2 models give rise to qualitatively similar results. Methodology: Our basic methods will be essentially the same as those described in ref. [7]. The F-term super- potential is given by W = κ ˆ S ( ˆ ¯ G ˆ G − M $^{2}$) where ˆ S is the singlet inflaton superfield and ˆ G , ˆ ¯ G are the waterfall fields responsible for the topological defects [4]. We in- clude the radiative corrections and minimal supergravity corrections, but ignore the curvature and tadpole terms. These terms were shown to have negligible effect in pre- vious work, where we assumed a positive sign for the tad- pole term. For the D-term model we use W = κ ˆ S ˆ ¯ G ˆ . Spontaneous breaking of U(1) is induced by the D-term contribution g $^{2}$( | G | 2 − | ¯ G | 2 + M $^{2}$)$^{2}$/ 8 to the potential. Without supergravity corrections, the predictions for in- flation and strings from the D-term model do not depend on the gauge coupling g . Taking account of minimal su- pergravity corrections, we find that for values of g > ∼ 0 . 1, the spectrum receives an additional blue-tilt, which cor- responds to a less-good fit to the data [7]. When com- pared to small g , the hybrid inflation prediction for n$_{S}$ lies substantially above the central value from the stan- dard 6-parameter fit. In this work, we neglect minimal supergravity corrections, corresponding to a restriction of parameter space to g < ∼ 0 . 1. Therefore in both the F- and D-term cases, the inflation model is specified by two parameters: the dimensionless coupling constant, κ , and the mass scale, M . It is possible to compute the three observable quantities n$_{S}$ , Gµ and the scalar ampli- tude P$_{R}$ from these two parameters, and hence the fit is for 6 parameters (with the baryon density, Ω$_{b}$ h $^{2}$, cold dark matter density Ω$_{c}$ h $^{2}$, acoustic scale, θ$_{A}$ and optical depth, τ , being the other 4). The reheat temperature is fixed to be T$_{R}$ = 10 $^{9}$GeV but allowing this to vary only has a minor effect on our results. We refer to more details on the models to ref. [7], but in the present context, it is useful to recall the basic features distinguishing the F- and D-term models phenomenolog- ically. For κ $^{2}$/g2 < 1 / 2 the string tension for the same value of M is larger in the D-term model than the F- term. Hence, in order to comply with upper bounds on the string contribution to the CMB, D-term models pre- dict a smaller M , which also leads to a close to scale invariant spectrum, n$_{S}$ ≈ 1. We use COSMOMC [20] to perform the analysis. We include data from WMAP5 [9], other CMB exper- iments [10] and the SDSS [11]. In addition we will also include constraints on Ω$_{b}$ h 2 from metal poor damped Lyman- α systems. These have been used to compute the deuterium abundance at z ≈ 2 . 6. One finds that log( D/H ) = − 4 . 55 ± 0 . 03, which implies that Ω$_{b}$ h 2 = 0 . 0213 ± 0 . 0010 [12]. Results: We find that the 4 cosmological parameters are close to the values preferred by the standard 6 param- eter fit. In Fig. 1, we present 2D likelihoods for various parameters of the F- and D-term models for cosmic string spectra A and B. The best-fitting values of M and κ are given in table I. We see that the values are not the same Concentrating on the case of CMB+SDSS+BBN, it is clear that the D-term model using both string spectra is a much worse fit than the 6 parameter model with Δ χ 2 = − 17 . 6 for string spectrum A and -12.2 for B. This shows that the D-term model is severely in tension with for the two string spectra. The central values for model A have changed from those reported in ref. [7] due to the inclusion of the new CMB and the SDSS data, although they remain within ∼ 1 σ . The size of the errorbars have not changed significantly. The results for model B are somewhat different reflecting different ranges of Gµ and n$_{S}$ which are favoured using the different string spec- tra [19]. Of particular importance is that model A re- stricts n$_{S}$ = 0 . 958 ± 0 . 013 in a 7 parameter fit including Gµ as the extra parameter, which is very similar to the 6 parameter case. However, n$_{S}$ = 0 . 970 ± 0 . 016 for model B, which is more compatible with n$_{S}$ = 1. FIG. 1: 2D likelihoods for D -Term (red, smaller values of κ ) and F -term (blue, larger values of κ ) for string model A (left set of two) and B (right set of two) using CMB+SDSS data. One can define the relative likelihood of two models, labelled 1 and 2, by Δ χ 2 = − 2 log( L$_{1}$ / L$_{2}$ ). We will take model 1 to be the standard 6 parameter model using n$_{S}$ and A$_{S}$ to define the initial power spectrum. Pos- itive values of this quantity indicate that model 2 fits the data better than the standard, whereas negative val- ues indicate a less good fit. This quantity was used in ref. [6] to quantify the level to which various variants of the standard cosmological model (for example, those with no reionization, or no dark matter) were poor fits to the data, We present the computed values of Δ χ 2 for the F- and D-term models using the two cosmic string spec- tra in table II. We see that if only CMB data is included there is little to tell between the 6 parameter model and the F/D-term models, although the D-term model using string spectrum A is the least good fit. If one includes more data from SDSS and BBN, typically the fit of the hybrid inflation models become less good. log$_{10}$ [ ] M (10 16  GeV) −4 −3 −2 −1 0 0.2 0.4 0.6 0.8 1 −5 −4 −3 −2 −1 log$_{10}$ [ ] log$_{10}$[ ] n s −5 −4 −3 −2 −1 0.975 0.98 0.985 0.99 0.995 1 1.005 log$_{10}$[ ] −4 −3 −2 −1