By implementing a genetic algorithm we search for stable vacua in Type IIB nongeometric flux compactification on an isotropic torus with orientifold 3-planes. We find that the number of stable dS and AdS vacua are of the same order. Moreover we find that in all dS vacua the multi-field slow-roll inflationary conditions are fulfilled. Specifically we observe that inflation is driven by the axio-dilaton and the Kähler moduli. We also comment on the existence of one stable dS vacuum in the presence of exotic orientifolds. 1 cesaredas@fisica.ugto.mx 2 luisreydb@fisica.ugto.mx 3 oloaiza@fisica.ugto.mx 4 msabido@fisica.ugto.mx 1 arXiv:1302.0529v3 [hep-th] 10 Nov 2013Recently, there has been a huge interest in the search for classical de Sitter (dS) vacua within the context of superstring compactification. In the last few years, some constraints have been imposed by estimating the contributions to the effective scalar potential from each of the components that play a role in the compactification process. For instance, there is a no-go theorem, indicating that the existence of dS vacua in compactifications threaded with standard NS-NS and R-R fluxes is incompatible with inflation[1]. Recently, in the context of these standar type IIB compactifications, it has been shown the existence of classical dS vacua in specific and suitable D-brane configurations with orientifold planes [2][3][4]. On the other hand, further studies show that by considering a bigger set of allowed fluxes and more general structures for the internal geometry, it is possible to find some stable dS vacua [5][6][7][8][9][10][11][12][13][14][15][16][17][18] although their compatibility with inflation has not been studied in detail. In this work we present some stable dS vacua consistent with inflation.There are some essential ingredients string compactifications should contain to enhance the chances of finding stable dS vacua: a negative curved internal manifold and a small number of moduli fields [19][20][21].Here, we take the approach consisting in computing the scalar potential from a superpotential with all the above features. Specifically, a compactification on a negatively curved manifold with a superpotential W that depends at tree level on a small set of moduli is achieved by considering a type II string compactification on a six-dimensional isotropic torus in the presence of non-geometric fluxes [22][23][24][25]. (2.12) where J = (j±, k) and M = (m±). The Bianchi identity Q · H 3 = 0 decomposes as A M J · A M J = (A M J ) δ (A M J ) λ η δλ = 0, (2.13) for j = j , diag(η) = {−1, 1, 1, 1} and for the combinations M = (0+), J = {(2, 0+), (1, 3−)} and M = (3−), J = {(1, 2−), (2, 1+)}, while Q · Q = 0 decomposes as,
It is commonly believed that a successful period of inflation driven by a single or several scalar fields requires a specific hierarchy of masses given by M inf H M heavy , where M inf can correspond to several or a single light field and M heavy corresponds to any heavy field that might be integrated out if it satisfies suitable conditions. This is at the heart of the so called η-problem in inflation, since large contributions to the masses of the inflatons might spoil the slow-roll conditions required for inflation. We show that, while this is an unavoidable conclusion in single field inflation, in multifield inflation, heavy fields as defined above, may be fully responsible for a successful period of what we call fat slow-roll inflation. Moreover we show that in this scenario, the turning rate of the inflationary trajectory, Ω/H, is larger than one. Thus, the η-problem is evaded with large turns in fat inflation. Depending on the perturbations' mass spectra, cosmological predictions will differ either slightly or largely with respect to those of the single field case. We illustrate this scenario in a concrete example in Type IIB string flux compactifications, where a probe D5-brane moving along the angular and radial directions in a warped throat drives fat D5-brane natural inflation. An instantaneous superplanckian decay constant can be defined, consistent with our low energy approximations, thanks to the strong warping of the geometry. We compute the cosmological observables, which differ from the single field case. We also discuss fat inflation in the context of recently proposed swampland de Sitter conjectures.
Abstract:We study the moduli space of type IIB string theory flux compactifications on the mirror of the CY quintic 3-fold in P 4 . We focus on the dynamics of the four dimensional moduli space, defined by the axio-dilaton τ and the complex structure modulus z. The z-plane has critical points, the conifold, the orbifold and the large complex structure with non trivial monodromies. We find the solutions to the Picard-Fuchs equations obeyed by the periods of the CY in the full z-plane as a series expansion in z around the critical points to arbitrary order. This allows us to discard fake vacua, which appear as a result of keeping only the leading order term in the series expansions. Due to monodromies vacua are located at a given sheet in the z-plane. A dS vacuum appears for a set of fluxes. We revisit vacua with hierarchies among the 4D and 6D physical scales close to the conifold point and compare them with those found at leading order in [1,2]. We explore slow-roll inflationary directions of the scalar potential by looking at regions where the multi-field slow-roll parameters and η are smaller than one. The value of depends strongly on the approximation of the periods and to achieve a stable value, several orders in the expansion are needed. We do not find realizations of single field axion monodromy inflation. Instead, we find that inflationary regions appear along linear combinations of the four real field directions and for certain configurations of fluxes.
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