There exists some tension on large scales between the Planck data and the \Lambda CDM concordance model of the Universe , which has been amplified by the recently claimed discovery of non-zero tensor to scalar ratio r .
At the same time , the current best-fit value of r suggests large field inflation \Delta \phi _ { inf } > M _ { p } , which requires a UV complete description of inflation .
A very promising working example that predicts large tensor modes and can be UV completed is axion monodromy inflation .
This realization of inflation naturally produces oscillating features , as consequence of a broken shift symmetry .
We analyse a combination of Planck , ACT , SPT , WMAP low \ell polarization and BICEP2 data , and show a long wavelength feature from an periodic potential can alleviate the tension at low multipoles with an improvement \Delta \chi ^ { 2 } \simeq 2.5 - 4 per degree of freedom , depending on the level of foreground subtraction .
As with an introduction of running , one expects that any scale dependence should lead to a worsened fit at high multipoles .
We show that the logarithmic nature of the axion feature in combination with a tilt n _ { s } \sim 1 allows the fit to be identical to a no-feature model at the 2 percent level on scales 100 \leq \ell \leq 3500 , and quite remarkable actually slightly improves the fit at scales \ell > 2000 .
We also consider possible unremoved dust foregrounds and show that including these hardly changes the best-fit parameters .
Corrected for potential foregrounds and fixing the frequency to the best fit value , we find an amplitude of the feature \delta n _ { s } = 0.095 ^ { +0.03 } _ { -0.05 } , a spectral index n _ { s } = 1.0 ^ { +0.03 } _ { -0.04 } , the overall amplitude \log 10 ^ { 10 } A _ { s } = 3.06 \pm 0.04 and a phase \phi = 0.85 ^ { +0.9 } _ { -1.6 } .
These parameters suggest an axion decay constant of f / M _ { p } \sim \mathcal { O } ( .01 ) .
We discuss how Planck measurements of the TE and EE spectra can further constrain axion monodromy inflation with such a large feature .
A measurement of the large scale structure power spectrum is even more promising , as the effect is much bigger since the tensor modes do not affect the large scales .
At the same time , a feature could also lead to a lower \sigma _ { 8 } , lifting the tension between CMB and SZ constraints on \sigma _ { 8 } .