Abstract
Based on a physical argument, we derive a new analytic formula for the amplitude of density perturbation at the threshold of primordial black hole formation in the Universe dominated by a perfect fluid with the equation of state for . The formula gives and , where and are the amplitude of the density perturbation at the horizon crossing time in the uniform Hubble slice and the amplitude measure used in numerical simulations, respectively, while the conventional one gives and . Our formula shows a much better agreement with the result of recent numerical simulations both qualitatively and quantitatively than the conventional formula. For a radiation fluid, our formula gives and . We also discuss the maximum amplitude and the cosmological implications of the present result.
- Received 17 September 2013
DOI:https://doi.org/10.1103/PhysRevD.88.084051
© 2013 American Physical Society