  We study the possibility that the approximate time shift symmetry during
inflation is promoted to the full invariance under time reparametrization t \to
\tilde t(t), or equivalently under field redefinition of the inflaton \phi \to
\tilde\phi(\phi). The symmetry allows only two operators at leading order in
derivatives, so that all n-point functions of scalar perturbations are fixed in
terms of the power spectrum normalization and the speed of sound. During
inflation the decaying mode only decays as 1/a and this opens up the
possibility to violate some of the consistency relations in the squeezed limit,
although this violation is suppressed by the (small) breaking of the field
reparametrization symmetry. In particular one can get terms in the 3-point
function that are only suppressed by 1/k_L in the squeezed limit k_L \to 0
compared to the local shape.
