Towards a purely gravitational effective theory of dark matter

[mitchell porter]

TL;DR

Constructing a purely gravitational, nonlocal action that reproduces CDM cosmology

"The Price of Abandoning Dark Matter Is Nonlocality" (Deffayet, Woodard)

written in response to

"What is the price of abandoning dark matter? Cosmological constraints on alternative gravity theories" (Pardo, Spergel)

In a nutshell, as explained after equation 34, by adding a nonlocal self-interaction to the metric, they can reproduce the effects normally attributed to CDM.

From the conclusion:

We stress that there can be no doubt about this model reproducing all the successes of CDM in cosmology. Those successes include the anisotropies of the cosmic microwave background, baryon acoustic oscillations, and linearized structure formation. All of this must come out right because this model was constructed by using the separate conservation of the CDM stress tensor to express it as a nonlocal functional of the metric. The only way this model can be falsified is by showing that CDM interacts with fields other than gravity, the evidence for which is weak. This model should put to rest the frequent claims that no modified gravity theory can supplant dark matter. It also demonstrates that the answer to the question of Pardo and Spergel about the price of abandoning dark matter: the price is nonlocality...

One thing our model does not do is to agree with the nonlocal extension of MOND [this refers to earlier work by the authors] which was constructed to reproduce the baryonic Tully-Fisher relation, with sufficient weak lensing, in gravitationally bound structure... It would be desirable to have a single formalism which connects both regimes.

It would also be desirable to derive these nonlocal models from fundamental theory. We believe they might arise from resumming the secular logarithms that are induced by loops of inflationary gravitons and which must eventually become nonperturbatively large during a prolonged period of inflation

edit: 2021 talk by Woodard

 

[kodama]

TL;DR Summary: Constructing a purely gravitational, nonlocal action that reproduces CDM cosmology

In a nutshell, as explained after equation 34, by adding a nonlocal self-interaction to the metric, they can reproduce the effects normally attributed to CDM.

is adding a nonlocal self-interaction to the metric similar to Deur claims of self-interaction to the metric?

 

[ohwilleke]

TL;DR Summary: Constructing a purely gravitational, nonlocal action that reproduces CDM cosmology

"The Price of Abandoning Dark Matter Is Nonlocality" (Deffayet, Woodard)

written in response to

"What is the price of abandoning dark matter? Cosmological constraints on alternative gravity theories" (Pardo, Spergel)

In a nutshell, as explained after equation 34, by adding a nonlocal self-interaction to the metric, they can reproduce the effects normally attributed to CDM.

From the conclusion:

edit: 2021 talk by Woodard

FWIW, while their model is very interesting, their implication that non-local gravity is the only gravitational approach that can give rise to the observed phenomena often attributed to dark matter is a claim that isn't supported by their paper in any rigorous way. A slightly different spin on their result would have been preferable.

 

[wumbo]

Abandoning locality is certainly an approach. I think some people forget that the general relativity is highly constrained by the equivalence principle and is mostly a consequence of that + the postulates of special relativity. So which postulate is broken and what evidence is there for it?

Unless they proved non-locality is a necessary aspect, which IIRC it isn't, I think it's safe to discount such approaches without a very good reason.

 

[ohwilleke]

Abandoning locality is certainly an approach.

FWIW, there are 83 non-local gravity papers on arXiv. The most recent was posted in April 2024, the oldest dates to September 2008.

One of the older ones, F. Darabi, "Dark matter, MOND or non-local gravity?" (July 2009) is facially addressing just the issue raised by wumbo.

 

[Mordred]

Although the approach is interesting I noticed they never looked into early scale structure formation which is attributed to the DM term. If I recall this is also a problem MOND never really addressed

 

[Mordred]

I wonder how the first article would weigh against Press-Schechter mass distributions as this method is often used to calculate the dark halo and galaxy distributions

Example here
https://www.roe.ac.uk/japwww/teaching/cos5_0910/cos5_0910_part5.pdf

 

[ohwilleke]

Although the approach is interesting I noticed they never looked into early scale structure formation which is attributed to the DM term. If I recall this is also a problem MOND never really addressed

Early structure formation has been addressed in MOND. Generically, MOND gives rise to structure formation more rapidly than particle DM. This is why the impossible early galaxies problem disfavors DM v. MOND, and for that matter, most modified gravity theories. I'll see if I can find some of the citations to papers on point.

 

[Mordred]

Please do as the MOND variations I am familiar with didn't address that so I would be interested if you can find some good citations. Complexity of mathematics isn't an issue.

 

[ohwilleke]

Please do as the MOND variations I am familiar with didn't address that so I would be interested if you can find some good citations. Complexity of mathematics isn't an issue.

Not a problem. I have them buried away in old blog posts and a somewhat elaborate set of folders with bookmarks for journal articles. It just takes a while to find them sometimes. It's probably been a year and a half since I looked at the question, and I add maybe twenty or thirty bookmarks a week.

 

[Mordred]

Sounds like my terabyte drive of pdfs and storage closet of textbooks lol. I too collect literature

 

[ohwilleke]

Why look for musty old stuff when I can give you something hot off the presses?

Galaxies in the early universe appear to have grown too big too fast, assembling into massive, monolithic objects more rapidly than anticipated in the hierarchical ΛCDM structure formation paradigm. The available data are consistent with there being a population of massive galaxies that form early (z≳10) and follow an approximately exponential star formation history with a short (≲1 Gyr) e-folding timescale on the way to becoming massive (M∗≈10¹¹M⊙) galaxies by z=0, consistent with the traditional picture for the evolution of giant elliptical galaxies. Observations of the kinematics of spiral galaxies as a function of redshift similarly show that massive disks and their scaling relations were in place at early times, indicating a genuine effect in mass that cannot be explained as a quirk of luminosity evolution. That massive galaxies could form by z=10 was explicitly predicted in advance by MOND. We discuss some further predictions of MOND, such as the early emergence of clusters of galaxies and the cosmic web.

Stacy S. McGaugh, James M. Schombert, Federico Lelli, Jay Franck, "Accelerated Structure Formation: the Early Emergence of Massive Galaxies and Clusters of Galaxies" arXiv:2406.17930 (June 25, 2024) (submitted to Apj).

 

[Mordred]

Why look for musty old stuff when I can give you something hot off the presses ?

Simple answer comparisons. As well as examining the different methodologies.

Thanks for the link I will examine it.

Edit : The portion of that paper referring to Jeans scale though applicable is a rather old method. There are more modern methods in regards to early inhomogenous mass distributions. Hopefully the paper details the modern methods used by LCDM.
It's late atm will have to examine it closer later on

 

[Mordred]

Ah found the methodology I was hoping they applied for DM halos (Press-Schechter formalism). Missed that detail last night. Decent paper thanks again.
Just a side note we still don't have a clear understanding of how early DM forms so this is also a factor beyond luminosity factors.

 

[kodama]

new paper


General Relativity and Quantum Cosmology
[Submitted on 1 Aug 2024]
Quasilocal Newtonian limit of general relativity and galactic dynamics
Marco Galoppo, David L. Wiltshire, Federico Re

A new Newtonian limit of general relativity is established for stationary axisymmetric gravitationally bound differentially rotating matter distributions with internal pressure. The self-consistent coupling of quasilocal gravitational energy and angular momentum leads to a modified Poisson equation. The coupled equations of motion of the effective fluid elements are also modified, with quasilocal angular momentum and frame-dragging leading to novel dynamics. The solutions of the full system reproduce the phenonomenology of collisionless dark matter for disc galaxies, offering an explanation for their observed rotation curves. Halos of abundant cold dark matter particles are not required.

Comments: 6 pages, 2 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc);

conclusion of the paper

In summary, we have shown that via a novel self-
consistent quasilocal Newtonian limit, general relativity
can explain the observed rotation curves of disc galaxies
without the need for halos of cold dark matter parti-
cles. The phenonomenology of collisionless dark matter
is reproduced by the regional gravitational energy and
angular momentum of the average spacetime geometry.

Cosmology and Nongalactic Astrophysics (astro-ph.CO); Astrophysics of Galaxies (astro-ph.GA); High Energy Physics - Phenomenology (hep-ph)
Cite as: arXiv:2408.00358 [gr-qc]

 

[ChrisF]

TL;DR: Constructing a purely gravitational, nonlocal action that reproduces CDM cosmology

"The Price of Abandoning Dark Matter Is Nonlocality" (Deffayet, Woodard)

written in response to

"What is the price of abandoning dark matter? Cosmological constraints on alternative gravity theories" (Pardo, Spergel)

In a nutshell, as explained after equation 34, by adding a nonlocal self-interaction to the metric, they can reproduce the effects normally attributed to CDM.

From the conclusion:

edit: 2021 talk by Woodard

Re: Constructing a purely gravitational, nonlocal action that reproduces CDM cosmology

Deffayet and Woodard are being admirably honest in that conclusion, which makes the paper worth taking seriously even if the result is uncomfortable.

The key admission is right there: their model reproduces all CDM cosmological successes by construction — they used the CDM stress tensor to build the nonlocal functional. That's not a prediction, it's an encoding. The model is
unfalsifiable unless CDM couples to something other than gravity, which they acknowledge the evidence for is weak. So what they've actually shown is that the CDM phenomenology has a purely gravitational, nonlocal description — not
that they've found the right one.

On the nonlocality itself:
The fact that they need two separate nonlocal models — one for CMB/BAO/structure formation and a different one for the MOND/Tully-Fisher regime — is the real signal here. If the nonlocality were fundamental, one action should cover
both. The gap between regimes suggests the nonlocality is being introduced as a mathematical patch in each domain rather than emerging from a single physical principle.

Their speculation about resumming secular logarithms from inflationary graviton loops is honest about this — they're saying "we don't know where the nonlocality comes from, but here's one place it might arise." That's a long way from
a derivation.

The question worth asking:
All the CDM successes they claim to reproduce — CMB anisotropies, BAO, linearized structure formation — are inferred from observations that depend on the assumed distance-redshift relationship. The standard cosmological distance
ladder carries assumptions about how photon energy evolves with redshift that are worth examining independently of the dark matter question. A nonlocal action constructed to reproduce CDM phenomenology inherits all those assumptions.
If any of them have systematic errors that accumulate with redshift, the nonlocal action is being fitted to a systematically shifted dataset.

It's also worth noting that standard cosmology already requires multiple diverging distance definitions for the same object — luminosity distance, angular diameter distance, comoving distance, and light-travel distance all give
different numerical answers and diverge increasingly at higher redshift. A framework that requires four non-equivalent ways to measure the same distance is carrying internal tension. When light-based distance measurements and
geometric distance calculations disagree and grow further apart with redshift, that divergence is itself a signal worth interrogating — it suggests something in the underlying distance formula may be wrong before you ever introduce
nonlocality to fix the downstream effects.

"Reproducing CDM cosmology" is only as good as the input assumptions that built CDM cosmology in the first place.

Christian Fuccillo

 

[PeterDonis]

The standard cosmological distance
ladder carries assumptions about how photon energy evolves with redshift that are worth examining independently of the dark matter question.

What assumptions are you referring to here?

 

[PeterDonis]

standard cosmology already requires multiple diverging distance definitions for the same object

No, it recognizes that the relationship between three different things--luminosity, apparent size, and redshift--is a key indicator for distinguishing between different candidate models for the expansion history of the universe. No claim is made that the "distances" that are used to express that relationship are actual, physical distances, and there is no issue at all with them being different. They're just three different critical variables expressed in distance units for convenience.

 

[ChrisF]

What assumptions are you referring to here?

Primarily two: first, that the (1+z) factors applied to photon flux across the rungs of the distance ladder are correctly accounted for — luminosity distance and angular diameter distance carry different powers of (1+z) and
K-corrections require assuming a spectral model. Second, and more broadly, that the cosmological model embedded in the luminosity distance integral is correct. The Hubble tension — H₀ = 67 from CMB inference versus 73 from the local
distance ladder — is observational evidence that these assumptions produce inconsistent results depending on which rung you stand on. That inconsistency is worth tracing to its source before attributing the residual to new physics like dark matter or dark energy.

 

[ChrisF]

No, it recognizes that the relationship between three different things--luminosity, apparent size, and redshift--is a key indicator for distinguishing between different candidate models for the expansion history of the universe. No claim is made that the "distances" that are used to express that relationship are actual, physical distances, and there is no issue at all with them being different. They're just three different critical variables expressed in distance units for convenience.

Fair correction — the multiple definitions are understood tools for encoding different observational relationships, not a flaw in the model. I stated that poorly.

The sharper version of the point is this: extracting any of those observables from raw data — flux, angular size, redshift — requires assuming a cosmological model to perform the conversion. The CDM successes that Deffayet and Woodard's nonlocal action is constructed to reproduce were themselves extracted using specific assumptions about the expansion history embedded in the distance integrals. A different expansion history would extract different numerical values from the same raw observations.

So when they claim their model reproduces "all the successes of CDM in cosmology," the claim is only as strong as the model-dependent pipeline that produced the CDM successes in the first place. If the expansion history assumptions carry systematic errors that accumulate with redshift, the nonlocal action is being fitted to systematically shifted outputs — not to raw observations directly. That's the constraint worth tracking, independent of whether the distance definitions themselves are internally consistent.

 

[PeterDonis]

luminosity distance and angular diameter distance carry different powers of (1+z)

Yes, for well understood reasons. These are not assumptions; they are consequences of the general class of FLRW models in GR.

K-corrections require assuming a spectral model.

Yes, which is based on our understanding of star and galaxy spectra. That understanding is incomplete, yes.

Second, and more broadly, that the cosmological model embedded in the luminosity distance integral is correct.

I'm not sure what you mean.

If you mean the specific function of time used for the scale factor, that's a free parameter in the model, and is adjusted to get the best match to the data. That's why looking at the relationship between multiple pieces of data is important: it puts tighter constraints on the model.

If you mean the general FLRW model framework itself, that's the framework everyone uses. If you want to propose a different one, PF is not the place to do it.

The Hubble tension

How much of an issue this is depends on which cosmologists you talk to. The latest rounds of data and calculations seem to have reduced it a lot, if not eliminated it, in the eyes of at least a fair number of workers in the field. We've had other PF threads on this.

 

[PeterDonis]

extracting any of those observables from raw data — flux, angular size, redshift — requires assuming a cosmological model to perform the conversion.

Um, no, it doesn't.

Apparent luminosity is a direct observable. Converting this to absolute luminosity requires a model of the emitting object--the star, galaxy, quasar, or whatever. Those models might have errors, yes, but they're not models of cosmological expansion. They're models of luminosity as it relates to other observed characteristics (such as supernova light curves).

Angular size is also a direct observable.

Redshift is obviously a direct observable.

The relationship between these three observables is model-dependent--but of course that's why we observe them: to put constraints on the model. But we don't have to assume a cosmological model to obtain the data.