Constraints on inflation from cosmic microwave background and Lyman-α forest

We constrain the spectrum of primordial curvature perturbations by using recent cosmic microwave background (CMB) and large scale structure data. Specifically, we consider CMB data from the COBE, Boomerang and MAXIMA experiments, the real space galaxy power spectrum from the IRAS point source catalogue redshifts survey, and the linear matter power spectrum inferred from Lyman-α forest spectra, where we for simplicity assume the absence of appreciable covariances. We study the case of single field slow roll inflationary models, and we extract bounds on the scalar spectral index, n, the tensor to scalar ratio, r, and the running of the scalar spectral index, ∂ln k, for various combinations of the observational data. We find that CMB data, when combined with data from Ly-α forest, place strong constraints on the inflationary parameters. Specifically, we obtain n≈0.9, r≲0.3 and ∂ln k≈0, indicating that big n, big r models (often referred to as hybrid models) are ruled out.