On the one loop corrections to inflation and the CMB anisotropies

TL;DR

The paper analyzes one-loop quantum corrections to inflation in a chaotic $\lambda\phi^4$ model, computing both the one-loop effective potential and the loop-corrected inflaton two-point function using a uniform curvature gauge and the Schwinger–Keldysh formalism. It finds that IR modes can accumulate over the total number of e-foldings, yielding corrections to slow-roll parameters and the power spectrum of up to a few percent, with enhancements proportional to $H_i^4/H^4$ for very long inflation. The leading corrections arise from IR contributions to $\langle\delta\phi^2\rangle_0$, while UV divergences are renormalized; the resulting power spectrum correction is approximately $P(k) \approx \dfrac{H^2}{4\pi^2}\left[1-\dfrac{15}{\pi^2}\lambda\Delta_N\left(10+\mathrm{Ci}(-2k\eta_0)\right)\right]$ on super-Hubble scales. Overall, the work shows that quantum loop effects in inflation can be non-negligible for long inflation and may encode information about the early inflationary era, motivating further study of potential observational signatures and non-Gaussianities within the EFT framework.

Abstract

We investigate the one loop effective potential of inflation in a standard model of chaotic inflation. The leading one loop corrections to the effective inflaton potential are evaluated in the quasi de Sitter background, and we estimate the one loop correction to the two-point function of the inflaton perturbations in the Hartree approximation. In this approximation, the one loop corrections depends on the total number of e-foldings of inflation and the maximal effect is estimated to be a correction to the power spectrum of a few percent. However, such a correction may be difficult to disentangle from the background in the simplest scenario.

Figures (6)

• Figure 1: The self-energy diagrams in the cactus approximation.
• Figure 2: The seagull diagram contributing to first order in $\lambda$.
• Figure 3: Different approximations to the integral $I_1(x_0)$ in $T^{(1)}(k)$. The solid line is the solution calculated in section 3.2 and the dashed line is the solution calculated above in eq.(\ref{['I1appr']}).
• Figure 4: The bubble diagram $T^{(2)}_1$.
• Figure 5: The tadpole sub-diagram in the $T^{(2)}$ contribution above, is canceled to higher order by the tadpole renormalization condition.