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Developing on the ideas of (section 4 of) [1] and [2] and using theformalisms of [3] and [4], after inclusion of perturbative and non-perturbativealpha' corrections to the Kaehler potential and (D1- and D3-) instantongenerated superpotential, we show the possibility of getting finite values forthe non-linear parameter f_{NL} while looking for non-Gaussianities in type IIBcompactifications on orientifolds of the Swiss Cheese Calabi-YauWCP^4[1,1,1,6,9] in the L(arge) V(olume) S(cenarios) limit. First we show thatin the context of multi-field slow-roll inflation, for the Calabi-Yau volumeV~10^5 and D3-instanton number n^s~10 along with N_e~18, one can realizef_{NL}~0.03, and for Calabi-Yau volume V~10^6 with D3-instanton number n^s~10resulting in number of e-foldings N_e~60, one can realize f_{NL}~0.01. Furtherwe show that with the slow-roll conditions violated and for the number of theD3-instanton wrappings n^s ~O(1), one can realize f_{NL} ~O(1). Using generalconsiderations and some algebraic geometric assumptions, we show that withrequiring a "freezeout" of curvature perturbations at super horizon scales, itis possible to get tensor-scalar ratio r ~O(10^{-3}) with the loss of scaleinvariance |n_R-1|=0.01 and one can obtain f_{NL} ~O(10^{-2}) as well in thecontext of slow-roll inflation scenarios in the same Swiss-Cheese setup. Forall our calculations the large values of the genus-zero Gopakumar-Vafainvariants for compact projective varieties, play in important role. We alsomake some observations pertaining to the possibility of the axionic inflatonalso being a cold dark matter candidate as well as a quintessence field usedfor explaining dark energy.

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