Volume modulus inflection point inflation and the gravitino mass problem

Several models of inflection point inflation with the volume modulus as the inflaton are investigated. Non-perturbative superpotentials containing two gaugino condensation terms or one such term with threshold corrections are considered. It is shown that the gravitino mass may be much smaller than the Hubble scale during inflation if at least one of the non-perturbative terms has a positive exponent. Higher order corrections to the Kahler potential have to be taken into account in such models. Those corrections are used to stabilize the potential in the axion direction in the vicinity of the inflection point. Models with only negative exponents require uplifting and in consequence have the supersymmetry breaking scale higher than the inflation scale. Fine-tuning of parameters and initial conditions is analyzed in some detail for both types of models. It is found that fine-tuning of parameters in models with heavy gravitino is much stronger than in models with light gravitino. It is shown that recently proposed time dependent potentials can provide a solution to the problem of the initial conditions only in models with heavy gravitino. Such potentials can not be used to relax fine tuning of parameters in any model because this would lead to values of the spectral index well outside the experimental bounds.Comment: 27 pages, 9 figures, comments and references added, version to be publishe

Inflation, moduli (de)stabilization and supersymmetry breaking

We study the cosmological inflation from the viewpoint of the moduli stabilization. We study the scenario that the superpotential has a large value during the inflation era enough to stabilize moduli, but it is small in the true vacuum. This scenario is discussed by using a simple model, one type of hybrid models.Comment: 17 pages, 7 figure

Supergravity Higgs Inflation and Shift Symmetry in Electroweak Theory

We present a model of inflation in a supergravity framework in the Einstein frame where the Higgs field of the next to minimal supersymmetric standard model (NMSSM) plays the role of the inflaton. Previous attempts which assumed non-minimal coupling to gravity failed due to a tachyonic instability of the singlet field during inflation. A canonical K\"{a}hler potential with \textit{minimal coupling} to gravity can resolve the tachyonic instability but runs into the $\eta$-problem. We suggest a model which is free of the $\eta$-problem due to an additional coupling in the K\"{a}hler potential which is allowed by the Standard Model gauge group. This induces directions in the potential which we call K-flat. For a certain value of the new coupling in the (N)MSSM, the K\"{a}hler potential is special, because it can be associated with a certain shift symmetry for the Higgs doublets, a generalization of the shift symmetry for singlets in earlier models. We find that K-flat direction has $H_u^0=-H_d^{0*}.$ This shift symmetry is broken by interactions coming from the superpotential and gauge fields. This direction fails to produce successful inflation in the MSSM but produces a viable model in the NMSSM. The model is specifically interesting in the Peccei-Quinn (PQ) limit of the NMSSM. In this limit the model can be confirmed or ruled-out not just by cosmic microwave background observations but also by axion searches.Comment: matches the published version at JCA

Inflation with racetrack superpotential and matter field

Several models of inflation with the racetrack superpotential for the volume modulus coupled to a matter field are investigated. In particular, it is shown that two classes of racetrack inflation models, saddle point and inflection point ones, can be constructed in a fully supersymmetric framework with the matter field F-term as a source of supersymmetry breaking and uplifting. Two models of F-term supersymmetry breaking are considered: the Polonyi model and the quantum corrected O'Raifeartaigh model. In the former case, both classes of racetrack inflation models differ significantly from the corresponding models with non-supersymmetric uplifting. The main difference is a quite strong dominance of the inflaton by the matter field. In addition, fine-tuning of the parameters is relaxed as compared to the original racetrack models. In the case of the racetrack inflation models coupled to the O'Raifeartaigh model, the matter field is approximately decoupled from the inflationary dynamics. In all of the above models the gravitino mass is larger than the Hubble scale during inflation. The possibility of having the gravitino much lighter than the Hubble scale is also investigated. It is very hard to construct models with light gravitino in which the volume modulus dominates inflation. On the other hand, models in which the inflationary dynamics is dominated by the matter field are relatively simple and seem to be more natural.Comment: 40 pages, 13 figures, references added, typos corrected, version to be publishe

Volume modulus inflation and a low scale of SUSY breaking

The relation between the Hubble constant and the scale of supersymmetry breaking is investigated in models of inflation dominated by a string modulus. Usually in this kind of models the gravitino mass is of the same order of magnitude as the Hubble constant which is not desirable from the phenomenological point of view. It is shown that slow-roll saddle point inflation may be compatible with a low scale of supersymmetry breaking only if some corrections to the lowest order Kahler potential are taken into account. However, choosing an appropriate Kahler potential is not enough. There are also conditions for the superpotential, and e.g. the popular racetrack superpotential turns out to be not suitable. A model is proposed in which slow-roll inflation and a light gravitino are compatible. It is based on a superpotential with a triple gaugino condensation and the Kahler potential with the leading string corrections. The problem of fine tuning and experimental constraints are discussed for that model.Comment: 28 pages, 8 figures, comments and references added, minor change in notation, version to be publishe

Inflation on an Open Racetrack

We present a variant of warped D-brane inflation by incorporating multiple sets of holomorphically-embedded D7-branes involved in moduli stabilization with extent into a warped throat. The resultant D3-brane motion depends on the D7-brane configuration and the relative position of the D3-brane in these backgrounds. The non-perturbative moduli stabilization superpotential takes the racetrack form, but the additional D3-brane open string moduli dependence provides more flexibilities in model building. For concreteness, we consider D3-brane motion in the warped deformed conifold with the presence of multiple D7-branes, and derive the scalar potential valid for the entire throat. By explicit tuning of the microphysical parameters, we obtain inflationary trajectories near an inflection point for various D7-brane configurations. Moreover, the open racetrack potential admits approximate Minkowski vacua before uplifting. We demonstrate with a concrete D-brane inflation model where the Hubble scale during inflation can exceed the gravitino mass. Finally, the multiple sets of D7-branes present in this open racetrack setup also provides a mechanism to stabilize the D3-brane to metastable vacua in the intermediate region of the warped throat.Comment: 29 pages, 15 figures, pre-print number and references adde

Yukawa unification in SO(10) with light sparticle spectrum

We investigate supersymmetric SO(10) GUT model with \mu<0. The requirements of top-bottom-tau Yukawa unification, correct radiative electroweak symmetry breaking and agreement with the present experimental data may be met when the soft masses of scalars and gauginos are non-universal. We show how appropriate non-universalities can easily be obtained in the SO(10) GUT broken to the Standard Model. We discuss how values of BR(b-->s \gamma) and (g-2)_\mu simultaneously in a good agreement with the experimental data can be achieved in SO(10) model with \mu<0. In the region of the parameter space preferred by our analysis there are two main mechanisms leading to the LSP relic abundance consistent with the WMAP results. One is the co-annihilation with the stau and the second is the resonant annihilation via exchange of the Z boson or the light Higgs scalar. A very interesting feature of SO(10) models with negative \mu is that they predict relatively light sparticle spectra. Even the heaviest superpartners may easily have masses below 1.5 TeV in contrast to multi-TeV particles typical for models with positive \mu.Comment: 23 pages, 5 figure

Constraining compressed supersymmetry using leptonic signatures

We study the impact of the multi-lepton searches at the LHC on supersymmetric models with compressed mass spectra. For such models the acceptances of the usual search strategies are significantly reduced due to requirement of large effective mass and missing E_T. On the other hand, lepton searches do have much lower thresholds for missing E_T and p_T of the final state objects. Therefore, if a model with a compressed mass spectrum allows for multi-lepton final states, one could derive constraints using multi-lepton searches. For a class of simplified models we study the exclusion limits using ATLAS multi-lepton search analyses for the final states containing 2-4 electrons or muons with a total integrated luminosity of 1-2/fb at \sqrt{s}=7 TeV. We also modify those analyses by imposing additional cuts, so that their sensitivity to compressed supersymmetric models increase. Using the original and modified analyses, we show that the exclusion limits can be competitive with jet plus missing E_T searches, providing exclusion limits up to gluino masses of 1 TeV. We also analyse the efficiencies for several classes of events coming from different intermediate state particles. This allows us to assess exclusion limits in similar class of models with different cross sections and branching ratios without requiring a Monte Carlo simulation.Comment: 18 pages, 5 figure

Accidental Inflation in the Landscape

We study some aspects of fine tuning in inflationary scenarios within string theory flux compactifications and, in particular, in models of accidental inflation. We investigate the possibility that the apparent fine-tuning of the low energy parameters of the theory needed to have inflation can be generically obtained by scanning the values of the fluxes over the landscape. Furthermore, we find that the existence of a landscape of eternal inflation in this model provides us with a natural theory of initial conditions for the inflationary period in our vacuum. We demonstrate how these two effects work in a small corner of the landscape associated with the complex structure of the Calabi-Yau manifold P^4_[1,1,1,6,9] by numerically investigating the flux vacua of a reduced moduli space. This allows us to obtain the distribution of observable parameters for inflation in this mini-landscape directly from the fluxes.Comment: 40 pages, 11 figure