Dark Matter -- Is it possible that Dark Matter has Planck mass and Spin two?

[reinhard55]

Is it possible that dark matter has Planckmass and Spin two?

 

[Drakkith]

Is there a reason that it should?

 

[ohwilleke]

There aren't any dark matter particle candidates that have been shown to work in all circumstances, and almost all of them have problems of some sort. There are myriad dark matter candidates that have been considered. And, since no dark matter candidates have been directly observed, we can rule out a lot of the parameter space for dark matter that couples at all via any of the Standard Model forces to ordinary matter or photons, but it is much harder to rule out dark matter candidates that have only gravitational couplings.

Planck mass is on the order of 10^18 GeV/c^2. This is very heavy for dark matter candidates.

Most of the focus in dark matter research has been on candidates in the 1-1000 GeV range (called WIMPs) or less (often much less for warm dark matter, sterile neutrino and axion-like particle candidates). Composite dark matter candidates made up of Standard Model particles (such as hexaquarks and stable glueballs) would likewise be too light, they would be in the tens of GeV mass range.

There are two main kinds of other dark matter candidates commonly considered that are heavier than 1000 GeV:

One is MACHOS (massive compact objects like brown dwarfs) that have been ruled out observationally.

The other is primordial black holes, which are not completely ruled out, but have to be much heavier than the Planck Mass to not dissolve through Hawking radiation through the present (but also can't be too heavy due to observational lensing data that would rule them out). The sweet spot that hasn't been ruled out with observations is at roughly asteroid mass, and Planck mass is about 21 micrograms, which is far, far smaller than that.

The dark matter hypothesis in cosmology, and for a variety of other purposes, requires that the aggregate dark matter mass in the universe be roughly constant from shortly after the Big Bang until the present, implying either (1) a basically stable dark matter candidate, in which case it needs to fit thermal freeze out conditions, or (2) be a dark matter candidate that is created and destroyed at rates that have been in equilibrium for almost all of the age of the universe (which is the loophole by which axion-like dark matter candidates might be allowed despite being far lighter than neutrinos which would otherwise make them hot dark matter).

Thermal freeze out models of dark matter give rise to a relationship between dark matter particle mass and dark matter particle mean velocity.

We can constrain the range of dark matter particle mean velocity from visible matter dynamics much more tightly than we can constrain dark matter mass directly. If the mean velocity is too high, you get "hot dark matter" which is ruled out, because the universe is too clumpy with too much structure for that. If dark matter particles have a mean velocity that is too low, i.e. it is too cold, in contrast, you get too much structure at the sub-galaxy scale that is not observed (e.g. lots of satellite galaxies and well defined sub-halos within galaxies).

The amount of structure that we see in the universe is consistent, crudely, with the amount of structure that we would expect from a thermal freeze out dark matter candidate with a mass in the range from about 1 keV to about 1 TeV (i.e. 1000 GeV), and tends to favor the low end of that range. So, a massive spin-2 boson as a dark matter candidate can't be a thermal freeze out candidate, since it is 10^15 times too cold.

So, any Planck mass dark matter candidate needs to be one that is not a thermal freeze out particle that is stable at all times since shortly after the Big Bang, and instead must be a particle that acquires a much higher mean velocity than one would expect from thermal freeze out due to some process that continuously creates and destroys it in a equilibrium process.

But a process that regularly creates and destroys particles with a mass on the order of 10^18 GeV in a manner that gives the particles that are created the right mean velocity while completely evading observational detection is hard to imagine. This is a huge amount of mass-energy compressed into a point-like space. The Large Hadron Collider can't do that, and a next generation collider would be hard pressed to do so. This is roughly the same as the energy scale needed to create the sphaleron interactions predicted to happen in the Standard Model, and the vast majority of the universe naively seems too cold to give rise to the kind of conditions that could create and destroy such particles.

Of course, a massive spin-2 boson doesn't tell us much unless we know it's couplings.

The only kind of massive spin-2 boson that has been explored theoretically at any length is one with the couplings of a graviton (i.e. proportional to the mass-energy of all possible particles). Massive graviton theory is normally explored not as a dark matter theory, but as a form of modified gravity theory, sometimes with a massless graviton and sometimes as the sole form of graviton.

The experimental boundaries on a massive graviton as the sole form of graviton is constrained to be much, much less than the Planck mass. https://pdglive.lbl.gov/DataBlock.action?node=G033M

Another important experimental boundary comes from the simultaneous detection of neutrinos and gravitational waves and photons from the merger of a black hole and a neutron star. The limitation from that observation also severely constrains a massive graviton based upon the negligible gap between the photon, neutrino and gravitational wave time of arrival from the same event as possible. A Planck mass wouldn't cut it.

Another way to think about the issue is that a force carried by a massive boson takes the form of a Yukawa force with an effective range that it a function of the mass of the carrier boson. For example, the primary carrier of the residual strong force that binds protons and neutrons in atoms to each other is the pion, which has a mass about 140 MeV and a range about the distance of a typical atomic nucleus. If a graviton had the Planck mass, it would be a Yukawa force with a range much smaller than the radius of a proton and closer to the Planck length, but we know that gravitons, in fact, have a range of not less than hundreds of light years, so a graviton has to be very light.

So, a massive spin-2 boson with Planck mass as a massive graviton doesn't work.

So, a massive spin-2 boson with Planck mass dark matter candidate needs to be arise from some means other than thermal freeze out in order to have the proper mean velocity, and can't have the couplings of a graviton. It also can't have any meaningful non-gravitational interactions with ordinary Standard Model particles (realistically, weaker interactions than neutrinos) because otherwise it could be directly detected.

But it would probably need to have a meaningful self-interaction as a subset of self-interacting dark matter theories, because otherwise you would have a cusp-core problem that plagues the most minimal collisionless dark matter theories, because the shape of inferred dark matter halos which is roughly speaking isothermal, is not the shape that truly collisionless non-self-interacting dark matter would produce (which is called an NFW distribution). So it would have to interact, at least, via gravity and via its own self-interactions.

Its self-interaction would probably have to be carried by some other carrier boson with a mass on the order of MeVs or less, if the interaction is a Yukawa interaction as we would expect a boson mediated self-interaction with roughly the right properties to be in order to turn the central cusp of a collisionless dark matter NFW distribution into a core of dark matter with an isothermal distribution.

Once you impose those conditions, observational constraints are relatively insensitive to particle spin and to particle mass. But there is really no positive evidence of any phenomena that would suggest that a Planck mass spin-2 dark matter particle is part of the dark matter particle parameter space that makes any sense to consider seriously. Even if it isn't absolutely ruled out in a model independent way, it is not well motivated.

 

[mfb]

Most of the focus in dark matter research has been on candidates in the 1-1000 GeV range (called WIMPs) or less (often much less for warm dark matter, sterile neutrino and axion-like particle candidates).

This is partially due to experimental constraints. Many dark matter detectors have a flat efficiency above ~100 GeV: They are equally likely to see a 1000 GeV particle as they are to see a 100 GeV particle. But their density is different: We know the mass density of dark matter, so we can calculate the density in terms of particles. The more massive the particles are the lower their density, which makes it less likely that one of them interacts in the detector. I'm sure you can write down models with 10¹⁰ GeV WIMP particles, but we wouldn't expect any of them to hit atoms in our detectors so we can't test these models.

The GeV range has another advantage - the amount of dark matter is very natural in terms of thermal production - but once you go to really high energies we don't know the density you would expect because we don't know the physics there well.There are proposals to search for Planck-scale particles via their gravitational effects, e.g. with a billion pendulums (NIST article).

 

[snorkack]

The dark matter hypothesis in cosmology, and for a variety of other purposes, requires that the aggregate dark matter mass in the universe be roughly constant from shortly after the Big Bang until the present, implying either (1) a basically stable dark matter candidate, in which case it needs to fit thermal freeze out conditions,

Thermal freeze out models of dark matter give rise to a relationship between dark matter particle mass and dark matter particle mean velocity.

We can constrain the range of dark matter particle mean velocity from visible matter dynamics much more tightly than we can constrain dark matter mass directly. If the mean velocity is too high, you get "hot dark matter" which is ruled out, because the universe is too clumpy with too much structure for that. If dark matter particles have a mean velocity that is too low, i.e. it is too cold, in contrast, you get too much structure at the sub-galaxy scale that is not observed (e.g. lots of satellite galaxies and well defined sub-halos within galaxies).

The amount of structure that we see in the universe is consistent, crudely, with the amount of structure that we would expect from a thermal freeze out dark matter candidate with a mass in the range from about 1 keV to about 1 TeV (i.e. 1000 GeV), and tends to favor the low end of that range. So, a massive spin-2 boson as a dark matter candidate can't be a thermal freeze out candidate, since it is 10^15 times too cold.

So, any Planck mass dark matter candidate needs to be one that is not a thermal freeze out particle that is stable at all times since shortly after the Big Bang, and instead must be a particle that acquires a much higher mean velocity than one would expect from thermal freeze out due to some process that continuously creates and destroys it in a equilibrium process.

What rules out stable dark matter that acquired mean energy well different from light matter by processes operating early in Big Bang?

 

[reinhard55]

Is there a reason that it should?

I am thinking about SU(5) Bosons.

 

[ohwilleke]

What rules out stable dark matter that acquired mean energy well different from light matter by processes operating early in Big Bang?

The thermal dark matter-mass relation is a very model independent analysis. Essentially, energy density, i.e. temperature, is a very general concept. There is a good summary with annotations to the literature here. See also this post at Physics Stack Exchange.

You can always, by hypothesis, assume that there are new physics that do exactly what you want them to do in the early Universe since we don't have any direct observational means of testing physics at those scales. So, you can't rule out a hypothesis like that completely.

But, if you do that, you have to evaluate how well motivated the hypothesis is. And, with the Higgs boson mass being 125 GeV, we don't need any new physics at all between the electroweak scale that is well tested experimentally and the GUT scale of 10^16 GeV for the Standard Model as renormalized at very high energy scales to be non-pathological.

The other hard constraint which I didn't discuss above, because it is a little hard to do in a general sense, is that high energy processes that are new physics in the early Universe have a strong tendency to upset Big Bang Nucleosynthesis (BBN). I'm not saying that this entirely rules out new physics at energies near the GUT scale, but it does tightly constrain them and it is hard to generalize regarding the properties that a process like this must have or lack to not screw up BBN which is validated empirically to be very close to right, although there is a moderate tension in the amount of a specific type of Lithium that is produced. As a rule of thumb, any new high energy physics process that affects ordinary matter as well as dark matter is highly likely to screw up BBN.

 

[snorkack]

The thing is, we have no lower bounds for present for any dark matter-light matter interactions. Only upper bounds. And then we have lower bounds for dark matter self-interaction, from halo shapes - but this is a lower bound on elastic scattering, not annihilation. There are searches for dark matter that annihilates into light matter, but this is only because such could be found, while dark matter that cannot so annihilate cannot be so found.
If dark matter interaction with light matter is arbitrarily weak now, it could have been stronger but still arbitrarily weak during nucleosynthesis.

 

[ohwilleke]

The thing is, we have no lower bounds for present for any dark matter-light matter interactions. Only upper bounds. And then we have lower bounds for dark matter self-interaction, from halo shapes - but this is a lower bound on elastic scattering, not annihilation. There are searches for dark matter that annihilates into light matter, but this is only because such could be found, while dark matter that cannot so annihilate cannot be so found.
If dark matter interaction with light matter is arbitrarily weak now, it could have been stronger but still arbitrarily weak during nucleosynthesis.

To be more clear, yes, you can imagine new physics that would make it possible. New physics can allow you to escape almost any constraint.

But, to avoid BBN and thermal freeze out viral theorems and other empirical observations, you can't just have any new physics, you've got to tailor it to a lot of constraints.

So, while it is possible to come out with theories that would make it possible to have a dark matter candidate like that to some extent, is there any real empirical motivation for doing so?

In an ideal world, we look for observations that our theories can't explain, and try to make hypotheses that tend to flow from those observations. Otherwise, one ends up in the dilemma of deciding the every problem is a nail because your solution is a hammer, whether that is really a good tool for a particular problem or not.

A motivation from SU(5) GUT unification, for example, is not a very good theoretical motivation, because SU(5) GUTs are plagued with all sorts of problems like excessive proton decay.

On the other hand, if we have two or three otherwise unexplainable results, that Planck mass dark matter candidates could explain in the gravitational based direct dark matter detection scheme referenced by mfb in his comment to this thread, then Planck mass dark matter candidates would start to look a lot more attractive.

 

[reinhard55]

I am not thinking about a SU(5) GUT.I am only thinking about the Spin 2 Bosons which come
from the adjoint representation of the SU(5).

 

[mfb]

Please cite a publication discussing this model. If there is none we can't discuss it here.

 

[reinhard55]

I don't need more discussion about it.I only wanted to know if there are ad hoc arguments against it.

 

[ohwilleke]

A timely new paper argues that a Planck mass dark matter candidate is not possible consistent with observational evidence.

Their findings – due to be published in Physical Letters B in March - radically narrow the range of potential masses for Dark Matter particles, and help to focus the search for future Dark Matter-hunters. The University of Sussex researchers used the established fact that gravity acts on Dark Matter just as it acts on the visible universe to work out the lower and upper limits of Dark Matter’s mass. The results show that Dark Matter cannot be either ‘ultra-light’ or ‘super-heavy’, as some have theorised, unless an as-yet undiscovered force also acts upon it. The team used the assumption that the only force acting on Dark Matter is gravity, and calculated that Dark Matter particles must have a mass between 10^-3 eV and 10^7 eV. That’s a much tighter range than the 10-^24 eV - 10^19 GeV spectrum which is generally theorised.

From here.

The abstract states that:

In this letter, we show that quantum gravity leads to lower and upper bounds on the masses of dark matter candidates. These bounds depend on the spins of the dark matter candidates and the nature of interactions in the dark matter sector. For example, for singlet scalar dark matter, we find a mass range 10^−3 eV≲mϕ≲10^7 eV. The lower bound comes from limits on fifth force type interactions and the upper bound from the lifetime of the dark matter candidate.

The lower bound is roughly the mass of the smallest neutrino mass eigenstate. The upper bound is about 10 MeV (between the mass of a down quark and a strange quark, and much lighter than the least massive hadron).

The body text states early on (end notes omitted) that:

In general, quantum gravitational effects will lead to a decay of any dark matter candidate that is not protected by Lorentz invariance or a gauge symmetry from decaying. Furthermore, gravity is universal, it will thus couple to all forms of matter and it will create portals between the Standard Model and any hidden sector. While these decays will be suppressed by powers of the Planck mass, they will still lead to an upper bound on dark matter particles given the large age of our universe. Furthermore, if the dark matter particles are light, the same quantum gravitational effects will lead to fifth force type interactions and these interactions are bounded by limits coming from the Eöt-Wash experiment. Finally, there is a well known lower bound coming from quantum mechanics and more specifically the spin-statistics theorem which applies to fermionic dark matter candidate. This last bound depends on the dark matter profile.

Putting all these bounds together, we obtain tight mass ranges for scalar, pseudo-scalar, spin 1/2 and spin 2 dark matter particles which are gauge singlets. These bounds can be relaxed if the fields describing these particles are gauged, we however note that there are fairly tight constraints on the strength of the interactions in the dark matter sector. Finally, we argue that spin-1 vector dark matter particles are less constrained by quantum gravity, because of the chiral nature of the fermions in the Standard Model.

 

[mfb]

The team used the assumption that the only force acting on Dark Matter is gravity

That's clearly not general enough to say everything else is ruled out.

I don't need more discussion about it.I only wanted to know if there are ad hoc arguments against it.

Time to close this thread then.