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74 References# Landscape, the Scale of SUSY Breaking, and Inflation

**Abstract**

We argue that in the simplest version of the KKLT model, the maximal value of the Hubble constant during inflation cannot exceed the present value of the gravitino mass, H< m_{3/2}. This may have important implications for string cosmology and for the scale of the SUSY breaking in this model. If one wants to have inflation on high energy scale, one must develop phenomenological models with an extremely large gravitino mass. On the other hand, if one insists that the gravitino mass should be O(1 TeV), one will need to develop models with a very low scale of inflation. We show, however, that one can avoid these restrictions in a more general class of KKLT models based on the racetrack superpotential with more than one exponent. In this case one can combine a small gravitino mass and low scale of SUSY breaking with the high energy scale of inflation. Comment: 7 pages, 4 figs, revtex, typos corrected

- CitationsCitations212
- ReferencesReferences74

- "On the one hand, the inflationary energy can destabilize the moduli. This was anticipated in [4], where it was shown that stabilizing the Kähler modulus in the simplest model of inflation leads to a bound H < m3 /2 on the inflationary Hubble scale H, related to the gravitino mass m3 /2 in the vacuum after inflation 1 . Conversely, the dynamics of the volume modulus may induce a backreaction which renders the inflaton scalar potential too steep to support inflation. "

[Show abstract] [Hide abstract]**ABSTRACT:**We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $\alpha$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $\alpha$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of e-folds due to the interplay with moduli.- "For our purposes it suffices to leave the precise mechanism of moduli stabilization unspecified, and instead assume the existence of a superpotential piece W mod (ρ i ) ⊂ W which satisfies D ρ i W mod = 0 for all relevant moduli fields ρ i . Examples are known in the literature, they include the racetrack setup of [39] and a less fine-tuned mechanism using an additional stabilizer field [40]. 2 In many string-effective inflation models the inflaton and the moduli interact even if the moduli are much heavier than the dynamical scale of inflation. Through supergravity couplings this even happens in models where the superpotential separates, "

[Show abstract] [Hide abstract]**ABSTRACT:**We study possible string theory compactifications which, in the low-energy limit, describe chaotic inflation with a stabilizer field. We first analyze type IIA setups where the inflationary potential arises from a D6-brane wrapping an internal three-cycle, and where the stabilizer field is either an open-string or bulk K\"ahler modulus. We find that after integrating out the relevant closed-string moduli consistently, tachyonic directions arise during inflation which cannot be lifted. This is ultimately due to the shift symmetries of the type IIA K\"ahler potential at large compactification volume. This motivates us to search for stabilizer candidates in the complex structure sector of type IIB orientifolds, since these fields couple to D7-brane Wilson lines and their shift symmetries are generically broken away from the large complex structure limit. However, we find that in these setups the challenge is to obtain the necessary hierarchy between the inflationary and Kaluza-Klein scales.- "Any discussion of dark matter must also include the discussion of the SUSY breaking sector of the theory. In particular, SUSY breaking must necessarily be decoupled from the inflationary sector such that the gravitino mass is less than the Hubble parameter during inflation, i.e. m 3/2 < H inf (see Refs. [22, 23, 24, 25]). In addition, the cosmological moduli [26, 27, 28, 29] and gravitino problems [30, 31, 32] must be ameliorated. "

[Show abstract] [Hide abstract]**ABSTRACT:**In this paper we present a model of subcritical hybrid inflation with a Pati-Salam [PS] symmetry group. Both the inflaton and waterfall fields contribute to the necessary e-foldings of inflation, while only the waterfall field spontaneously breaks PS hence monopoles produced during inflation are diluted during the inflationary epoch. The model is able to produce a tensor-to-scalar ratio, $r < 0.09$ consistent with the latest BICEP2/Keck and Planck data, as well as scalar density perturbations and spectral index, $n_s$, consistent with Planck data. For particular values of the parameters, we find $r = 0.084$ and $n_s = 0.0963$. The energy density during inflation is directly related to the PS breaking scale, $v_{PS}$. The model also incorporates a $\mathbb{Z}_4^R$ symmetry which can resolve the $\mu$ problem and suppress dimension 5 operators for proton decay, leaving over an exact $R$-parity. Finally the model allows for a complete three family extension with a $D_4$ family symmetry which reproduces low energy precision electroweak and LHC data.

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