A Combination of Perturbative and Non-perturbative Kähler Moduli Stabilization Can Connect String Theory to Inflation

In recent years, cosmological experiments like PLANCK-2018 and BICEP/KECK have shown the efficacy of single field slow-roll inflaton potential in explaining various experimental parameters regarding LSS, CMBR anisotropy and polarization data with significant precision. Therefore, obtaining a low energy effective inflationary theory consistent with such a class of potentials from superstring theory has been a subject of major efforts, although it is seriously at tension with swampland conjecture and trans-Planckian censorship conjecture (TCC). In this paper, we have proposed that, such a connection is in principle possible in a pleasant way, if we stabilize all Kähler moduli by incorporating several perturbative and non-perturbative quantum corrections in the Kähler potential and super-potential respectively, a suitable uplifting mechanism and a novel canonical normalization technique. Our framework is based on 10d type-IIB superstring theory compactified on a \(T^6/Z_N\) Calabi-Yau (CY) orientifold, equipped with three magnetized non-interacting and intersecting D7 branes, O7 planes and the non-trivial quantised RR and NS closed 3-form world volume fluxes threading the 4-cycles of CY -volume. The perturbative corrections arising from \({\alpha ^{\prime }}^3\) expansion in LVS, multi-graviton scattering upto one-loop with log-correction and non-perturbative corrections related to E3-instanton and gaugino condensation break the supersymmetric no-scale structure giving an F-term \(AdS_4\) potential which is dynamically uplifted by D-term potential originating from U(1) charges of D7 branes in gravitational sector thereby providing the inflaton potential after normalization. All the parameters of the derived \(dS_4\) potential are carefully tuned to maintain the inflationary plateau region. Cosmological parameters are obtained by \(k-\) space analysis of cosmological perturbations by dynamical horizon exit method and found to be consistent with PLANCK and BICEP/KECK constraints viz., \(n_s = 0.9652 - 0.9662\) , \(r = 5.8 \times 10^{-4} - 6.2 \times 10^{-4}\) , \(N = 55.0 - 56.7\) , \(n_t = (-7.28 \times 10^{-5}) - (-7.76 \times 10^{-5})\) at \(k = 0.001 - 0.009\) \(\textrm{Mpc}^{-1}\) .