Sneutrino Tribrid Inflation in Flipped $\mathbf{SU(5)}$: Confronting ACT DR6 and Planck
We construct a realization of sneutrino tribrid inflation within the $R$-symmetric flipped $SU(5)$ grand unified theory. A vector-like pair of matter multiplets, $10_V+\overline{10}_V$, provides a $D$-flat inflaton direction along the right-handed sneutrino component, with an additional $Z_2$ symmetry forbidding a direct inflaton mass term so that the leading inflationary interaction is a non-renormalizable Kähler-driven operator. Unlike previous studies, we treat the superpotential cutoff scale $M_s$ as independent of the reduced Planck mass, $m_P$, substantially enlarging the viable parameter space. Confronting the model with the ACT DR6/Planck determination $n_s=0.9734\pm0.0034$ and the $2σ$ bound on the running of the spectral index, we identify broad regions of viable parameter space in which the flipped $SU(5)$ symmetry-breaking scale can approach the conventional GUT scale, $M\simeq M_{\rm GUT}$, and the tensor-to-scalar ratio can reach observable values, $r\gtrsim10^{-3}$, within reach of forthcoming CMB $B$-mode experiments such as LiteBIRD and CMB-S4. We further study the post-inflationary dynamics, identifying the inflaton with the lightest right-handed sneutrino in a conventional type-I seesaw sector, whose out-of-equilibrium decay generates a lepton asymmetry that is converted into the observed baryon asymmetry via non-thermal leptogenesis and electroweak sphalerons, for a reheating temperature consistent with both successful leptogenesis and the gravitino constraint.