Reconciliation of High Energy Scale Models of Inflation with Planck

TL;DR

The paper addresses how unknown high-scale physics can imprint non-Bunch-Davies initial states on inflationary perturbations and thereby modify CMB observables. By formalizing these states with Bogoliubov coefficients and enforcing backreaction constraints, it derives modified scalar and tensor power spectra ${\mathcal P}_S={\mathcal P}_{BD}\,\gamma_S$ and ${\mathcal P}_T={\mathcal P}_{BD}^T\,\gamma_T$, yielding a tensor-to-scalar ratio $r=16\epsilon\,\gamma$ with $\gamma=\gamma_T/\gamma_S$. The analysis shows that for $M$ up to about $20 H$, tensor suppression occurs and the $m^2\phi^2$ chaotic inflation can be reconciled with Planck data, while non-Gaussianity remains within Planck limits (e.g., $f_{NL}^{\rm local}\sim \mathcal{O}(1)$). The work thus links high-energy initial-state physics to observable inflationary spectra, expanding the viability of simple inflationary models under non-BD initial conditions.

Abstract

The inflationary cosmology paradigm is very successful in explaining the CMB anisotropy to the percent level. Besides the dependence on the inflationary model, the power spectra, spectral tilt and non-Gaussianity of the CMB temperature fluctuations also depend on the initial state of inflation. Here, we examine to what extent these observables are affected by our ignorance in the initial condition for inflationary perturbations, due to unknown new physics at a high scale $M$. For initial states that satisfy constraints from backreaction, we find that the amplitude of the power spectra could still be significantly altered, while the modification in bispectrum remains small. For such initial states, $M$ has an upper bound of a few tens of $H$, with $H$ being the Hubble parameter during inflation. We show that for $M\sim 20 H$, such initial states always (substantially) suppress the tensor to scalar ratio. In particular we show that a general choice of initial conditions can satisfactorily reconcile the simple $1/2 m^2 φ^2$ chaotic model with the Planck data.

Figures (1)

• Figure 1: $n_s$ vs. $r$$1\sigma$ and $2\sigma$ contours, Planck results Planck-data. The grey shaded trapezoid region shows the acceptable region for the $m^2\phi^2$ model. The upper oblique line corresponds to the BD vacuum and the Left and Right sides correspond to $N_e=50$ and $N_e=60$ respectively.