Luke-warm dark matter: Bose-condensation of ultra-light particles

Galaxy Rotation Curves. Source: http://www.philica.com

What are ultra-light scalar particles? Particle physicists have already detected the Higgs boson. The Higgs is the first fundamental spin zero particle ever found! It weighs 120some GeV (more than 120 times heavier than a proton) and is produced by colliding particle beams at energies of several trillion electron volts in the largest particle accelerator on Earth.

However, there has been little exploration of the light side of the spectrum. The ultra-light scalar particles that I study should be comparable in size to a galaxy and have really light masses of about 10⁻²³ eV. The mass of such ultralight dark matter particle is about 10⁻²⁹ lighter than that of an electron!

Ultralight scalar field dark matter
 Agglomerations of ultra light scalar particles could form dark matter halos that prohibit structure formation on scales much smaller than the "size" of the particle. They thus avoid the overabundance of dwarf galaxies matching more closely to observations than other models. They also may be favored by observed dark matter distributions. Such particles would be photon-like if they roamed freely. However, given a large particle-antiparticle asymmetry, they Bose condense into dark matter halos. The condensate ends up being very pure with most particles in the ground state. The ones in excited states end up photon-like. The amount of hot dark matter is constrained more tightly by the latest Planck measurements.

Lukewarm dark matter
Ultralight scalar particles can Bose condense at finite temperatures when the temperature of the condensate is significantly larger than the mass of one boson (Urena-Lopez 2008). The light particles we know have a non-zero temperature. The temperature of CMB photons is 2.73 K, neutrinos decoupled at 1.9 K, and dark matter particles could also be lukewarm. We find that the temperature of these dark matter particles would be around 0.9 K if they decouple from regular matter before Standard model particles annihilate.

Constraints by Planck
Planck found that the effective number of neutrinos is 3.3±0.5. The standard deviation is still large and they have to combine their data with other surveys to obtain stricter constrains. More Planck data will also help. For our model, an Neffective of 3.3 corresponds to a T < 1.35 K for the scalar field, which is met by easily met since the natural temperature for scalar field dark matter is T ~ 0.9 K. If Neffective was 3.1, then the constraint would be tighter - T < 0.96 K but still within bounds. So, it not likely that this model will be ruled out by Planck observations or other similar experiments in the near future.

Why are ultralight scalar fields interesting in cosmology?
Ultralight scalar fields can be used to explain dark matter and dark energy with relatively simple mathematical models. Of course, they are also used in particle physics and string theory models. They are simple and they are seen pretty much everywhere in fundamental physics. The Higgs particle was recently detected, but there is no hint of other fundamental spin zero particles or of supersymmetry so far, which, in some sense, makes it easier for theorists .... why? ... well, because imaginary particles can have any properties whatsoever as long as they do not violate known experiments.

How do go about studying invisible matter? Well, direct studies can only be done on the Higgs particle because that is the one scalar particle we have found so far. There are experiments that search for dark matter particles on Earth looking for much heavier dark matter particles than the ones we consider, but their results have been null to date. Indirectly, we count galaxies, look at their sizes, mass distributions to try learn about dark matter.  We have looked at primordial light with WMAP and now with the Planck satellite, which tells us about the composition of the universe and provide limits on the amount of hot dark matter. Big Bang Nucleosynthesis measurements constrain the relic abundances of deuterium and ⁴He putting a bound on Neffective. There are also tests for violations of the Einstein's equivalence principle (EEP) on Earth and proposed tests of the EEP in space that could detect hints of dark matter or dark energy.

How to rule out ultralight scalar fields?
The direct way would be to somehow find dark matter particles and prove that they are heavier and that they are the dominant dark matter constituents. We could find "small" scale dark matter substructure, e.g., proof of the existence of a dark matter halo around the Sun or the Earth. It is also totally not clear how the huge particle-anti-particle asymmetry arose in the early universe. Without the asymmetry there would be noting to cause the particles to Bose condense to become halos. They could not all exist as hot dark matter because Planck and other experiments have not seen any excess of neutrinos, and so they would be ruled out. However, there is much more matter than antimatter in visible matter as well and we could not think of a good reason why there would not be an asymmetry for fundamental spin zero particles.
 
This post was motivated by an informal seminar by my brother, Mihai Bondarescu, on our  2010 Astrophysical Journal Letter at the University of Zurich. I was surprised at how much I forgot about this project.  Mihai gave a very  good talk that was followed by an interesting discussion. Since this discussion could result in potential collaborations, I thought I would summarize both our own work to remind myself of what we learned and why we did it and some of the work that has been done on this topic since 2010.

Note to self: I finished this post one year and 4 months after initially publishing it. I procrastinate too much to publish unfinished posts. Therefore the experiment should not be repeated.