Non-Gaussian and loop effects of inflationary correlation functions in BRST formalism

We investigate inflationary correlation functions in single-field inflation models. We adopt a BRST formalism where locality and covariance at the subhorizon scale are manifest. The scalar and tensor perturbations are identified with those in the comoving gauge which become constant outside the cosmological horizon. Our construction reproduces the identical non-Gaussianity with the standard comoving gauge. The accumulation of almost scale-invariant fluctuations could give rise to IR logarithmic corrections at the loop level. We investigate the influence of this effect on the subhorizon dynamics. Since such an effect must respect covariance, our BRST gauge has an advantage over the standard comoving gauge. We estimate IR logarithmic effects to the slow-roll parameters at the one-loop level. We show that $\epsilon$ receives IR logarithmic corrections, while this is not the case for $\eta$. We point out that IR logarithmic effects provide the shift-symmetry-breaking mechanism. This scenario may lead to an inflation model with a linear potential.

Figure 1

These one-loop diagrams contribute IR logarithmic correction to the one-point operator. The broken line denotes the scalar propagator, and the wavy line denotes the graviton propagator. The diagrams in (a) are from soft gravitational fluctuation, and (b) is from the soft inflaton. The propagator which contains derivatives has no IR logarithmic correction.

Figure 2

The one-loop diagrams contribute an IR logarithmic correction from soft gravitational fluctuation to the two-point operator.

Figure 3

The one-loop diagrams contribute an IR logarithmic correction from the soft inflaton to the two-point operator.