“Finite” non-Gaussianities and tensor–scalar ratio in large volume Swiss-cheese compactifications

Abstract

Developing on the ideas of (Section 4 of) [A. Misra, P. Shukla, Moduli stabilization, large-volume dS minimum without anti- D3-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi–Yau's, Nucl. Phys. B 799 (2008) 165–198, arXiv: 0707.0105] and [A. Misra, P. Shukla, Large volume axionic Swiss-cheese inflation, Nucl. Phys. B 800 (2008) 384–400, arXiv: 0712.1260 [hep-th]] and using the formalisms of [S. Yokoyama, T. Suyama, T. Tanaka, Primordial non-Gaussianity in multi-scalar slow-roll inflation, arXiv: 0705.3178 [astro-ph]; S. Yokoyama, T. Suyama, T. Tanaka, Primordial non-Gaussianity in multi-scalar inflation, Phys. Rev. D 77 (2008) 083511, arXiv: 0711.2920 [astro-ph]], after inclusion of perturbative and non-perturbative α ′ corrections to the Kähler 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. We show the same in two contexts. First is multi-field slow-roll inflation with D3-instanton contribution coming from a large number of multiple wrappings of a single (Euclidean) D3-brane around the “small” divisor yielding f NL ∼ O ( 1 ) . The second is when the slow-roll conditions are violated and for the number of the aforementioned D3-instanton wrappings being of O ( 1 ) but more than one, yielding f NL ∼ O ( 1 ) . Based on general arguments not specific to our (string-theory) set-up, we argue that requiring curvature perturbations not to grow at horizon crossing and at super-horizon scales, automatically picks out hybrid inflationary scenarios which in our set up can yield f NL ∼ O ( 1 ) and tensor–scalar ratio of O ( 10 −2 ) . For all our calculations, the world-sheet instanton contributions to the Kähler potential coming from the non-perturbative α ′ corrections, are restricted to appropriate choices of the degrees of genus-zero rational curves that correspond to very large values of Gopakumar–Vafa invariants for the chosen compact projective variety. To our knowledge, such values of non-Gaussianities and tensor–scalar ratio in slow-roll inflationary and/or slow-roll violating scenarios, have been obtained for the first time from string theory. 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. Our calculations predict, however, loss of scale invariance of the spectral index of curvature perturbations beyond the existing experimental bounds if one requires “freeze-out” of curvature perturbations at horizon crossing and super-horizon scales. The violation of scale invariance is within experimental bounds if the freeze-out is required only at super-horizon scales—in such scenarios, one can get f NL ∼ O ( 1 ) and r ∼ 10 −2 .