Microwave background anisotropies and large scale structure constraints on isocurvature modes in a two-field model of inflation

In this paper we study the isocurvature mode contribution to the cosmic microwave background anisotropies and the large scale structure power spectrum, for a two-field model of inflation proposed by Linde and Mukhanov. We provide constraints on the parameters of the model by comparing its predictions with observations of the microwave background anisotropies, large scale structure data on the galaxy power spectrum, and the number density of nearby galaxy clusters. We find that such models are consistent with observations for a narrow range of parameters. As our main result, we find that only a very small isocurvature component is allowed, $\al \le 0.06$, for any underlying Friedmann model. Furthermore, we give the expected resolution with which the model parameters will be determined from future satellite missions like MAP and Planck, for a fiducial flat $\Lambda$CDM model. We find that Planck mission will be able to detect such small contributions, especially if polarization information is included. The isocurvature spectral index $\niso$ will also be determined with better than 8% precision.