Generalising axion-like particle as the curvaton: sourcing primordial density perturbation and non-Gaussianities

Abstract We investigate the non-perturbatively generated axion-like particle (ALP) potential, involving fermions in the dark sector that couple to the ALP, in an early universe cosmological inflationary stage with the ALP being a spectator field. The potential here deviates from the standard cosine nature due to the presence of the two dark sector fermion masses $$m_u$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>u</mml:mi> </mml:msub> </mml:math> and $$m_d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:math> which couple to the ALP. The ALP is a spectator field during inflation but it starts to oscillate and dominates the energy density of the universe after inflation ends, thereby sourcing isocurvature perturbations, while standard curvature fluctuations from the inflaton are assumed to be sub-dominant. Subsequently the ALP decays converting the isocurvature perturbations to adiabatic perturbations thereby acting as the origin of the primordial density perturbations. We identify the parameter space involving the axion decay constant $$f_{\phi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>ϕ</mml:mi> </mml:msub> </mml:math> , scale of confinement $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> , ALP mass m and the masses of the fermions, $$m_u$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>u</mml:mi> </mml:msub> </mml:math> and $$m_d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:math> where it can satisfactorily behave as the curvaton and source the observed primordial density perturbation. We also predict local non-Gaussianity signals for bi-spectrum and tri-spectrum $$f_{NL}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi>NL</mml:mi> </mml:mrow> </mml:msub> </mml:math> and $$g_{NL}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mi>NL</mml:mi> </mml:mrow> </mml:msub> </mml:math> , as a function of the ratio $$m_u/m_d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>u</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:mrow> </mml:math> , which are within the allowed range in the latest Planck observations and are detectable with future observations. Particularly we find that the value of $$f_{NL}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi>NL</mml:mi> </mml:mrow> </mml:msub> </mml:math> and $$g_{NL}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mi>NL</mml:mi> </mml:mrow> </mml:msub> </mml:math> are dependent on the ratio of $$m_u$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>u</mml:mi> </mml:msub> </mml:math> and $$m_d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:math> : $$f_{NL}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi>NL</mml:mi> </mml:mrow> </mml:msub> </mml:math> is more or less positive for all scenarios except $$m_u = m_d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>u</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:mrow> </mml:math> and $$g_{NL}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mi>NL</mml:mi> </mml:mrow> </mml:msub> </mml:math> is always positive irrespective of the ratio between $$m_u$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>u</mml:mi> </mml:msub> </mml:math> and $$m_d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:math> . The results of our analysis in th