Abstract:
We demonstrate novel features in the behavior of the second- and third-order nonlinearity parameters of
the curvature perturbation, namely
f
NL
and
g
NL
, arising from nonlinear motion of the curvaton field. We
investigate two classes of potentials for the curvaton—the first has tiny oscillations superimposed upon the
quadratic potential. The second is characterized by a single ‘‘feature’’separating two quadratic regimes with
different mass scales. The feature may either be a bump or a flattening of the potential. In the case of the
oscillatory potential, we find that, as the width and height of superimposed oscillations increase, both
f
NL
and
g
NL
deviate strongly from their expected values from a quadratic potential.
f
NL
changes sign from
positive to negative as the oscillations in the potential become more prominent. Hence, this model can be
severely constrained by convincing evidence from observations that
f
NL
is positive.
g
NL
, on the other hand,
acquires very large negativevalues. Further, this model can give rise to a large running of
f
NL
, with respect to
scale. For the single-feature potential, we find that
f
NL
and
g
NL
exhibit oscillatory behavior as a function of
the parameter that controls the feature. The running of
f
NL
with respect to scale is found to be small.
