# Constraints to axions in modified thermal histories

I showed that if the radiation domination era began not long before big-bang nucleosynthesis (a novel but empirically allowed possibility), constraints to thermally produced axions are significantly relaxed.

**Results published in **arXiv:0711.1352 (Phys. Rev. D 77, 085020).

**Collaborators: **Tristan Smith and Prof. Marc Kamionkowski.

Most experimental searches for axions and astrophysical constrains depend on their two-photon coupling (e.g. ADMX, CAST, PVLAS, gamma-eV, globular cluster stellar evolution, and our telescope searches). Since this number is model-dependent and may even vanish in some parts of theoretical parameter space, it is important to look for evidence of axions using couplings not subject to this problem. The axion-hadron couplings do not vanish in any allowed region of parameter space. For example, consider axion interactions with nucleons.

Nuclear resonances in Li, Fe, Kr in the sun would produce a beam of axions detectable via the same resonances on Earth. Some constraints using these techniques already exist and work is ongoing to explore more of the axion parameter space with these techniques.The hadronic couplings of axions are also responsible for the rates keeping them in thermal equilbrium in the early universe.

~eV axions would thermalize through interactions with pions and freeze-out in the early universe, leaving behind a relic population that is relativistic when structure forms, suppressing the galaxy correlation power spectrum on small scales. This is similar to the effect of standard model neutrinos, and indeed the best constraints to the absolute scale of neutrino masses comes from cosmology. This was used by Hannestad and collaborators to place an upper limit on the axion mass of 1.4 eV using WMAP1 and the Sloan Digital Sky Survey (SDSS). They evaluated constraints leaving both the freeze-out temperature (parameterized by gs, the number of relativistic degrees of freedom at axion freeze-out) and the relic density in axions as free parameters, even though in standard QCD axion models, there is a one-to-one correspondence between the axion mass and its decoupling temperature. The constraints they derived are shown below:

The combined purple-pink region is excluded at 2 standard deviations. If axions froze out earlier (higher gs) than in the usual scenario, their free-streaming length would be small enough that it falls into a regime that cannot be probed by the galaxy auto-correlation power spectrum. In fact, the flattened contour at high gs corresponds to the minimum length scale at which SDSS accurately measures the galaxy auto-correlation power spectrum. At this point, constraints to thermal axions are completely relaxed. This got us thinking: Is there any way to change the cosmological scenario to relax constraints on axions without spoiling the successes of the standard big-bang cosmology? In other words, is there a physically plausible way to realize the high gs (at freeze-out) part of the allowed parameter space?

I realized that the answer is yes! Prior to BBN, we really know very little about the expansion history of the universe. If the universe is dominated by an unstable scalar of mass in the TeV range, its decay will generate entropy, delaying the start of the standard radiation dominated expansion phase of the universe until the radiation has a temperature of T> ~ 4 MeV, just in time for BBN not to be messed up. This will wash out the abundance of any species that freeze out at earlier times and leave the relevant particles much colder than species coupled to the plasma. Prior work on these low-temperature reheating (LTR) or entropy-generating cosmologies showed that they provide an excellent way to widen the parameter space available for a slew of dark matter candidates, such as WIMPs, sterile neutrinos, non-thermal axions, standard-model neutrinos, and even WIMPzillas! Considering low-temperature reheating models is not just an intellectual exercise. They are a real possibility. Light (~TeV) scalars abound in some versions of string theory, and they may dominate the energy of the universe at some time.

Unresolved, however, was the question of how constraints to thermally-produced 1-20 eV axions change in such scenarios. Using the standard pionic interaction rates, I wrote code to calculate the abundance and free-streaming length of axions in such unconventional scenarios. I re-mapped the constraints of Hannestad et al. into the space of abunance/free-streaming length, using them in concert with my code to obtain new constraints to thermal axions in an entropy-generating cosmology, shown below:

The red region is excluded by WMAP1+SDSS, while the yellow region is excluded by the simple requirement that thermal axions not have an abundance greater than the total dark matter abundance. As you can see, at sufficiently low reheating-temperatures, the cosmological constraints to thermal axions are almost completely relaxed. This follows from the smaller free-streaming length and lower abundance of axions in these scenarios, as shown below:

I also considered the promise of future surveys (LSST, better probes of the power-spectrum on small scales such as Ly-alpha forest measurements) for improving these constraints. I found that entropy generation is crucial to relax constraints; less dramatic changes in the expansion history, such as a kination phase dominated by the kinetic energy of a scalar field, offer far less dramatic changes in constraints.