## Author(s)

Maleknejad, Azadeh, Kopp, Joachim## Abstract

The minimal coupling of massless fermions to gravity does not allow for their gravitational production solely based on the expansion of the Universe. We argue that this changes in presence of realistic and potentially detectable stochastic gravitational wave backgrounds. We compute the resulting energy density of Weyl fermions at 1-loop using in--in formalism. If the initially massless fermions eventually acquire mass, this mechanism can explain the dark matter abundance in the Universe. Remarkably, it may be more efficient than conventional gravitational production of superheavy fermions.

## Figures

The graviton--fermion cubic and quartic vertices.

GW-induced freeze-in of dark matter for a GW background with a broken power-law spectrum. Colored lines show the phase transition temperature $T_*$ and DM mass $M$ required to explain the observed DM density. We have assumed a spectral index $m=3$ below the peak frequency, $q_\text{peak}$, while above the peak we have used $n=1$ (green, e.g.\ from bubble collisions in a first-order phase transition), $n=5/3$ (blue, e.g.\ from turbulence), and $n=4$ (orange, e.g.\ from sound waves) as benchmark values. Below the lines, GW-induced freeze-in can still contribute a fraction of the DM. The bottom edges of the shaded bands indicate where that fraction is 1\%. For comparison, we show in yellow the parameter region in which conventional cosmological production of supermassive fermions by the expansion of the Universe (``CGPP'') \cite{Kolb:2017jvz, Ema:2019yrd, Kolb:2023ydq} or graviton-mediated annihilation (``GMA'') \cite{Bernal:2018qlk, Clery:2021bwz} yield the correct relic density. Inside the gray area, fermions are massive already at the time $T_*$ of GW production, so our mechanism is not applicable. \emph{Gravitational-wave induced freeze-in can successfully explain the observed DM relic abundance in large swaths of parameter space, favoring $T_*$ well above the electroweak scale.}

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