An analytic evaluation of gravitational particle production of fermions via Stokes phenomenon. (arXiv:2206.14204v1 [hep-th])
<a href="http://arxiv.org/find/hep-th/1/au:+Hashiba_S/0/1/0/all/0/1">Soichiro Hashiba</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Ling_S/0/1/0/all/0/1">Siyang Ling</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Long_A/0/1/0/all/0/1">Andrew J. Long</a>
The phenomenon of gravitational particle production can take place for
quantum fields in curved spacetime. The abundance and energy spectrum of
gravitationally produced particles is typically calculated by solving the
field’s mode equations on a time-dependent background metric. For purposes of
studying dark matter production in an inflationary cosmology, these mode
equations are often solved numerically, which is computationally intensive,
especially for the rapidly-oscillating high-momentum modes. However, these same
modes are amenable to analytic evaluation via the Exact
Wentzel-Kramers-Brillouin (EWKB) method, where gravitational particle
production is a manifestation of the Stokes phenomenon. These analytic
techniques have been used in the past to study gravitational particle
production for spin-0 bosons. We extend the earlier work to study gravitational
production of spin-1/2 and spin-3/2 fermions. We derive an analytic expression
for the connection matrix (valid to all orders in perturbations) that relates
Bogoliubov coefficients across a Stokes line connecting a merged pair of simple
turning points. By comparing the analytic approximation with a direct numerical
integration of the mode equations, we demonstrate an excellent agreement and
highlight the utility of the Stokes phenomenon formalism applied to fermions.
We discuss the implications for an analytic understanding of catastrophic
particle production due to vanishing sound speed, which can occur for a
spin-3/2 Rarita-Schwinger field.
The phenomenon of gravitational particle production can take place for
quantum fields in curved spacetime. The abundance and energy spectrum of
gravitationally produced particles is typically calculated by solving the
field’s mode equations on a time-dependent background metric. For purposes of
studying dark matter production in an inflationary cosmology, these mode
equations are often solved numerically, which is computationally intensive,
especially for the rapidly-oscillating high-momentum modes. However, these same
modes are amenable to analytic evaluation via the Exact
Wentzel-Kramers-Brillouin (EWKB) method, where gravitational particle
production is a manifestation of the Stokes phenomenon. These analytic
techniques have been used in the past to study gravitational particle
production for spin-0 bosons. We extend the earlier work to study gravitational
production of spin-1/2 and spin-3/2 fermions. We derive an analytic expression
for the connection matrix (valid to all orders in perturbations) that relates
Bogoliubov coefficients across a Stokes line connecting a merged pair of simple
turning points. By comparing the analytic approximation with a direct numerical
integration of the mode equations, we demonstrate an excellent agreement and
highlight the utility of the Stokes phenomenon formalism applied to fermions.
We discuss the implications for an analytic understanding of catastrophic
particle production due to vanishing sound speed, which can occur for a
spin-3/2 Rarita-Schwinger field.
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