# Multi-field inflation, non-Gaussianity, Planck and a new paper

Earlier this year, the first, long awaited, analysis of cosmological data from the Planck satellite was released. In a series of papers, the Planck team told us the outcome of the years the satellite spent observing the cosmic microwave background (CMB). In particular, they greatly improved constraints on the statistical properties of primordial perturbations. These perturbations imprint themselves on the CMB as temperature fluctuations. To those of us who study inflation, which is thought to produce these perturbations, and who research methods to better predict the statistics a given model of inflation gives rise to, it was a disappointment to learn that there was no detection confirming the statistics are non-Gaussian. Instead the bounds on how much the three-point correlation function, the first non-Gaussian statistic, can vary from zero were considerably tightened. This is summarized by the constraints on the $f_{\rm nl}$ parameter which parametrises the amplitude of the three-point function: $f_{\rm nl} = 2.3 \pm 5.8$. We see that $f_{\rm nl}$ is consistent with zero.

The simplest models of inflation — one field with standard kinetic energy and a smooth potential — predict $f_{\rm nl} \ll 1$, while models with more than one field can produce a much larger $f_{\rm nl}$ that would have been detected by Planck. It has been argued, therefore,  that the Planck results for $f_{\rm nl}$, in combination with results on other parameters, support single field models. In a new paper, myself and collaborators Joe Elliston and Reza Tavakol argue something slightly different: the results tell us that there is no pressure to consider multi-field models, but that such models are still consistent for large regions of their feasible initial condition and parameter spaces. Moreover, there are other reasons that might lead us to consider multi-field models rather than single field ones, such as asking where in fundamental physics the inflaton field comes from, and whether it is likely that just one field contribute to inflation in that context.

I think that most researchers who work on inflation would agree with our point that multi-field inflation is far from ruled out, and wouldn’t need our paper to convince them. Yet it seems that researchers working in other areas, even cosmologists, have taken the data to prefer single field models. So our paper serves to counter that impression. To make it more useful for the experts, however, as well as making this point the paper studies exactly what the constraints are on certain multi-field models in more generality than has been done previously. The Planck team has done an amazing job and for particular models the data implies some interesting necessary conditions for them to be consistent.

After Planck, studies of inflationary non-Gaussainity have entered a new era. In the past researchers often proposed models which gave rise to a large non-Gaussianity ($f_{\rm nl} >10$) in part because the best data before Planck had a small hint that this might be the case, and in part because this showed us that behaviour different from single field behaviour was possible and detectable. However, now and in the near future the goal will be to ensure that models of inflation actively being developed or studied are consistent with the new constraints. This will still require the development of novel techniques for the most complex models, such as the ones I have written about elsewhere.

Of course further in the future the game could well change again. New experiments might even detect non-Gaussianity or at least improve the constraints even further. Its wise to prepare the theory to take advantage of such future developments, and that’s something I hope to keep working to do.