content_image/305237.jpg content_image/305236.jpg content_image/305235.jpg
where B$_{ζ}$ ( k$_{1}$, k$_{2}$, k$_{3}$ ) is a function called the Bispectrum , being given by 

<img src='content_image/305237.jpg'>

where f$_{NL}$ ( k$_{1}$, k$_{2}$, k$_{3}$ ) effectively parameterises the bispectrum (it is 5 6 the value of the reduced bispectrum) and P$_{ζ}$ ( k ) is the spectrum of the curvature perturbation (the spectrum that is being used in this thesis is that defined by P $_{ζ}$( k ) ≡ k 3 2 π $_{2}$P$_{ζ}$ ( k ) ). 

The 4-point (connected) correlator for the curvature perturbation is 

where T$_{ζ}$ is a function called the Trispectrum , being given by [51] 

<img src='content_image/305236.jpg'>

<img src='content_image/305235.jpg'>

where k$_{13}$ ≡ | k$_{1}$ + k$_{3}$ | and τ$_{NL}$ and g$_{NL}$ effectively parameterise the trispec- trum. 

We will consider what is termed local non-Gaussianity, which for the bispectrum corresponds to the “squeezed” configuration of the momenta triangle, in that the magnitude of one of the momentum vectors is much smaller than the other two, which are of similar magnitude to each other, e.g. k$_{3}$ ≪ k$_{1}$, k$_{2}$ and k$_{1}$ ≈ k$_{2}$ . Within the framework of the δN formalism, the 

