Navin first overviewed the basics of inflation. He stressed that for a theory of inflation to be predictive, it must ensure that the amplitude of the initial quantum fluctuations becomes frozen in during inflation or physical processes such as preheating will affect the pattern of fluctuations.
We know the cosmic microwave background (CMB) has almost Gaussian fluctuations (Gaussian meaning the random field is completely specified by the 2-point correlation function). However, primordial non-Gaussianities (i.e. not caused by late time effects such as lensing, but formed during inflation) can discriminate between models of inflation. To investigate these non-Gaussianities, we define the quantity fNL, which is related to the bispectrum (from the three point correlation function) normalised by the power spectrum squared.
If a multi-field inflation model is considered, one runs into the problem that now curvature fluctuations can evolve after crossing the Hubble scale (superhorizon evolution) and the theory becomes unpredictive. To avoid this, the isocurvature mode must somehow be removed. The goal for Joel and Navin‘s work is to find a two field model with only the adiabatic mode remaining.
Working with a two field model is difficult because challenging p.d.e.’s must be solved. However, one can “cheat” and use “delta N perturbations”. This method comes from the fact that different regions of space during inflation will have different densities and thus inflation will experience a slightly different number of e-foldings (N). Delta N tracks the density perturbations and is easier to work with.
In order to generate a large fNL (thus distinguishing this model from a single field model), you have to “go round a bend” in the field space of the two fields. However, this generates an isocurvature mode. If that mode is given a large mass, it causes the mode to exponentially decay. Joel and Navin found that if the isocurvature mode is driven to zero, the dominant part of fNL is driven to zero as well leaving it of order 1.
Navin said that future work would include looking at different potentials (perhaps numerically), seeing if forcing an adiabatic mode always kills fNL and investigating the possibility of killing the isocurvature mode and generating large fNL at different times (either during or after inflation).