Radiative Plateau Inflation with Conformal Invariance: Dynamical Generation of Electroweak and Seesaw Scales

Abstract

We investigate a scale-invariant $B-L$ scenario where the Standard Model (SM) is supplemented with a dark scalar $\varphi$ which has gauge \& Yukawa interactions, with the couplings $g_{BL}$ and $y$, respectively, leading to radiative plateau inflation at scale $\varphi =M$ in the ultraviolet (UV), while dynamically generating the Electroweak and Seesaw scales \textitá lá Coleman-Weinberg in the infrared (IR). This is particularly achieved by implementing threshold corrections at an energy scale ${\mu }_T$ arising due to the presence of vector-like fermions. We show that implementing the inflationary observables makes the couplings solely dependent on the plateau scale $M$, leaving us with only two independent parameters $M$ and ${\mu }_T$. Within the theoretically consistent parameter space defined by $m_{Z_{BL}}>850\mathrm{GeV}$, from the assumption of independent evolution of the dark sector couplings from the SM couplings and $M<5.67M_P$ required for the realisation of inflationary \textit{plateau-like} behaviour of the potential around $\varphi =M$, where $M_P=2.4\times 10^{18}$ GeV is the reduced Planck mass, we identify the parameter space that is excluded by the current LHC results from the search for the heavy $Z_{BL}$ boson. For typical benchmark points in the viable parameter regions, we estimate the reheating temperature to be $\mathcal{O}(TeV)$ thus consistent with the standard Big Bang Nucleosynthesis (BBN) constraints. For typical benchmark points ($M=5.67,1,0.1M_P$) we predict the scales of inflation to be ${\mathcal{H}}_{inf}=2.79\times 10^{12}$ GeV, $1.53\times 10^{10}$ GeV and $1.53\times 10^7$ GeV, respectively.

Comments: 27 pages, 4 figures, Published in PRD