Q-Balls As Dark Matter?

A new preprint, entitled "Can Q-balls describe cosmological and galactic dark matter?" by Susobhan Mandal and S. Shankaranarayanan proposes "Q-Balls" as a dark matter candidate (hat tip to neo). The abstract and introduction to the preprint, excerpts of which explains the hypothesis (but contradict each other on the question of Q-ball mass, a probably that may be fixed in edits to the pre-print). I have interlineated my commentary in square brackets.

Abstract 

Q-balls, which are localized, non-topological solitons, can be a bridge between the two hypotheses. Q-balls formed in the early Universe can mimic CDM at cosmological scales. Interestingly, Q-balls can exhibit MOND-like behavior in the late Universe at galactic scales, providing a unified framework. Specifically, we demonstrate that millicharged composite Q-balls formed from complex scalar fields, decoupled from the background radiation, can naturally arise during the radiation-dominated epoch. From the matter-radiation equality, we also obtain the mass of Q-balls to be 1 eV [Ed. the body text says 41 eV], which are much smaller than the electron mass. Using the constraints from the invisible decay mode of ortho-positronium, we obtain Q<3.4×10^−5. We also establish an upper bound on the number density of Q-balls, which depends on the charge of the Q-ball and the small initial charge asymmetry. . . .  

Introduction 

The most convincing evidence for dark matter (DM) is found at the cosmological scales. The Λ-Cold-Dark-Matter (ΛCDM) model, in which DM is composed of collisionless particles, fits the temperature fluctuations of the Cosmic Microwave Background (CMB), the matter power spectra, and the abundance and mass function of galaxy clusters extraordinarily well. The foundation of the conventional cold dark matter hypothesis is the existence of non-relativistic, collision-free dark matter particles. Also, dark matter constituents cannot possess an electric charge comparable to that of electrons unless they are extremely heavy. 

However, this does not rule out the intriguing possibility of electrically millicharged particles. Millicharged particles have an electric charge e′ = εe, where e is the electron charge and ε ≪ 1. These particles can be either bosons or fermions, and they naturally arise in a wide range of models. [Ed. the exquisite sensitivity of physics measurements to even slight electromagnetic charges makes an EM millicharged particle hypothesis highly unlikely. For example, this would impact muon g-2 measurements in ways that are not observed and are at parts per billion levels.]

This naturally raises the question: Is there a framework where the DM behaves as a CDM in the cosmological scales and can mimic MOND in the galaxy scales? In other words, is there a mechanism where CDM and MOND share a common ancestry?  

This work proposes an alternative mechanism with the same origin but behaves differently in the cosmological and galactic scales. We demonstrate that non-topological solitons — the Q-balls — can be formed in the early Universe and mimic CDM at the cosmological scales. Specifically, we show that Q-balls from complex scalar field decoupled from the background radiation can naturally form in the radiation-dominated epoch. In contrast, they mimic MONDat galactic scales in the late Universe. 

Q-balls can naturally form in a wide range of particle physics models and can be produced in the early Universe, and can be stable. Recently, the existence of Q-balls in the dark sector of the Universe and its astrophysical consequences have gained interest. [Ed. actually, Q-ball models are far out of the mainstream in particle physics, involve Byzantine contortions to produce a questionable physics model disfavored by Occam's Razor, and aren't well-motivated.]

For a class of complex scalar field theory, we show that Q-ball configurations exist in the recombination epoch during the radiation-dominated (RD) era in the early Universe. We show that the Q-balls formed satisfy the two conditions — stability and existence. We show that the density perturbations that reenter during the recombination epoch increase the production of Q-balls and compute the number density of the thin-wall Q-balls in the Universe. We also compute the upper bound on the number density of Q-balls based on its global U(1) charge and small primeval charge asymmetry, which might be created due to primordial anomaly due to helical magnetic fields. It is also possible to generate charge asymmetry due to the helicity of the gravitational waves. From the matter-radiation equality, we also obtain the mass of Q-balls to be 41 eV, which are much smaller than the electron mass. Combined with the invisible decay mode of ortho-positronium leads to Q < 3.4×10^−5. Suggesting that the millicharged Q-balls are DM candidates responsible for the early structure. 

Since the Q-balls decay as 1/a3(η) in the early epoch, they behave like CDM in the cosmological scales. Later, we look at the possibility of forming Bose-Einstein condensate (BEC) and superf luidity by these Q-balls in the present Universe (dominated by dark energy). 

We find the Q-balls can indeed form these phases of matter, which eventually lead to the law predicted by Modified Newtonian dynamics at the galactic scale. Thus, we show that the cosmological and galactic dark matter share a common ancestry, representing distinct phases of a single background fluid. 

The possibility that galactic DM can be a superfluid has recently attracted attention. This is based on two key ideas: The first notion that the DM forms a superfluid within galaxies with a coherence length equal to the size of the galaxies is widespread. Second, the DM superfluidity phenomenon occurs frequently if the DM particle is sufficiently light and has a significant self-interaction. A superfluid is a state of matter where impurity particles flow without dissipation as long as they remain below a critical velocity, a phenomenon known as Landau’s criterion. Superfluidity and Bose-Einstein condensation are intimately related phenomena. In order to acquire a superfluid phase, BoseEinstein condensation must first occur; however, the converse is not true, as the superfluidity property disappears in the absence of interactions. Thus, we show that Q-balls can be considered a DM candidate, which acts as a composite object at the cosmological scale and behaves as collective excitation on the galactic scale.

The background analysis of why other solutions to explaining dark matter phenomena don't work in the introduction is also interesting, although not very rigorous: 

On cosmological scales, CDM accurately predicts the formation of structure. At smaller distance scales, however, the accurate picture is nebulous. As galaxy simulations and measurements have advanced, the CDM paradigm has encountered several challenges. Contradictory predictions concerning structure on galactic and sub-galactic scales, however, seem to result from it. Local group dwarf satellite galaxies present the main obstacles. Dwarf satellites are excellent candidates for in-depth studies of DM microphysics due to their DM dominance. With the discovery of ultra-faint dwarfs, the old ”missing satellite” problem has been gradually resolved, and other, more pressing problems have emerged. Recent attempts to match populations of simulated subhaloes and observed Milky Way (MW) dwarf galaxies uncovered a “too big to fail” issue. The most massive black halos are too dense to contain the brightest MW satellites. Even more perplexing is that most MW and Andromeda (M31) satellites co-rotate within immense planar structures. This can not be explained within the ΛCDM model. Also, recently, it has been suggested that the growth rate of perturbations is higher than predicted by the ΛCDM model. These issues raise the possibility or implication that dark matter is not cold or collision free. 

Weakly interacting massive particles (WIMPS) or axions, the two generally accepted possibilities for dark matter, would be excluded in that case. 

The defining feature of the thermal WIMP is its relic abundance naturally explained by the freeze-out process with a weak-scale cross-section. This cross-section would account for the elusive non-gravitational interactions of dark matter (DM). WIMP candidates naturally appear around the weak scale in many theories beyond the standard model (BSM). While a simple thermal WIMP is not the only possibility for DM, it is a compelling scenario that demands definitive testing. If WIMPs constitute the DM in the Universe, including our Galaxy’s DM halo, they should be ubiquitous, even in our immediate vicinity. This raises the question of directly detecting these WIMPs in the laboratory. This possibility was first explored by M Goodman and E Witten in 1985. They proposed that WIMPs elastically scattering off nuclei of chosen detector materials might leave recoiling nuclei with detectable kinetic energies. Goodman and Witten suggested that coherent elastic scattering of WIMPs off nuclei, with the cross-section proportional to A (A is the mass number of the nucleus), could yield a detectable rate of scattering events. Subsequently, numerous experiments worldwide, employing diverse detection techniques and materials, have sought WIMPs. However, to date, none of these experiments have definitively claimed WIMP detection. 

In contrast, Modified Newtonian Dynamics (MOND) provides a radical alternative to DM by modifying the Newtonian force law. According to MOND, the modification to Newtonian force law occurs at low acceleration. Thus, MOND can be understood as either a change to the Poisson equation that modifies gravity or a shift in inertia that modifies inertia by breaking the inertial and gravitational mass equivalence. This empirical force law has astonishingly explained a broad range of galactic events. It predicts asymptotically flat rotation curves for spiral galaxies and provides an excellent fit to exact rotation curves. The only free parameter is the critical acceleration a(0), whose best-fit value is the Hubble constant. Interestingly, the Baryonic Tully Fisher Relation (BTFR) is a direct result of this force law deep within the MOND regime. In ΛCDM, galaxies are surrounded by extensive DM halos, so a merger cannot be avoided. In contrast, in MOND, there is only stellar dynamical friction so that a merger can be avoided. According to MOND, tidal dwarf galaxies should have flat rotation curves and reside on the BTFR, consistent with NGC5291’s dwarfs. On extragalactic scales, however, MOND faces more severe problems. 

MOND and CDM are, therefore, effective in almost mutually exclusive regimes. The Λ-CDM model can explain the expansion and linear growth histories and the abundance of clusters, but on a galactic scale, it has certain limitations. MOND explains the observable features of galaxies reasonably well in general, notably the empirical scaling relations. However, it is highly improbable that it can be consistent with the complex shape of the CMB and matter power spectra. [Ed. this speculation is false.] 

To our knowledge, it is difficult to have CDM and MOND behaviors through particle dark matter models. As mentioned earlier, WIMPS or Axions cannot connect these theories in their respective mutually exclusive domains. More than that, WIMPs and axions cannot explain the low energy theory of phonon modes at the galactic scale as their rest mass energy is very high. [Ed. WIMPS are indeed largely ruled out. This paper has no solid support for the claims it makes about axion-like particle dark matter, which relies on mechanism similar to Q-balls to come closer to reproducing MOND than CDM does.]

Recently, the interest in Primordial Blackholes (PBHs) as a dark matter candidate over particle dark matter candidates is to fill this gap. Also, PBHs are not subject to the Big Bang nucleosynthesis (BBN) constraints of Baryons, making them non-baryonic entities that exhibit similar characteristics to CDM particles. [Ed. the paper fails to note that PBH is largely ruled out as the primary source of DM, but dismisses this hypothesis anyway without explanation. "For reasonable assumptions on those PBH binaries' properties before their evolution inside dark matter halos, we get that fraction to be in the range of 5×10^−3 to 0.1, for PBH masses of 5-80M⊙." Of course, the linked paper itself has issues, because PBH's are largely ruled out for masses other than asteroid masses, by micro-lensing for larger PBH's and by evaporation via Hawking radiation for smaller ones. There is also strong suggestive evidence from other sources that asteroid sized PBH's don't exist. PBH's of 5-80⊙ aren't what the DM candidate PBH's are talking about.]