# ForecastAxions

The axion constraints are made on the model as described in http://arxiv.org/abs/1410.2896

The parameters in the model are standard LCDM, but then we allow a fraction of the total dark matter to be made of axions.

This is $\Omega_a/(\Omega_c+\Omega_a)$

The mass ranges allowed in the model are masses between $10^{-33}\mathrm{eV} < m_a < 10^{-22}\mathrm{eV}.$

The current constraints from Planck on this model are shown here:

• We assumed a single channel (e.g. 150 GHz) at 1 uK/amin in T and 1.4uK/amin in P, 3 arcmin resolution as the baseline model.
• We assume only white noise, with no FG inflation
• For these plots I show the error bars as function of noise level in 1-10 uK/arcmin range and resolution in range 1-10 arcmin. [Next update will include varying both at the same time]
• S4 TT/TE/EE/kk over 40% of sky, 30<ell < lmax
• Planck TT/TE/EE from 30<l<2500 over additional 20% of sky. Use these 'Planck-pol' specs for noise:File:Planck pol.pdf
• Planck TT at l<30 over 80% of sky
• Tau prior 0.06+-0.01

lmax(TT)=3000 unless explicit foreground cleaning is done in code for kSZ etc lmax(TE,EE)=5000 unless explicit foreground cleaning done in code kk reconstructed from 30<l<lmax using MV estimate

We assume a fixed mass of m_a = 1e-28 eV and a fraction of 2% relative to the dark matter content, and only adiabatic fluctuations for the first plot.

We then consider the joint constraints on the axion fraction and H_inflation, which propagates into the isocurvature constraints through the following equation:

The amplitude of isocurvature depends on the value of $H_{inf}$ (which we step in) and the value of $\phi_{i}$ (which is determined by the mass and energy density in axions, or the axion fraction) $A_i = H_{inf}^2/(\pi^2\phi_{i}^2)$ $r_{axion} = 2H_{inf}^2/(\pi^2A_s)$ $\alpha_{ax} = A_i/A_s$

The axion isogurvature is completed uncorrelated, and so the spectrum is added to the adiabatic spectrum independently. Note that we compute the fraction relative to the adiabatic spectrum after the fact, but this is not the primary variable we step in. We show the marginalised 1D constraints on $\Omega_a/\Omega_d$ and $H_{inf}$ below; both are varied simulataneously.

Note that for $H_{inf}$ it is more important to keep the noise levels down than to improve resolution, whereas for the axion fraction constraints resolution is important.