"Finite" Non-Gaussianities and Tensor-Scalar Ratio in Large Volume Swiss-Cheese Compactifications

TL;DR

This work investigates whether finite non-Gaussianities and tensor modes can arise from type IIB string theory in large-volume Swiss-Cheese Calabi–Yau orientifolds by incorporating perturbative and non-perturbative $\alpha'$ corrections. Employing a multi-field axionic inflaton and the $\delta N$ formalism, the authors demonstrate that slow-roll scenarios can yield $f_{NL} \sim {\cal O}(10^{-2})$ and $r \sim {\cal O}(10^{-3})$ with $N_e \sim 60$, while slow-roll violation can produce $f_{NL} \sim {\cal O}(1)$ alongside $N_e \sim 60$. They further show that beyond slow-roll, a freezeout of curvature perturbations on super-horizon scales can maintain $r$ at ${\cal O}(10^{-3})$ and keep $|n_R-1|$ within observational bounds, with explicit parameter choices giving $|n_R-1|$ around ${\cal O}(0.001-0.014)$. A central role is played by large genus-zero Gopakumar–Vafa invariants, enabling the required corrections and slow-roll properties, and the results hint at intriguing possibilities where the inflaton also acts as dark matter or quintessence via NS-NS axions.

Abstract

Developing on the ideas of (section 4 of) [1] and [2] and using the formalisms of [3] and [4], after inclusion of perturbative and non-perturbative alpha' corrections to the Kaehler potential and (D1- and D3-) instanton generated superpotential, we show the possibility of getting finite values for the non-linear parameter f_{NL} while looking for non-Gaussianities in type IIB compactifications on orientifolds of the Swiss Cheese Calabi-Yau WCP^4[1,1,1,6,9] in the L(arge) V(olume) S(cenarios) limit. First we show that in the context of multi-field slow-roll inflation, for the Calabi-Yau volume V~10^5 and D3-instanton number n^s~10 along with N_e~18, one can realize f_{NL}~0.03, and for Calabi-Yau volume V~10^6 with D3-instanton number n^s~10 resulting in number of e-foldings N_e~60, one can realize f_{NL}~0.01. Further we show that with the slow-roll conditions violated and for the number of the D3-instanton wrappings n^s ~O(1), one can realize f_{NL} ~O(1). Using general considerations and some algebraic geometric assumptions, we show that with requiring a "freezeout" of curvature perturbations at super horizon scales, it is possible to get tensor-scalar ratio r ~O(10^{-3}) with the loss of scale invariance |n_R-1|=0.01 and one can obtain f_{NL} ~O(10^{-2}) as well in the context of slow-roll inflation scenarios in the same Swiss-Cheese setup. For all our calculations the large values of the genus-zero Gopakumar-Vafa invariants for compact projective varieties, play in important role. We also make some observations pertaining to the possibility of the axionic inflaton also being a cold dark matter candidate as well as a quintessence field used for explaining dark energy.