Kavli Affiliate: Misao Sasaki
| First 5 Authors: Tomohiro Fujita, Ryodai Kawaguchi, Misao Sasaki, Yuichiro Tada,
| Summary:
We consider models of inflation that contain a transient non-slow-roll stage
and investigate the conditions under which a dip appears in the power spectrum
of the curvature perturbation. Using the $delta N$ formalism, we derive a
general relation between the comoving curvature perturbation ${cal{R}}$ and
the scalar field perturbation $deltavarphi$ and its velocity perturbation
$deltapi$. Compared with the result obtained in linear perturbation theory,
it turns out that properly taking account of the $deltapi$ contribution is
essential to reproduce the dip in the power spectrum. Namely, the curvature
perturbation is proportional to a specific linear combination of
$deltavarphi$ and $deltapi$ at the linear order. We also investigate the
non-linearity at the dip scale and find that models with a bump or an upward
step exhibit much larger non-linearity than ultra-slow-roll and Starobinsky’s
linear potential models. Finally, we demonstrate the importance of
non-linearity by computing the probability density functions (PDFs) for the
above-mentioned models and show that highly asymmetric PDFs are realised for
models with a bump or a step.
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