Modifications To Gravity Continue To Look Attractive Relative To Dark Matter

One of the ongoing debates in modern physics is between the dark matter hypothesis and the hypothesis that phenomena attributed to dark matter is actually a result of us using inaccurate laws of gravity that require modification.

* At the beginning of this year, I provided my predictions for this area and recapped the status of the research. Then, I said:

The hunt for dark matter will continue, probably inconclusively as it did in 2014, in 2015. Fundamentally, the problem is that the interpretation of any signals or dark matter exclusions is highly model dependent, and we don't know enough about background processes intergalactic space or even in our own Sun's nuclear dynamics and atmospheric physics, to rule out non-dark matter alternatives to observational results.

Particularly notable will be the extent to which claims of cold dark matter theorists that feedback effects from baryonic matter can solve that theory's failure to reproduce a universe like the one observed can be convincingly supported without self-interacting dark matter. I expect that they will fail. Another worry in the cold dark matter camp is that the Bullet Cluster data is incompatible with many versions of this theory. Cold dark matter proponents may start to migrate into the warm dark matter camp at the margins.

Warm dark matter theorists, in contrast, face renewed arguments that the narrow parameter space of this theory is over constrained by Lyman alpha data and other data points, but proponents will ignore or theorize around this limitations.

DAMA is claiming a seasonal direct dark matter detection signal in the warm dark matter mass range in a late December pre-print, but I suspect that upon further inspection, this will turn out to be merely seasonal variation in the solar neutrino background. DAMA has cried wolf before and been disproved by LUX and others.

It also remains to be seen if the 3.5 keV X-ray signal touted this year, which could be a warm dark matter annihilation signal, will really turn out to be something more than emissions of potassium atoms as the "banana camp" has argued. I suspect that either the banana camp will ultimately win this argument, or that the signal will ultimately prove to be too inconsistent across different galaxies to fit a dark matter annihilation interpretation. Fortunately for warm dark matter proponents, the loss of this piece of evidence is not fatal to warm dark matter in general, since its annihilation properties are model dependent.

Modified gravity proponents have marshaled some arguments such as those related to the tightness of fit of galactic rotation curves to MOND predictions with a couple of minor well reasoned adjustments that are inconsistent with both of those theories. But, the leading MOND theory itself, of course, has always underestimated dark matter in galactic clusters and is missing a theoretically well motivated mechanism. Notably, MOND does particularly poorly in the case of non-spherical galactic clusters. And, it can't explain the Bullet cluster.

I am currently inclined to believe that Deur is right in attributing all dark matter phenomena and much or all of dark energy phenomena to non-linear self-interactions of canonical spin-2 gravitons, and that general relativity theorists have failed to correctly model the self-interaction terms of gravitional fields (a quantum gravity analysis using analogies to QCD highlights this conclusions although it isn't an inherently quantum gravitational observation and could be reproduced in a less transparent way with classical GR equations). If Deur is right, we have already discovered all particles that exist except the graviton and all forces that exist. Basically, GR math has had the right basic axioms, but not quite the right mathematical implementation in complex non-spherically symmetric cases, for a century. But, I don't think that this will gain wide acceptance or even recognition in 2015. Certainly, some researchers disagree (and here). Correspondence with Deur indicates that he has limited resources in the next year to devote to this not part of the day job project, and there isn't yet a critical mass of investigators coordinated in investigating this class of non-linear evaluations of GR axioms with gravitons. Others have also noted the critical role that assumptions other than spherical symmetry have on the non-linear effects in GR.

A scalar theory of gravity with a coupling dependent upon the tightness of matter-clustering produces similar results for similar reasons. Others also note that only mild modifications to GR are necessary to eliminate the need for dark matter.

In general, there is not a strong consensus on the way that the non-linear aspects of GR play out in all but the simplest matter distributions. There are strong suggestions that important, but largely unmodeled configurations like the multi-level cellular structure that seems to characterize the actual distribution of matter in the universe, can amplify these non-linear effects to orders of magnitude sufficient to account for a material share of dark matter and dark energy phenomena (see also here arguing that slight inhomogenities in matter-energy density in the radiation density can replicate the effect of dark matter in the lamda CDM model).

Moffat's MOG theory arguably outperforms MOND and has a larger domain of applicability, but like MOND and unlike Deur's analysis, is a purely phenomenological theory without a solid theoretical basis behind it. The formulas derived by each of the investigators is not all that different, which is reassuring (and, of course, necessary for the formulas to match reality). There has been at least one serious effort, however, to reproduce MOG in a manner with a more solid theoretical basis that is generalized to address dark energy as well.

One powerful new dark matter data point we are likely to get in 2015 is increasingly precise data on Milky Way dynamics in previously unobservable parts of our galaxy that can be used to more precisely model a hypothetical Milky Way dark matter halo, and to fine tune modified gravity model parameters.

* A year later, the evidence in favor of gravity modification is strengthening, while the dark matter hypothesis continues to be problematic. I don't have time to do a full fledged analysis of the issue (a did a better one in honor of the 100th anniversary of General Relativity a while ago), but do summarize below some of the notable research on the topic that has taken place in 2015.

* A good place to start the discussion, however, is with a 2014 summary of the state of warm dark matter and cold dark matter models:

Recent high-resolution simulations that include Cold Dark Matter (CDM) and baryons have shown that baryonic physics can dramatically alter the dark matter structure of galaxies. These results modify our predictions for observed galaxy evolution and structure. Given these updated expectations, it is timely to re-examine observational constraints on the dark matter model. A few observations are reviewed that may indirectly trace dark matter, and may help confirm or deny possible dark matter models. Warm Dark Matter (WDM) and Self-Interacting Dark Matter (SIDM) are currently the favorite alternative models to CDM. Constraints on the WDM particle mass require it to be so heavy that WDM is nearly indistinguishable from CDM. The best observational test of SIDM is likely to be in the dark matter distribution of faint dwarf galaxies, but there is a lack of theoretical predictions for galaxy structure in SIDM that account for the role of baryons.

Alyson Brooks, "Re-Examining Astrophysical Constraints on the Dark Matter Model" (July 28, 2014).

SIDM models, because they introduce a new force and not just a new particle, also fair less well in Occam's Razor relative to gravity modification models, than simple singlet dark matter models that struggle mightily to be reconciled with empirical data, for which the consensus is that the answer is "warm dark matter or bust."

A year later, Brooks is co-author of an article that compares CDM to SIDM in simulations with baryonic matter feedback and finds that the differences are surprisingly modest.

This past November, Brooks noted that baryonic feedback can help to partially explain the surprisingly number of bulgeless galaxies that are observed, but still struggles to reproduce the relative number of bulgeless and bulgeful galaxies which are observed in real life. Stating that:

After reviewing the results of relevant research that has been published to date, we use cosmological simulations to explore the ability of feedback to reduce or even prevent bulge growth during mergers. In dwarf galaxies, mergers actually reduce the central concentration of galaxies as the induced burst of star formation drives out low angular momentum material. This result shows the potential for feedback to reduce central mass growth. However, we also demonstrate that it is very difficult for current stellar feedback models to reproduce the small bulges observed in more massive disk galaxies like the Milky Way. We argue that feedback models need to be improved, or an additional source of feedback such as AGN is necessary to generate the required outflows.

The large number of bulgeless galaxies is not nearly so challenging for modified gravity theories.

* The baryonic Tully-Fischer relation is a formula that relates the rotation velocity of galaxies with the estimated amount of non-dark matter (i.e. baryonic matter) in the galaxy which holds true over six orders of magnitude in galaxy mass.  Historically, it was this idea that led to the formulation of modifications to gravity as an alternative to dark matter.

How accurate is the baryonic Tully-Fischer relation?

It turns out that it is much more tight than any common formulation of the dark matter hypothesis would predict it to be.

In a LCDM cosmology, the baryonic Tully-Fisher relation (BTFR) is expected to show significant intrinsic scatter resulting from the mass-concentration relation of dark matter halos and the baryonic-to-halo mass ratio. We study the BTFR using a sample of 118 disc galaxies (spirals and irregulars) with data of the highest quality: extended HI rotation curves (tracing the outer velocity) and Spitzer photometry at 3.6 μm (tracing the stellar mass). Assuming that the stellar mass-to-light ratio (M*/L) is nearly constant at 3.6 μm, we find that the scatter, slope, and normalization of the BTFR systematically vary with the adopted M*/L. The observed scatter is minimized for M*/L > 0.5, corresponding to nearly maximal discs in high-surface-brightness galaxies and BTFR slopes close to ~4. For any reasonable value of M*/L, the intrinsic scatter is ~0.1 dex, below general LCDM expectations. The residuals show no correlations with galaxy structural parameters (radius or surface brightness), contrary to the predictions from some semi-analytic models of galaxy formation. These are fundamental issues for LCDM cosmology.

Federico Lelli, Stacy S. McGaugh, and James M. Schombert, "The small scatter of the baryonic Tully-Fisher relation" (December 14, 2015).

* Another empirically supported fact that is supported by gravity modification but should not be true in a conventional dark matter theory is that the number of tidal dwarf satellite galaxies that a galaxy has is a function of its bulge index.

We show that a significant correlation (up to 5sigma) emerges between the bulge index, defined to be larger for larger bulge/disk ratio, in spiral galaxies with similar luminosities in the Galaxy Zoo 2 of SDSS and the number of tidal-dwarf galaxies in the catalogue by Kaviraj et al. (2012). In the standard cold or warm dark-matter cosmological models the number of satellite galaxies correlates with the circular velocity of the dark matter host halo. In generalized-gravity models without cold or warm dark matter such a correlation does not exist, because host galaxies cannot capture in-falling dwarf galaxies due to the absence of dark-matter-induced dynamical friction. However, in such models a correlation is expected to exist between the bulge mass and the number of satellite galaxies, because bulges and tidal-dwarf satellite galaxies form in encounters between host galaxies. This is not predicted by dark matter models in which bulge mass and the number of satellites are a priori uncorrelated because higher bulge/disk ratios do not imply higher dark/luminous ratios. Hence, our correlation reproduces the prediction of scenarios without dark matter, whereas an explanation is not found readily from the a priori predictions of the standard scenario with dark matter. Further research is needed to explore whether some application of the standard theory may explain this correlation.

Martin Lopez-Corredoira and Pavel Kroupa, "The number of tidal dwarf satellite galaxies in dependence of bulge index" (November 30, 2015).

* Other research on tidal dwarf satellite galaxies which had been used to support dark matter theories has been discredited.

The location of dark-matter free, tidal dwarf galaxies (TDGs) in the baryonic Tully Fisher (bTF) diagram has been used to test cosmological scenarios, leading to various and controversial results. Using new high-resolution 3D spectroscopic data, we re-investigate the morpho-kinematics of these galaxies to verify whether or not they can be used for such a purpose. We find that the three observed TDGs are kinematically not virialized and show complex morphologies and kinematics, leading to considerable uncertainties about their intrinsic rotation velocities and their locations on the bTF. Only one TDG can be identify as a (perturbed) rotation disk that it is indeed a sub-component of NGC5291N and that lies at less than 1σ from the local bTF relation. It results that the presently studied TDGs are young, dynamically forming objects, which are not enough virialized to robustly challenge cosmological scenarios.

H. Flores, F. Hammer, S. Fouquet, M. Puech, P. Kroupa, Y. Yang, M. Pawlowski, "Young tidal dwarf galaxies cannot be used to probe dark matter in galaxies" (December 7, 2015).

* Existing problems with the dark matter paradigm have not been resolved, as dark matter theorists had hoped, by including gravitational interactions between ordinary matter and dark matter. Modified gravity theories explain why satellite galaxies tend to align in a plane around a central galaxy, while dark matter theories do not.

We investigate the degree to which the inclusion of baryonic physics can overcome two long-standing problems of the standard cosmological model on galaxy scales: (i) the problem of satellite planes around Local Group galaxies, and (ii) the "too big to fail" problem. By comparing dissipational and dissipationless simulations, we find no indication that the addition of baryonic physics results in more flattened satellite distributions around Milky-Way-like systems. Recent claims to the contrary are shown to derive in part from a non-standard metric for the degree of flattening, which ignores the satellites' radial positions. If the full 3D positions of the satellite galaxies are considered, none of the simulations we analyse reproduce the observed flattening nor the observed degree of kinematic coherence of the Milky Way satellite system. Our results are consistent with the expectation that baryonic physics should have little or no influence on the structure of satellite systems on scales of hundreds of kiloparsecs. Claims that the "too big to fail" problem can be resolved by the addition of baryonic physics are also shown to be problematic. 

Marcel S. Pawlowski, Benoit Famaey, David Merritt, Pavel Kroupa, "On the persistence of two small-scale problems in ΛCDM" (October 27, 2015).

Pawlowksi, et al. describe the "to be to fail" problem as follows:

The TBTF problem is concerned with the internal dynamics of dwarf galaxies. When comparing the central masses of MW dwarf Spheroidal (dSph) satellites deduced from their kinematics with those of dark matter sub-halos in simulations, found that simulations of MW equivalents each contain ≈ 10 (actually 5 to 40) denser subhalos than those compatible with the most-luminous observed dSphs. . . . the observationally deduced DM halo masses of the MW satellites show a significant overabundance of M0.3kpc ≃ 107M⊙ halos and a lack of both less and more massive values compared to the theoretically predicted distribution for luminous sub-halos. This would indicate that the most-massive sub-halos do not host the most-luminous dSphs but remain virtually dark, while the most-luminous dSphs live in sub-halos of only intermediate mass. This raises the question of what prevented the massive sub-halos from forming galaxies. The TBTF problem has been identified not only among the MW satellite galaxies, but also for the M31 satellite galaxies, within the Local Group and also appears to be present for field galaxies.

The TBTF problem is more difficult to resolve than the missing satellites problem since it requires either that luminous galaxies do not form in the sub-halos with the largest central dark matter density, or that one introduces a process which reduces the central dark matter density of these most massive sub-halos to values consistent with the observed velocities in dwarf galaxies. One suggested solution to this problem has been a ‘light’ MW. If the MW halo is less massive than generally assumed (at least . 8×1011M⊙ instead of 1 to 2×1012M⊙) this translates into a lower number of massive sub-halos, thus alleviating the TBTF problem. However, in general such a low MW mass is disfavoured, for example by the Local Group timing argument, the analysis of the positions, line-of-sight velocities and proper motions of the MW satellite population, the Galactic escape speed as a function of radius, and the modelling of stellar streams in the MW halo. Furthermore, that the TBTF problem is also present for the M31 satellites, for more distant dwarfs in the Local Group and possibly even beyond is a strong argument against purely local or environment-dependent solutions.

* It also appears that a significant part of the disparity between modified gravity predictions and dark matter predictions for galactic clusters is due to the failure of modified gravity predictions to accurately include all baryonic matter, because clusters have a great deal of hot gas made of ordinary atoms that is not found in ordinary galaxies.

MOND reduces greatly the mass discrepancy in clusters of galaxies, but does leave a consistent global discrepancy of about a factor of two. It has been proposed, within the minimalist and purist MOND, that clusters harbor some indigenous, yet-undetected, cluster baryonic (dark) matter (CBDM). Its total amount has to be comparable with that of the observed hot gas. Following an initial discovery by van Dokkum & al. (2015a), Koda & al. (2015) have recently identified more than a thousand ultra-diffuse galaxy-like objects (UDGs) in the Coma cluster. Robustness of the UDGs to tidal disruption seems to require, within Newtonian dynamics, that they are much more massive than their observed stellar component. Here, I propound that a considerable fraction of the CBDM is internal to UDGs, which endows them with robustness. The rest of the CBDM objects formed in now-disrupted kin of the UDGs, and is dispersed in the intracluster medium. While the discovery of cluster UDGs is not in itself a resolution of the MOND cluster conundrum, it lends greater qualitative plausibility to CBDM as its resolution, for reasons I discuss. Alternatively, if the UDGs are only now falling into Coma, their large size and very low surface brightness could result from the adiabatic inflation due to the MOND external-field effect, as described in Brada & Milgrom (2000). I also consider briefly solutions to the conundrum that invoke more elaborate extensions of purist MOND, e.g., that in clusters, the MOND constant takes up larger-than-canonical values of the MOND constant.

Mordehai Milgrom, "Ultra-diffuse cluster galaxies as key to the MOND cluster conundrum" (October 14, 2015).

* One of the major problems with modified gravity theories like MOND is that they don't have an adequate theoretical basis.  But, Alexandre Deur has propposed, since 2003, a very subtle modification of General Relativity, focused on graviton-graviton interactions analogous to QCD which give rise to non-abelian effects comparable to MOND that may solve this problem  in a very elegant way that also addresses at least some of what is observed and described as "dark energy."

The non-abelian symmetry of a lagrangian invalidates the principle of superposition for the field described by this lagrangian. A consequence in QCD is that non-linear effects occur, resulting in the quark-quark linear potential that explains the quark confinement, the quarkonia spectra or the Regge trajectories. Following a parallel between QCD and gravitation, we suggest that these non-linear effects should create an additional logarithmic potential in the classical newtonian description of gravity. The modified potential may account for the rotation curve of galaxies and other problems, without requiring dark matter.

A. Deur, "Non-Abelian Effects in Gravitation" (September 17, 2003).

Our present understanding of the universe requires the existence of dark matter and dark energy. We describe here a natural mechanism that could make exotic dark matter and possibly dark energy unnecessary. Graviton-graviton interactions increase the gravitational binding of matter. This increase, for large massive systems such as galaxies, may be large enough to make exotic dark matter superfluous. Within a weak field approximation we compute the effect on the rotation curves of galaxies and find the correct magnitude and distribution without need for arbitrary parameters or additional exotic particles. The Tully-Fisher relation also emerges naturally from this framework. The computations are further applied to galaxy clusters.

A. Deur, "Implications of Graviton-Graviton Interaction to Dark Matter" (May 6, 2009).

One empirical test that has supported Deur's analysis has been the demonstrated relationship between the extent to which elliptical galaxies appear to have non-baryonic dark matter and the extent to which they are not perfectly spherical.

We discuss the correlation between the dark matter content of elliptical galaxies and their ellipticities. We then explore a mechanism for which the correlation would emerge naturally. Such mechanism leads to identifying the dark matter particles to gravitons. A similar mechanism is known in Quantum Chromodynamics (QCD) and is essential to our understanding of the mass and structure of baryonic matter.

Alexandre Deur,"A correlation between the amount of dark matter in elliptical galaxies and their shape" (28 Jul 2014).

* Another vein of theoretical work similar to that of Deur's in approach which has also been fruitful has been the exploration of "massive gravity" theories which like Deur's focus on the effect of graviton-graviton interactions have shown a resurgence in interest.

[S]tarting in 2011, Fawad Hassan and Rachel Rosen from Stockholm University (ie next door), succeeded in formulating a theory of massive gravity that does not suffer from the ghost instability. The key to success was a generalization of the de Rahm-Gabadadze approach in which the second metric is also fully dynamic, and the interaction terms between the two metrics take on a specific form. The specific form of the interaction terms is chosen such that it generates a constraint which removes the ghost field. The resulting theory is to best present knowledge fully consistent and symmetric between the two metrics. . . .

In the last years, the Stockholm group has produced a series of very interesting papers that not only formalizes their approach and shows its consistency, but they also derived specific solutions. This is not a small feat as it is already difficult to find solutions in general relativity if you have only one metric and having two doesn’t make the situation easier. Indeed, not many solutions are presently known, and the known ones have quite strong symmetry assumptions. . . . Meanwhile, others have studied how well this modification of general relativity fares as an alternative to ΛCDM. It has been found that massive gravity can fit all cosmological data without the need to introduce an additional cosmological constant. But before you get too excited about this, note that massive gravity has more free parameters than ΛCDM, that being the coupling constants in the interaction terms.

As noted in a June 3, 2015 post at this blog:

A new pre-print calculates the mass of the graviton in a massive gravity theory consistent with the single parameter that explains galactic rotation curves in MOND theory, the Hubble constant, the proportion of mass-energy in the universe that is dark energy (Omega lambda), the speed of light, and Planck's constant. The formula is h bar/c^2 times the Hubble constant times the square root of three times Omega lambda.

The result is 4*10^-69 kilograms, which is equivalent to 2*10^-33 eV/c^2, which is equivalent to 2*10^-61 times the Planck mass. The Compton wavelength of a graviton with this mass would be on the order of 100,000 light years (roughly the same as the diameter of the Milky Way galaxy).

Massive gravity theories are candidates for resolving both the dark energy and the dark matter problems of astrophysics.

I am skeptical that gravitons have rest mass. But, experimental evidence cannot rule out of graviton mass of the scale suggested: the current experimental limit is less than 6*10^-32 eV/c^2 (about thirty times heavier than the predicted value in this preprint).

* To recap some previous recent developments:

** From an October 7, 2015 blog post here:

There are new combined limits on dark matter product from the ATLAS and CMS experiments at the Large Hadron Collider (LHC) based upon complete Run I data. No dark matter signal has been observed at the LHC.

The LUX direct dark matter detection experiment still places the most strict bounds on a cross-section of interaction with nucleons for spin independent dark matter (about 10^-45 per cm^2) for dark matter particles of about 10 GeV/c^2 or more of mass. But, for lighter dark matter particles (certainly below 1 GeV), the maximum cross section of interaction with nucleons is set by CMS at about 10^-40 per cm^2 for spin independent dark matter and about 10^-41 per cm^2.

The cross-section of interaction of a neutrino with a nucleon is on the order of 4*10^-39 to 8*10^-39 per cm^2/GeV. Thus, the bounds on dark matter cross-sections of interaction from CMS are comparable to those of neutrinos with hundreds of MeV/c^2 of kinetic energy for dark matter particles up to about 10 GeV. For dark matter particles with masses of 10 GeV or more, exclusion from LUX is comparable to that of neutrinos with less than 10 eV/c^2 of kinetic energy (still relativistic by about three orders of magnitude, but nevertheless a very low energy for a neutrino).

Also, as recently noted, experimental observations of cosmic rays emitted by dwarf galaxies which are dark matter dominated in the dark matter particle theories, place strict bounds on the mean lifetime and dark matter annihilation cross-sections of any potential dark matter particle. Dark matter must have a mean lifetime much longer than the age of the universe and must very rarely annihilate. But, this limitation is more model dependent than some of the other boundaries.

None of these experiments, of course, can rule out any kind of dark matter particles whose only interactions with ordinary matter are via gravity, a particularly simple kind of dark matter model that is increasingly favored.

** The Planck satellite observations impose similar limitations on dark matter decay.

** There are also all sorts of other direct detection experiment based limits on dark matter models.  See also here.

** Conventional heavy dark matter particle theories are disfavored by the data from the El Gordo galactic cluster collision.

** The parameter space of dark photons is highly constrained.  Dark photons are important in many self-interacting dark matter theories.  They would probably be governed by a Proca model (basically a "massive photon" theory) if they did exist.

* Of course, of the general class of modified gravity models, not all of them are better than dark matter models with respect to all empirical tests of them.