Supersymmetry based hybrid inflation models (called spontaneously broken supersymmetry by the Planck collaboration) are attractive for a number of reasons including the nice feature that inflation is associated with a local gauge symmetry breaking in the early universe. Models based on a minimal superpotential and a canonical Kähler potential have the important property that there is no eta problem and the supergravity corrections are adequately suppressed. Following Planck’s notation, the inflationary potential with sub-Planckian inflaton field values is approximately given by $V\simeq {\mathrm{\Lambda }}^4[1+{\alpha }_h\log (\varphi /M_{\mathrm{Pl}})]-m_{3/2}{\mathrm{\Lambda }}^2\varphi +{\mathrm{\Lambda }}^{4}O(\varphi /M_{\mathrm{Pl}}{)}^4$. Here $\mathrm{\Lambda }=\sqrt{\kappa }M$ denotes the energy scale of inflation, $M$ is the gauge symmetry breaking scale, $\kappa$ is a dimensionless parameter which fixes the inflaton mass ($\sqrt{2}\kappa M$), ${\alpha }_h$ is determined from quantum corrections in terms of $\kappa$ and the underlying gauge group, and the soft supersymmetry breaking term proportional to the gravitino mass $m_{3/2}$ ($\sim 10\mathrm{TeV}$) and linear in the inflaton field $\varphi$ is present during inflation. The final term in $V$ represents the leading supergravity correction which is well suppressed since $\varphi \lesssim M_{pl}$ [Note that the last two terms were not taken into account in the Planck analysis.] We provide estimates for the parameters $\kappa$ (and ${\alpha }_h$) that yield a scalar spectral index $n_s$ in the 0.96–0.98 range, which is fully consistent with the recent P-ACT-LB measurements presented by the Atacama Cosmology Telescope (as well as earlier measurements by Planck.) The gauge symmetry breaking scale $M$ is determined to be on the order of ${10}^{15}\mathrm{GeV}$ or so. We recall that In the absence of the soft SUSY breaking term proportional to $m_{3/2}$ in $V$, the spectral index $n_s\simeq 1-1/N=0.98$, where $N=50$ denotes the number of e-foldings. The tensor-to-scalar ratio $r$ in this minimal model is tiny, but it can reach values in the observable range, $r\lesssim 0.01$, in nonminimal models.

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• Baryogenesis & leptogenesis
• Grand unified models
• Inflation
• Supergravity
• Supersymmetric models