Conformal GUT inflation, proton lifetime and non-thermal leptogenesis
  In this paper, we generalize Coleman-Weinberg (CW) inflation in grand unified
theories (GUTs) such as $\text{SU}(5)$ and $\text{SO}(10)$ by means of
considering two complex singlet fields with conformal invariance. In this
framework, inflation emerges from a spontaneously broken conformal symmetry.
The GUT symmetry implies a potential with a CW form, as a consequence of
radiative corrections. The conformal symmetry flattens the above VEV branch of
the CW potential to a Starobinsky plateau. As a result, we obtain $n_{s}\sim
1-\frac{2}{N}$ and $r\sim \frac{12}{N^2}$ for $N\sim 50-60$ e-foldings.
Furthermore, this framework allow us to estimate the proton lifetime as
$\tau_{p}\lesssim 10^{40}$ years, whose decay is mediated by the superheavy
gauge bosons. Moreover, we implement a type I seesaw mechanism by weakly
coupling the complex singlet, which carries two units of lepton number, to the
three generations of singlet right handed neutrinos (RHNs). The spontaneous
symmetry breaking of global lepton number amounts to the generation of neutrino
masses. We also consider non-thermal leptogenesis in which the inflaton
dominantly decays into heavy RHNs that sources the observed baryon asymmetry.
We constrain the couplings of the inflaton field to the RHNs, which gives the
reheating temperature as $10^{6}\text{ GeV}\lesssim T_{R}<10^{9}$ GeV.
