New Higgs inflation in a no-scale supersymmetric SU(5) GUT

Higgs inflation is attractive because it identifies inflaton with the electroweak Higgs boson. In this work, we construct a new class of supersymmetric Higgs inflationary models in no-scale supergravity with an SU(5) grand unified theory (GUT) group. Extending the no-scale Kähler potential and SU(5) GUT superpotential, we derive a generic potential for Higgs inflation that includes the quadratic monomial potential and a Starobinsky-type potential as special limits. This type of models can accommodate a wide range of the tensor-to-scalar ratio $r=\mathcal{O}({10}^{-3}-{10}^{-1})$ as well as a scalar spectral index $n_s\sim 0.96$.

Figure 1

The predictions of our no-scale SUSY GUT model of Higgs inflation for the spectral index $n_s$ and tensor-to-scalar ratio $r$. The green (yellow) dots and curves represent predictions with 50(60) $e$-foldings. In plot (a), the condition ${\beta }_2=\frac{1}{3}{\beta }_1(1-\zeta )u^2$ is imposed and the round (square) dots correspond to $\zeta =0(\zeta =1)$. The horizontal strips attached to the lower round dots correspond to the effect of varying $\zeta \in [0,0.1]$ (from right to left), while the upper strips attached to the square dots depict the effect of varying $\zeta \in [0.9,1]$ (from left to right). In plot (b), the three pairs of dots from top to bottom correspond to $\zeta =(1,0.98,0.95)$ and $\delta =0$. The strip attached to each round dot describes the effect of varying $\delta$ over the range $\pm (1.2\times {10}^{-3})$, via the shifted relation ${\beta }_2=\frac{1}{3}{\beta }_1(1-\zeta +\delta )u^2$. In each plot, the shaded red and blue (pink and light-blue) contours represent the observational limits at the 68% (95%) confidence level as given by Ref. [3].