Isocurvature forecast in the anthropic axion window

TL;DR

This work investigates axion-induced isocurvature fluctuations within the anthropic window where $f_a \gg 10^{12}$ GeV and $|\Theta_i|\ll1$, framing the problem inside a $\Lambda$CDM cosmology with a subdominant scale-invariant isocurvature component. It derives how the axion energy density and the isocurvature fraction $\alpha$ depend on $f_a$, $H_I$, and $\Theta_i$, and it quantifies the observational reach of current and future CMB experiments. The authors perform MCMC analyses on mock data to forecast limits, finding current bounds $\alpha<0.09$ (95% C.L.) and projected Planck and cosmic-variance-limited sensitivities of $\alpha<0.042$ and $\alpha<0.017$, respectively, with a small region in $(H_I,f_a)$ potentially detectable cosmologically. The results highlight cosmic variance as a fundamental limit and provide guidance for where to direct future axion searches if no isocurvature signal is observed, while keeping the anthropic axion window a plausible scenario for high-$f_a$ axions.

Abstract

We explore the cosmological sensitivity to the amplitude of isocurvature fluctuations that would be caused by axions in the "anthropic window" where the axion decay constant f_a >> 10^12 GeV and the initial misalignment angle Theta_i << 1. In a minimal Lambda-CDM cosmology extended with subdominant scale-invariant isocurvature fluctuations, existing data constrain the isocurvature fraction to alpha < 0.09 at 95% C.L. If no signal shows up, Planck can improve this constraint to 0.042 while an ultimate CMB probe limited only by cosmic variance in both temperature and E-polarisation can reach 0.017, about a factor of five better than the current limit. In the parameter space of f_a and H_I (Hubble parameter during inflation) we identify a small region where axion detection remains within the reach of realistic cosmological probes.

Figures (4)

• Figure 1: CMB angular power spectra for purely adiabatic initial conditions ($\alpha = 0$, dark red lines) with $n_{\rm ad} = 0.96$ and for purely CDM isocurvature initial conditions ($\alpha = 1$, light red lines) with a scale invariant spectrum $n_{\rm iso} = 1$. All other cosmological parameters are kept fixed.
• Figure 2: Scale dependence of the "signal to noise" for isocurvature fractions of $\alpha = 0.1$ (blue lines), and $\alpha = 0.001$ (pale blue lines). Plotted is the distortion $\Delta \mathcal{C}_\ell$ of the CMB angular power spectra caused by adding a subdominant scale-invariant uncorrelated CDM isocurvature component, given in units of the cosmic variance $\Delta_{\rm CV}$.
• Figure 3: Degeneracies of the isocurvature fraction $\alpha$ with the other parameters of the standard $\Lambda$CDM-model for different data sets. Plotted are the marginalised two-dimensional 95% credible contours for WMAP data only (pale red), WMAP+SDSS-LRG+SN (red), and for simulated data from Planck (thin pale blue dotted) and a cosmic variance limited experiment (thin blue dotted lines).
• Figure 4: Exclusion and sensitivity regions in the plane of $H_I$ (Hubble rate during inflation) and $f_{\rm a}$ (axion decay constant), assuming axions are all of the dark matter. The isocurvature exclusion region based on current data is shown in light blue with a boundary given by equation (\ref{['eq:currentconstraint']}). The sensitivity forecasts for Planck and CVL of equation (\ref{['eq:sensitivities']}) are also indicated. The dashed lines indicate the required $\Theta_{\rm i}$ for a given $f_{\rm a}$ to obtain the full amount of axion dark matter. We also show the region of excessive tensor modes and the region $f_{\rm a}<H_I$ where our late-inflation scenario is not applicable.