  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.
