Creation of spin-$$ \frac{3}{2} $$ dark matter via cosmological gravitational particle production

A bstract We study the cosmological gravitational particle production (CGPP) of spin- $$ \frac{3}{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> particles during and after cosmic inflation, and map the parameter space that can realize the observed dark matter density in stable spin- $$ \frac{3}{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> particles. Originally formulated by Rarita and Schwinger, the relativistic theory of a massive spin- $$ \frac{3}{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> field later found a home in supergravity as the superpartner of the graviton, and in nuclear physics as baryonic resonances and nuclear isotopes. We study a minimal model realization, namely a free massive spin- $$ \frac{3}{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> field minimally coupled to gravity, and adopt the name raritron for this field. We demonstrate that CGPP of raritrons crucially depends on the hierarchy between the raritron mass m 3/2 and the Hubble parameter at the end of inflation H e , with high-mass and low-mass cases distinguished by the evolution of the sound speed c s of the longitudinal (helicity- $$ \frac{1}{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> ) mode, which is approximately unity at all times for heavy (relative to Hubble) raritrons and can become small or vanish for lighter raritrons, leading to a dramatic enhancement of production of high momentum particles in the latter case. Assuming the raritrons are stable, this leads to a wide parameter space to produce the observed dark matter density. Finally, we consider a time-dependent raritron mass, which can be chosen to remove the vanishing sound speed of the longitudinal mode, but which nonetheless enhances the production relative to the constant high-mass case, and in particular does not necessarily tame the high momentum tail of the spectrum. We perform our calculations using the Bogoliubov formalism and compare, when applicable, to the Boltzmann formalism.