TTK-10-01 Tight constraints on F- and D-term hybrid inflation scenarios Richard Battye, 1, ∗ Bj¨ orn Garbrecht, 2, † and Adam Moss 3, ‡ $^{2}$Institut f¨ ur Theoretische Physik, RWTH Aachen, 52056 Aachen, Germany 3 Department of Physics & Astronomy, University of British Columbia, Vancouver, BC, V6T 1Z1 Canada (Dated: November 3, 2018) $^{1}$Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Manchester, M13 9PL UK We use present cosmological data from the cosmic microwave background, large-scale structure and deuterium at high redshifts to constrain supersymmetric F- and D-term hybrid inflation sce- narios including possible contributions to the CMB anisotropies from cosmic strings. Using two different realizations of the cosmic string spectrum, we find that the minimal version of the D-term model is ruled out at high significance. F-term models are also in tension with the data. We also discuss possible non-minimal variants of the models. PACS numbers: 98.80.Cq, 98.80.Jk Introduction: Present observations of the Universe pro- vide strong evidence for a topology which is close to spa- tially flat and a close to scale invariant spectrum of den- sity fluctuations. These are both predications of the sim- plest models of inflation based on the slow-roll approx- imation and hence provide prima-facie evidence for an inflationary epoch in the Early Universe. One of the ba- sic features of inflation is that the potential needs to be very shallow in order to give rise to perturbations with the observed amplitude. This can be difficult to arrange in many particle physics motivated scenarios since it typ- ically requires parametric fine-tuning in the theory or a trans-Planckian field-range for the inflaton. One class of models which naturally circumvents this issue are the Supersymmetric (SUSY) Hybrid Inflation scenarios which have F- and D-term variants [1–3]. In these models the tree level potential is completely flat and the slow-roll is induced by the radiative corrections. There are two key observational features of the minimal version of these scenarios: a spectral index of density fluctuations, n$_{S}$ , which is 0.98–1.0, and cosmic strings are often produced during the phase transition which ends inflation [4], for example, if the broken symmetry is U (1). For typical model parameters the amplitude of cosmic microwave background (CMB) anisotropies from strings will be ∼ 10% of those produced by inflation [5]. This is particularly interesting since the data from the Wilkinson Microwave Anisotropy Probe (WMAP) 3 year release suggested that n$_{S}$ = 0 . 958 ± 0 . 016 which ap- pears to disfavor such models [6]. In subsequent work we pointed out that this discrepancy could be ameliorated by the inclusion of a component of the CMB anisotropies from cosmic strings [7]. In particular, we found that the minimal version of the F- and D-term scenarios, which have 6 free parameters, fitted the data as well as or better In this letter we will revisit the constraints on the SUSY hybrid inflation models focusing on the minimal F- and D-term variants and on those that are extended by a possible additional mass-square term for the infla- ton [13–16]. We will take into account the cosmic string component using two possible models. In model A we use the unconnected segment model [17] (USM) to pro- duce the string spectrum using an evolution model for the correlation length, rms string velocity and string wiggli- ness. This spectrum was used in our previous work [7] and also in refs. [18]. We also include results based on another spectrum created using the USM, which we will call model B. This spectrum, with different parameters from model A, was designed to match the results of the Abelian-Higgs simulations reported in ref. [8] (see ref. [19] for a discussion). It is our opinion that model A is likely to be closest to the true cosmic string spectrum, but the two spectra span the different possibilities reported in the literature. We note that since the cosmic string spectrum will be ∼ 10% of the total, the level of accuracy required is much less than for the adiabatic spectrum, and the two Since then cosmological data has moved on. WMAP have released their 5 year data [9], other CMB data on smaller angular scales has been published [10], the SDSS has been used to compute the matter power spec- trum [11] and tight constraints have been derived on the baryon density, quantified by the value relative to the critical density, Ω$_{b}$, using Big Bang Nucleosynthe- sis (BBN) from measurements of deuterium at high red- shift [12]. The last two of these are particularly interest- ing in this context since we found in our earlier analysis that models which fitted the data due to the inclusion a string component with n$_{S}$ ≈ 1 typically have values of h = H$_{0}$/ 100 km sec − $^{1}$Mpc − 1 and Ω$_{b}$ h 2 which are larger than the standard values [7]. than the standard 6 parameter fit. Similar results, based on a different cosmic string spectrum, were reported by Bevis et al , although they did not specifically refer to the SUSY hybrid inflation models, rather they investigated a 6 parameter model with the string tension, Gµ , allowed to vary and n$_{S}$ = 1 fixed [8]. arXiv:1001.0769v1 [astro-ph.CO] 5 Jan 2010 $^{∗}$Electronic address: rbattye@jb.man.ac.uk $^{†}$Electronic address: garbrecht@physik.rwth-aachen.de $^{‡}$Electronic address: adammoss@phas.ubc.ca