About the isocurvature tension between axion and high scale inflationary   models
  The present work suggests that the isocurvature tension between axion and high energy inflationary scenarios may be avoided by considering a double field inflationary model involving the hidden Peccei-Quinn Higgs and the Standard Model one. Some terms in the lagrangian we propose explicitly violate the Peccei-Quinn symmetry but, at the present era, their effect is completely negligible. The resulting mechanism allows a large value for the axion constant, of the order $f_a\sim M_p$, thus the axion isocurvature fluctuations are suppressed even when the scale of inflation $H_{inf}$ is very high, of the order of $H_{inf}\sim M_{gut}$. This numerical value is typical in Higgs inflationary models. An analysis about topological defect formation in this scenario is also performed, and it is suggested that, under certain assumptions, their effect is not catastrophic from the cosmological point of view. 
Mariel Estevez and O. Santill\'an
hep-ph astro-ph.CO hep-th