Field theory in cosmology

Field theory in cosmology applies classical and quantum fields to the homogeneous universe and its perturbations.

A $P(X,\varphi )$ scalar theory has Lagrangian density $P$ depending on the field and $X=-g^{\mu \nu }{\partial }_{\mu }\varphi {\partial }_{\nu }\varphi /2$. It includes canonical scalar theory and models with noncanonical kinetic interactions.

On a homogeneous background with $X=\bar{X}$, a $P(X,\varphi )$ perturbation has sound speedThe denominator is its time-kinetic coefficient and $P_X$ is its spatial-gradient coefficient.

Primordial non-Gaussianity is any departure of the primordial perturbations from Gaussian random fields. Cubic interactions generate a nonzero three-point correlation function at leading order.

Statistical homogeneity defines the primordial bispectrum by