On the slope of curvature power spectrum in non-attractor inflation. (arXiv:1912.01061v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Ozsoy_O/0/1/0/all/0/1">Ogan Özsoy</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Tasinato_G/0/1/0/all/0/1">Gianmassimo Tasinato</a>
The possibility that primordial black holes constitute a fraction of dark
matter motivates a detailed study of possible mechanisms for their production.
Black holes can form by the collapse of primordial curvature fluctuations, if
the amplitude of their small scale spectrum gets amplified by several orders of
magnitude with respect to CMB scales. Such enhancement can for example occur in
single-field, non-attractor inflation: in this work, we make a detailed
investigation of the shape of the curvature spectrum in this scenario. We make
use of an analytical approach based on a gradient expansion of curvature
perturbations, which allows us to follow the changes in slope of the spectrum
during its way from large to small scales. After encountering a dip in its
amplitude, the spectrum can acquire steep slopes with a spectral index up to
$n_s-1,=,8$, to then relax to a more gentle growth towards its peak as found
in previous literature. After the peak associated with the non-attractor phase,
the spectrum amplitude then mildly decays, during a transitional stage from
non-attractor back to attractor evolution. Our analysis indicates that this
gradient approach offers a transparent understanding of the contributions
controlling the slope of the curvature spectrum. As an application of our
findings, we characterise the slope in frequency of a stochastic gravitational
wave background generated at second order from curvature fluctuations.
The possibility that primordial black holes constitute a fraction of dark
matter motivates a detailed study of possible mechanisms for their production.
Black holes can form by the collapse of primordial curvature fluctuations, if
the amplitude of their small scale spectrum gets amplified by several orders of
magnitude with respect to CMB scales. Such enhancement can for example occur in
single-field, non-attractor inflation: in this work, we make a detailed
investigation of the shape of the curvature spectrum in this scenario. We make
use of an analytical approach based on a gradient expansion of curvature
perturbations, which allows us to follow the changes in slope of the spectrum
during its way from large to small scales. After encountering a dip in its
amplitude, the spectrum can acquire steep slopes with a spectral index up to
$n_s-1,=,8$, to then relax to a more gentle growth towards its peak as found
in previous literature. After the peak associated with the non-attractor phase,
the spectrum amplitude then mildly decays, during a transitional stage from
non-attractor back to attractor evolution. Our analysis indicates that this
gradient approach offers a transparent understanding of the contributions
controlling the slope of the curvature spectrum. As an application of our
findings, we characterise the slope in frequency of a stochastic gravitational
wave background generated at second order from curvature fluctuations.
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