Testing for double inflation with WMAP

With the WMAP data we can now begin to test realistic models of inflation involving multiple scalar fields. These naturally lead to correlated adiabatic and isocurvature (entropy) perturbations with a running spectral index. We present the first full ($9$ parameter) likelihood analysis of double inflation with WMAP data and find that despite the extra freedom, supersymmetric hybrid potentials are strongly constrained with less than $7\%$ correlated isocurvature component allowed when standard priors are imposed on the cosomological parameters. As a result we also find that Akaike and Bayesian model selection criteria rather strongly prefer single-field inflation, just as equivalent analysis prefers a cosmological constant over dynamical dark energy in the late universe. It appears that simplicity is the best guide to our universe.

Figure 1

Two-dimensional likelihood constraints for the double inflationary parameters for the potential (7). We show $1\sigma$ and $2\sigma$ contour bounds from ${\overline{\chi }}^2$ data (shaded contours) and the contours which contain $68\%$ and $95\%$ of all the points in our MC chains (solid lines, see discussion in the text).

Figure 2

Two-dimensional likelihood constraints for the initial conditions of the field, $\{{\varphi }_{\mathrm{in}}/{\varphi }_c,{\chi }_{\mathrm{in}}/{\chi }_0\}$.

Figure 3

Marginalized 1D likelihood of the number of $e$ folds occurring during the 2nd phase of inflation. The solid line is based on the number of MCMC points, while the dotted line weighs each point based on its ${\overline{\chi }}^2$ value, as described in the caption to Fig. 1.

Figure 4

Two-dimensional likelihood contours for the amplitudes of the power spectra, with adiabatic against isocurvature (left) and adiabatic against correlated (right). Despite the freedom in allowing running of the spectra index the isocurvature component is severely constrained.

Figure 5

The CMB angular power spectra for five different cases: (i) our best-fit double-inflation model, (ii) isocurvature dominating over the adiabatic, (iii) the isocurvature is comparable to the adiabatic (mixed), (iv) the best-fit single-field model with potential (12) and (v) a model with blue-tilted spectrum ($n_s>1$) on large scales. The spectra are significantly different from the standard one when the isocurvature is dominant.

Figure 6

Two-dimensional likelihood contours for the spectral index $n_s$ and the number of $e$ folds during the second stage of inflation $N_{2\mathrm{nd}}$.