Alleviating the tension at low l through axion monodromy

There exists some tension on large scales between the Planck data and the.CDM concordance model of the Universe, which has been amplified by the recently claimed discovery of nonzero 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 analyze a combination of Planck, ACT, SPT, WMAP low l polarization, and BICEP2 data and show a long wavelength feature from a periodic potential can alleviate the tension at low multipoles with an improvement Delta chi(2) similar or equal to 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) similar to 1 allows the fit to be identical to a no-feature model at the 2% level on scales 100 <= l <= 3500 and quite remarkably actually slightly improves the fit at scales l > 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(-0.05)(+0.03), a spectral index n(s) = 1.0(-0.04)(+0.03), the overall amplitude log 10(10)A(s) = 3.06 +/- 0.04, and a phase phi = 0.85(-1.6)(+0.9). These parameters suggest an axion decay constant of f/M-p similar to O(.01). We discuss how Planck measurements of the temperature-Emode polarization (TE) and Emode polarization-Emode polarization (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 cosmic microwave background and Sunyaev-Zel'dovich (SZ) constraints on sigma(8).