Standard-smooth hybrid inflation

We consider the extended supersymmetric Pati-Salam model which, for $\mu >0$ and universal boundary conditions, succeeds to yield experimentally acceptable $b$-quark masses by moderately violating Yukawa unification. It is known that this model can lead to new shifted or new smooth hybrid inflation. We show that a successful two-stage inflationary scenario can be realized within this model based only on renormalizable superpotential interactions. The cosmological scales exit the horizon during the first stage of inflation, which is of the standard hybrid type and takes place along the trivial flat direction with the inflaton driven by radiative corrections. Spectral indices compatible with the recent data can be achieved in global supersymmetry or minimal supergravity by restricting the number of e-foldings of our present horizon during the first inflationary stage. The additional e-foldings needed for solving the horizon and flatness problems are naturally provided by a second stage of inflation, which occurs mainly along the built-in new smooth hybrid inflationary path appearing right after the destabilization of the trivial flat direction at its critical point. Monopoles are formed at the end of the first stage of inflation and are, subsequently, diluted by the second stage of inflation to become utterly negligible in the present universe for almost all (for all) the allowed values of the parameters in the case of global supersymmetry (minimal supergravity).

Figure 1

Spectral index in standard-smooth hybrid inflation versus $N_{\mathrm{st}}$ in global SUSY for $p=\sqrt{2}\kappa M/m=1/\sqrt{2}$. The values of the parameter $\alpha =⟨H^c⟩|/|⟨\varphi ⟩|$ range from 0.2 to 1.6 with steps of 0.2.

Figure 2

Spectral index in standard-smooth hybrid inflation versus $N_{\mathrm{st}}$ in minimal SUGRA for $p=\sqrt{2}\kappa M/m=1/\sqrt{2}$. The values of the parameter $\alpha$ range from 0.2 to 0.7 with steps of 0.1.