Higgs-otic inflation and string theory

Luis E. Ibanez 0 1 2 3 Fernando Marchesano 0 1 2 Irene Valenzuela 0 1 2 3 0 Open Access , c The Authors 1 Cantoblanco , 28049 Madrid , Spain 2 Instituto de F sica Te orica UAM/CSIC, Universidad Aut onoma de Madrid 3 Departamento de F sica Te orica UAM, Universidad Aut onoma de Madrid extension of the SM, in a chaotic-like inflation setting. The SUSY breaking soft term masses are of order 1012 1013 GeV, which is identified with the inflaton mass scale and is just enough to stabilise the SM Higgs potential. The fine-tuned SM Higgs has then a mass around 126 GeV, in agreement with LHC results. We point out that the required large field excursions of chaotic inflation may be realised in string theory with the (complex) inflaton/Higgs identified with a continuous Wilson line or D-brane position. SM gauge group and MSSM Higgs sector. In this case the inflaton/Higgs fields correspond to D7-brane positions along a two-torus transverse to them. Masses and monodromy are induced by closed string G3 fluxes, and the inflaton potential can be computed directly from the DBI+CS action. We show how this action sums over Planck suppressed corrections, which amount to a field dependent rescaling of the inflaton fields, leading to a linear potential in the large field regime. We study the evolution of the two components of the Higgs/inflaton and compute the slow-roll parameters for purely adiabatic perturbations. For large regions of initial conditions slow roll inflation occurs and 50-60 efolds are obtained with r > 0.07, testable in forthcoming experiments. Our scheme is economical in the sense that both EWSB and inflation originate in the same sector of the theory, all inflaton couplings are known and reheating occurs efficiently. ArXiv ePrint: 1411.5380 1 Introduction The Higgs mass and high scale SUSY-breaking Large field inflation, string theory and the Higgs String theory embeddings of an inflaton-Higgs The MSSM Higgs system in heterotic orbifolds The MSSM Higgs system in type IIB orientifolds Fluxes and the Higgs/inflaton potential 7 Inflaton potential corrections, backreaction and moduli fixing Planck mass suppressed corrections Backreaction and induced RR-tadpoles Decoupling of moduli fixing from inflation sector Some further cosmological issues Final comments and conclusions A The DBI+CS computation Flux induced scalar potential from DBI+CS Kaloper-Sorbo Lagrangian Estimation of the scales of the model The Higgs/inflaton scalar potential N = 1 supergravity description Slow roll equations of motion Single field limit cases The general 2-field Higgs/inflaton case Results for small field Results for large field Computing slow roll parameters for large inflaton The discovery [1, 2] at LHC of a scalar particle with the properties of the Standard Model (SM) Higgs boson has completed the minimum set of particles required for a consistent understanding of the properties of the SM. Still, it has also triggered new questions and made more evident the existence of a hierarchy problem of the fundamental scales of physics. One of the issues raised is the stability of the Higgs potential [35]. The Higgs mass, around Although such a metastable vacuum may not be necessarily problematic, it may lead to some difficulties in the cosmological evolution of the universe. One elegant way to avoid any vacuum instability is to consider a SUSY extension of the SM like the MSSM. The scalar potential is then always positive definite in the ultraviolet and no instabilities appear. In fact the usual MSSM with low scale SUSY breaking soft one could say that a Higgs mass around 126 GeV could be good news for SUSY. However this value is a bit high, and implies squarks and gluino masses into the multi-TeV region, the SUSY parameters is required. Although this is consistent with the fact that no trace of SUSY particles has been observed as yet at LHC, this high level of fine-tuning casts some doubts on the presence of SUSY at low scales ' 1 TeV. The theoretical motivations for supersymmetry go beyond the solution of the hierarchy problem in terms of low-energy SUSY. Admitting the possible presence of Higgs mass finetuning, one can consider leaving the scale of soft masses MSS as a free parameter and ask for consistency with the measured Higgs mass [69] (see also [1013]). It was remarked in SM Higgs survives below that scale, then necessarily one obtains mh ' 126 GeV, consistent with LHC data. This is true if one assumes a unification boundary condition for the two as a hint for large scale SUSY breaking in a unification scheme. It is natural to discuss a possible fine-tuning of a light SM Higgs in the context of the string landscape. In the latter an enormous set of string solutions allow for some of them which are selected on anthropic grounds, allowing for a sufficiently light SM Higgs. On the other hand SUSY is a fundament symmetry of string theory and guarantees the absence of tachyons in string compactifications. Since string theory is at present our only complete candidate as a unified theory, one could consider a scenario in which SUSY could be still present at a higher scale but not be relevant for the understanding of the hierarchy problem. In a different direction, evidence is mounting in favour of the existence of a second fundamental scalar in the theory, the inflaton. Simple models of inflation are able to reproduce more and more qualitative and quantitative cosmological data (for reviews in the context of string theory see e.g. [1418]). The description of the CMB anisotropies in terms of primordial perturbations induced by an inflaton is outstanding. One of the simplest inflation models is chaotic inflation [19], which features a simple polynomial potential in which the slow roll regime is achieved due to trans-Planckian excursions of the inflaton. An interesting property of these models is that they generically predict large tensor perturbations at a level detectable in future measurements. If the BICEP2 hints [20] for large tensor perturbations were confirmed, chaotic inflation would be a favoured class of models. On the theoretical side, the requirement of trans-Planckian inflaton excursions requires good control of Planck scale physics, i.e., a theory of quantum gravity like string theory. In fact in the last decade a framework to embed large trans-Planckian excursions into string theory has been worked out in terms of the so-called monodromy inflation [21, 22], see [17, 18] for reviews and further references. Given these two inputs, an obvious question has been around for some time: Can the Higgs boson be identified with the inflaton?. Before we knew the value of the Higgs boson mass this possibility looked unlikely, since the Higgs potential is quartic with no obvious region which could lead to slow roll inflation (see e.g. [23] for a review). However, as we at a scale 1011 Planck scale Mp. It has been proposed that this could be the signal of some new conformally invarian (...truncated)