums over Lorentz-invariant terms. Setting n = 0 gives L = [δφδφ], the Lagrangian for Newtonian dynamics. This result is consequent on suppressing higher order (n>0) terms in the Lagrangian and assuming v/c <<1. This asserts that the system under consideration is homogeneous and isotropic, effectively spherically symmetric by setting the Page 7 of 15 energy-momentum tensor, Tµν to be diagonal. Nonlinearities are always part of the full Lagrangian but their effects are suppressed where the system is homogeneous and isotropic. Nonlinearities which arise in the Lagrangians for both GR and QCD are consequent on field self-interaction.
...
Most galaxies and clusters of galaxies are clearly inhomogeneous and far from uniform. The additional terms that give rise to the nonlinearity or field self-interaction start to become important when √ (GM/L) >~ 10-3 (in “natural” units, see van Remortel, N. (2016) ),where L is the characteristic scale for the system (Deur et al, 2020).

The paper doesn't seem to be peer-reviewed though.

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ohwilleke
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