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Register a new userSecond Order Perturbations During Inflation Beyond Slow-roll
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We numerically calculate the evolution of second order cosmological perturbations for an inflationary scalar field without resorting to the slow-roll approximation or assuming large scales. In contrast to previous approaches we therefore use the full non-slow-roll source term for the second order Klein-Gordon equation which is valid on all scales. The numerical results are consistent with the ones obtained previously where slow-roll is a good approximation. We investigate the effect of localised features in the scalar field potential which break slow-roll for some portion of the evolution. The numerical package solving the second order Klein-Gordon equation has been released under an open source license and is available for download.
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The next generation of space-borne gravitational wave detectors may detect gravitational waves from extreme mass-ratio inspirals with primordial black holes. To produce primordial black holes which contribute a non-negligible abundance of dark matter and are consistent with the observations, a large enhancement in the primordial curvature power spectrum is needed. For a single field slow-roll inflation, the enhancement requires a very flat potential for the inflaton, and this will increase the number of $e$-folds. To avoid the problem, an ultra-slow-roll inflation at the near inflection point is required. We elaborate the conditions to successfully produce primordial black hole dark matter from single field inflation and propose a toy model with polynomial potential to realize the big enhancement of the curvature power spectrum at small scales while maintaining the consistency with the observations at large scales. The power spectrum for the second order gravitational waves generated by the large density perturbations at small scales is consistent with the current pulsar timing array observations.
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