solution for small κ is essen tially the same as t he min- imal case. Here, M is hig her and a non-zero c 2 H = 0 does not effect the inflation d ynamics. We find lo g$_{10}$ κ = − 4 . 45 ± 0 . 22 and M = (0 . 20 3 ± 0 . 032) × 10 $^{16}$G eV, with Δ χ 2 = − 8 . 6. The other solution has a lo wer value of M , an d a non- zero c 2 H flattens the potential near horizon exit. One gets sufficient e-foldings when the inflaton is placed close to the top of the potential and the resulting n$_{S}$ is redder, with the same slightly impr oved Δ χ 2 = 1 . 2 a s in the F-term model. For this branc h larger values of κ are al- Acknowledgments: This research was supported by the Natural Sciences and Engineering Research Council of Canada and the British Columbia Knowledge Develop- ment Fund. We thank Douglas Scott for useful discus- sions. Con clusions: Minimal models of hybrid inflation rely only o n two parameters ( κ and M ), and they do not suf- fer fro m the potential problem of trans-Planckian values of the inflaton field. Therefore they are predictive and it is poss ible to derive parametric constraints from cosmo- logical data. In Refs. [7, 8], it has been found that a close to sca le invariant spectrum of adiabatic perturbations is in agr eement with CMB data, when a sizable string com- ponen t is present. In particular, minimal models of hy- brid inflation which predict these features appeared to be via ble in that light, a finding that may open inter- esting directions in model building [16]. Using recent CMB data, SDSS and measurements of the deuterium abundance leads us to a revison of this picture: Mini- mal D-term models are ruled out at a level that can be estimated to be ≈ 4 σ (the same is true for the HZ spec- trum) and the tension between minimal F-term models and the data is increasing. Non-minimal scenarios in- clude the negative mass-square term models discussed here and also the possibility of adding a negative-sign tadpole term [21]. This way, one can entirely remove tension with the data, but at the same time, also the very distinct predictions of minimal hybrid inflation for the range of the spectral index are lost. lowed, since the lower M leads to a smaller string tension. We fin d log$_{10}$ κ = − 3 . 78 ± 0 . 44, M = (0 . 116 ± 0 . 071) × 10 $^{16}$G eV and − log$_{10}$ ( 10 $^{18}$c2 $_{H}$/ GeV $^{2}$) = 1 . 63 ± 1 . 50. We note t hat the upper bound on κ is related to the upper bound on Gµ . 4 FIG. 2: 2D likelihoods for non -minimal F- (top set of two) and D-term (bottom set of two ) for string model A . In the D-term case the two sets of con tours show the two solutions admitted by the potential, as ex plained in the text. [1] A. D. Linde, Phys. Rev. D 49 (1994) 748. E. J. C opeland, A. R. Liddle, D. H. Lyth, E. D. Stewart and D. Wands, Phys. Rev. D 49 (1994) 6 4 10. [2] G. R. Dvali, Q. Shafi and R. K. Schaefer, Ph ys. Rev. Lett. 73 (1994) 1886. [3] P. Binetruy and G. R. Dva li, Phys. Lett. B 3 8 (1996) 241. E. Halyo, Phys. Lett. B 387 (1996) 43. [4] R. Jeannerot, J. Rocher and M. Sakellariadou, P hys. Rev. D 68 , 103514 (2003) [5] R. Jeannerot, Phys. Rev. D 56 (1997) 6205. C. Con- taldi, M. Hindmarsh and J . Magueijo, Phys. R ev. Lett. 82 (1999) 679. R. A. Batty e and J. Weller, Phys . Rev. D 61 (2000) 043501. [6] D. N. Spergel et al. , ApJS 170 (2007) 377. [7] R. A. Battye, B. Garbrecht and A. Moss, JCAP 0 9 (2006) 007. [8] N. Bevis, M. Hindmarsh, M. Kunz and J. U rrestilla, Phys. Rev. Lett. 100 (200 8) 021301. [9] E. Komatsu et al. , ApJS 1 80 (2009) 330. [10] R. Reichardt et al. , ApJ 69 4 (2009) 1200. W. .C. Jones et al. , ApJ 647 (2006) 823. J. S ievers et al. , arXiv:0 901.4540. C. Pryke et al. , ApJ 692 (2009) 1247. [11] M. Tegmark et al , Phys. Rev. D 74 (2006) 123507. [12] M. Pettini et al , arXiv:0805.0594. [13] M. Bastero-Gil, S. F. King and Q. Shafi, Phys. Lett. B 651 (2007) 345. [14] L. Boubekeur and D. H. Lyth, JCAP 0507 (2005) 010. [15] C. M. Lin and J. McDonald, Phys. Rev. D 74 (2006) 063510. [16] M. Haack, R. Kallosh, A. Krause, A. Linde, D. Lust and M. Zagermann, Nucl. Phys. B 806 (2009) 103. [17] A. Albrecht, R. A. Battye and J. Robinson, Phys. Rev. Lett. 79 (1997) 4736. Phys. Rev. D 59 (1999) 023508. L. Pogosian and T. Vachaspati, Phys. Rev. D 60 (1999) 083504. [18] M. Wyman, L. Pogosian and I. Wasserman, Phys. Rev. D 72 (2005) 023513; Erratum-ibid. D 73 (2006) 089905. [19] R. A. Battye and A. Moss, to appear. [20] A. Lewis and S. Bridle, Phys. Rev. D 66 (2002) 103511. [21] M. U. Rehman, Q. Shafi and J. R. Wickman, arXiv:0908.3896 [hep-ph]. n$_{s}$ C H 2 −0.06 −0.04 −0.02 0 0.02 log$_{10}$ [ ] n$_{s}$ − log 10 [10 18  C H 2 /GeV 2 ] 0.92 0.94 0.96 0.98 1 −2 0 2 4 log$_{10}$[ ] −4 −3 −2 −1