The line between a modifications of gravity including quantum gravity effects, and a fifth force is very thin.
In the first, it is possible, but not necessary, to have no beyond the Standard Model particles. In the second, you generally assume that existence of beyond the Standard Model dark matter particles (usually, but not always, fermionic) and some sort of carrier boson.
Dark Matter Without An Additional Force
Without such a force, you get some form of collisionless Λ Cold Dark Matter theory, in which the only interaction that cold dark matter particles have in the post-matter creation era is gravitational. In such a model, there are a limited number of variables.
For each species of dark matter particle you have a mass and a velocity distribution of particles in that species, and then you determine how many species of dark matter there are in the model. In a thermal freezeout scenario, each species as a very specific and narrow velocity distribution that is purely a function of its mass. You also need to determine if each species of dark matter particle is a fermion or boson.
Each dark matter species can basically be divided into truly cold dark matter particle models, with particles of 1 GeV or more of mass, and "warm dark matter" models, with particles on the order of keV in mass (with the masses serving as proxies for mean velocity as determined in a thermal freezeout scenario), with the light dark matter displaying some quantum behavior that influences its distribution.
When I first started looking into this seriously (i.e. when I started reading scientific journal articles on dark matter), the models with only one species of truly collisionless Cold Dark Matter almost always fit the observational data better than those with multiple species. Alas, I haven't been able to find any of those old papers lately since I've looked into again.
But the bottom line is that such simple theories don't do a good job a producing the dark matter phenomena that are observed, for example, in galaxies. The halo shapes observed from gravitational lensing are the wrong shape (especially for cold as opposed to warm dark matter) and the correspondence between baryonic (i.e. ordinary) matter distributions and dark matter effects are too closely aligned.
Footnote: The Gravity Only Condition
The condition that dark matter particles only interact via gravity is stronger than it needed to actual match observations. Dark matter needs to be "almost collisionless" for purposes of cosmology applications, for example, by not completely collisionless.
Astronomy observations, for example, don't rule out dark matter particles that have the same weak force charge as Standard Model fundamental fermions, but don't have electromagnetic charge.
But direct dark matter detection experiments have ruled out dark matter particles with a weak force charge as strong as that of neutrinos over a wide range of dark matter particle masses: roughly 1 GeV to 1 TeV. Dark matter particles with masses of 1 TeV or more would have mean velocities too low to fit observations in thermal freezeout scenarios.
So, the original supersymmetric WIMP (weakly interacting massive particle) candidate for dark matter, which would be stable, interact via the weak force and gravity only, be formed in thermal freezeout, and have a mass in the 1 GeV to 1 TeV range, has been ruled out pretty definitively.
Footnote: True One Species Dark Matter Particle Models Are Almost Indistinguishable From One Dominant Species Models.
This wouldn't imply that there was actually only one kind of dark matter particle. It could just mean that one kind of stable particle is dominant for cosmology applications.
By analogy, there are hundreds of possible ground state hadrons (i.e. possible composite particles made of quarks and/or gluons bound by gluons), but the longest lived mesons (the charged pion and the K-long meson) have mean lifetimes on the order of 10^-8 seconds, and there are only two baryons with mean lifetimes on the order of more than 10^-10 seconds: the proton (which is stable) and the neutron (which is stable when bound and has a mean lifetime of about 880 seconds when bound in an atom).
Likewise, for many applications you can ignore the existence of muons which have a mean lifetime of 10^-6 seconds and tau leptons with a mean lifetime on the order of 10^-13 seconds, and can ignore the fact that there are distinct electron neutrinos, muon neutrinos and tau neutrinos, and act as if there are only electrons.
For most purposes, a protons, neutrons, electron model in which protons and neutrons are the only hadrons, neutrons are composite particles made up of a proton, electron and an electron neutrino that decays when free of the nuclear binding force with a mean lifetime of 880 seconds, and and there is an additional nuclear force binding protons and neutrons whose behavior is described by a phenomenologically determined formula works just fine, because those hadrons are dominant. For example, this simplified model is more than sufficient for even sophisticated nuclear physics applications like building nuclear weapons and designing and operating nuclear power plants.
Moreover, while there are hundreds of stable or metastable atomic elements, some of which have several stable or metastable isotopes, the baryonic mass of the universe is roughly 73.9% hydrogen, 24.6% helium, and 1.5% "metals" (i.e. all atoms other than hydrogen and helium). Two atomic element baryonic matter model can give you something quite close to the truth for astronomy purposes, and a three atomic element baryonic matter model in which a single particle statistically blending the properties of oxygen, carbon and neon.
The reason I detour at length to recognize the possibility of a rich number of species of dark matter with a dominant species (possibly even a composite one, rather than a fundamental one) is because it is important not to rule out theoretically complex models that may be a better fit to the Standard Model in some respects merely because the observed phenomena are best described by one to three dominant particles from within a richer array of possibilities.
Self-Interacting Dark Matter (SIDM) v. Fifth Forces
Once you've reconciled yourself to the idea that a pure collisionless dark matter particle theory doesn't work, a modified gravity theory that adds no new dark matter particles but modifies (at least) the weak field behavior of general relativity, possibly via a quantum gravity effect, becomes the most conservative option, i.e. it changes core theory the least.
The possibility of a new force that operates only within the dark sector, allowing dark matter particles to interact with each other, but not with Standard Model particles, is addressed by self-interacting dark matter theories, with the carrier boson (often a light boson with some rest mass giving rise to a Yukawa force) of the self-interaction force sometimes called a "dark photon".
The main benefit of SIDM is that it fixes the discrepancy between the observed shape of inferred dark matter halos based upon gravitational lensing observations, and the NFW halo shape predicted in the case of truly collisionless dark matter.
There are observational bounds on the strength and nature of a self-interaction force from astronomy observations, which suggest a medium range, medium strength force with a strength roughly on the order of strength of the electromagnetic force if we were carried by a carrier boson with a mass on the order of tens or hundreds of MeVs.
The trouble with SIDM theories is that they don't explain the tight match between baryonic matter distributions and dark matter phenomena. To get that, you need a "fifth force" between dark matter and ordinary matter.
Of course, by the time you have added both new particles and a new force that interacts with Standard Model particles and has never been seen, the special case of modified gravity without dark matter particles starts to look more conservative and more favored by Occam's Razor.
A new pre-print concludes (not for the first time that someone has done so) that you can't explain dark matter phenomena without a fifth force within the dark matter particle paradigm.
[Submitted on 10 Aug 2020]
Paradigms and Scenarios for the Dark Matter~Phenomenon
Well known scaling laws among the structural properties of the dark and the luminous matter in disc systems are too complex to be arisen by two inert components that just share the same gravitational field. This brings us to critically focus on the 30-year-old paradigm, that, resting on a priori knowledge of the nature of Dark Matter (DM), has led us to a restricted number of scenarios, especially favouring the collisionless Λ Cold Dark Matter one.
Motivated by such observational evidence, we propose to resolve the dark matter mystery by following a new Paradigm: the nature of DM must be guessed/derived by deeply analyzing the properties of the dark and luminous mass distribution at galactic scales. The immediate application of this paradigm leads us to propose the existence of a direct interaction between Dark and Standard Model particles, which has finely shaped the inner regions of galaxies.
From the body text:
The mass distribution in Spirals is largely dominated by a dark component as it is evident from their
kinematics and their other tracers of the mass distribution (e.g., see [1]). More in general, many other
observations indicate the presence of such “substance” in the Universe. Among those, the gravitational
lensing of background objects, the extraordinary Bullet Cluster [2], the temperature distribution in Clusters
of galaxies (e.g., [3]) and, more recently, the pattern of anisotropies in the cosmic microwave background
(CMB) radiation ([4]). Furthermore, the theory of Big Bang nucleosynthesis indicates that the vast majority
of dark matter in the Universe cannot be made by baryons. With the caveat of an (exotic) population
of primordial Black Holes, the Dark Matter is therefore thought to be made of massive particles that
interact with Standard Model particles and with themselves mainly via Gravitation: the non-gravitational
interactions are believed to have cross sections very small (for WIMPS: 10−26 cm2
) and no role in the
building of the cosmological structures. Noticeably, the current belief is that such DM-Luminous Matter
(hereafter LM) interactions provide us with messengers of the dark particle.
In the past 30 years, the leading approach to the ’DM mystery’ has not been astrophysical or
experimental but has followed a particular route that in Physics has often been successful. Everything starts
by adopting the Paradigm according to which strong theoretical arguments on how nature could be made
lead us to the correct cosmological scenario and, in turn, to the actual dark particle in which the detectability
via experiments and astrophysical observations results as a bonus of the same arguments above. This Paradigm has pointed especially to a stable Weakly Interacting Massive Particle (WIMP), likely coming
from SuperSymmetric extensions of the Standard Model of Elementary Particles [5,6] and has opened
the way for the collisionless ΛCDM scenario. In spite of a good agreement of its predictions with many
cosmological observations, at galactic scales, the above scenario runs in serious problems including the
well known one for which the predicted structural properties of DM halos result in strong disagreement
with respect to those inferred from the internal motions of galaxies (see, e.g., [1]). It has been claimed that
these strong discrepancies could be eliminated by astrophysical processes (e.g., [7]) in which supernovae
explosions eventually flatten the originally cusped DM density profiles, however, as new data come in, the
DM halos density profiles appear to be always more difficult to be accounted by such processes (e.g., [8,9]).
As an example of this, the presence of very large DM halo core radii in Low Surface Brightness galaxies [8].
Furthermore, it is important to stress that, despite the large efforts made in searching for them, the WIMP
particles have not turned up in direct, indirect and LHC collider searches (see, e.g., [10,11]).1 . . . .
The three features reported and the three newly presented in this section, that ultimately stem from
the entangled dark-luminous mass distribution in galaxies, strongly suggest that some non gravitational
energy has been directly exchanged between atoms (or photons and/or neutrinos) and DM particles
via processes currently unknown and seemingly not explainable within the First Principles underlying
the ongoing Paradigm for the Dark Matter Phenomenon. More specifically,5
the DM–LM entanglement
in galaxies presented in previous sections works as a strong motivation for advocating a change of
Paradigm, in the direction in which the nature of the dark particle and its related Cosmological Scenario
are determined from reverse-engineering the galactic observations characterizing the DM Phenomenon.
