Axions and CASPEr/ADMX

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As is well known (e.g. Fox et al, 2004), axion DM with a large decay constant is inconsistent with a large value for the Hubble rate during inflation. The proposed experiment "CASPEr" (Budker et al, 2014) has sensitivity to detect the QCD axion as DM for f_a\gtrsim 10^{16}\text{ GeV}. If CASPEr detects DM, this implies two important points (assuming standard, single field, minimally coupled, slow roll inflation):

  • S4 will not detect a tensor to scalar ratio
  • A detection of uncorrelated CDM isocurvature measures H_I (or bounds it)

The converse of these statements is that a detection of axions by CASPEr and non-zero r by S4 would require non-trivial models of inflation and/or the axion sector (e.g. Fairbairn et al, 2014).

A similar story holds, with some caveats, for axions with lower decay constant detectable by the already-running experiment, ADMX. Thus, a detection of QCD axion DM in well-motivated parts of parameter space makes predictions for S4, and allows S4 to be sensitive to very low scale inflation (H_I\lesssim 10^{10}\text{ GeV} or less). There is a plot in the science book demonstrating these benchmark cases with the QCD axion.

Is there more work to be done to consider these implications more widely? Current considerations use a Fisher forecast for the isocurvature amplitude.

In the case of an ADMX detection, is there a way to use S4 or other observations to sort out some of the "caveats" mentioned above, which apply assuming only an upper bound on isocurvature? These may include, for example, bounds on the power spectrum from axion strings.