A singlet scalar assisted $$N_{2}$$ leptogenesis and pseudo-scalar dark matter

Abstract We study the Leptogenesis and Dark Matter in the presence of an extra singlet complex scalar field in an extended discrete $$\mathcal {Z_{\textrm{3}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mtext>3</mml:mtext> </mml:msub> </mml:math> symmetry. The vacuum expectation value of the new scalar spontaneously breaks the $$\mathcal {Z_{\textrm{3}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mtext>3</mml:mtext> </mml:msub> </mml:math> symmetry. A remnant CP-like $$\mathcal {Z_{\textrm{2}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mtext>2</mml:mtext> </mml:msub> </mml:math> symmetry stabilizes the imaginary part of the complex scalar field, which can act as a pseudo-Goldstone Dark Matter. The real part of the complex scalar couples to RHN opens up new decay channels, which can lead to a larger CP-violation in generating the lepton asymmetry. Thus, the singlet complex scalar plays a crucial role in understanding the Leptogenesis and Dark Matter parameter space. This singlet complex scalar is also responsible for the First-Order Phase Transition (FOPT), which may provide observable stochastic gravitational wave signatures. We discuss the possible correlations among these three phenomena.