Because the inflationary mechanism is extremely sensitive to UV-physics , the construction of theoretically robust models of inflation provides a unique window on Planck-scale physics .
We review efforts to use an axion with a shift symmetry to ensure a prolonged slow-roll background evolution .
The symmetry dictates which operators are allowed , and these in turn determine the observational predictions of this class of models , which include observable gravitational waves ( potentially chiral ) , oscillations in all primordial correlators , specific deviations from scale invariance and Gaussianity and primordial black holes .
We discuss the constraints on this class of models in light of the recent Planck results and comment on future perspectives .
The shift symmetry is very useful in models of large-field inflation , which typically have monomial potentials , but it can not explain why two or more terms in the potential are fine-tuned against each other , as needed for typical models of small-field inflation .
Therefore some additional symmetries or fine-tuning will be needed if forthcoming experiments will constrain the tensor-to-scalar ratio to be r~ { } \mbox { \raisebox { -2.58 pt } { $ \stackrel { < } { \sim } $ } } ~ { } 0.01 .