Twisting inflation to sub-Planckian axion decay constants

Abstract

We study pseudoscalar inflation in the Einstein-Cartan-Palatini (first-order) formulation of gravity while allowing for torsion. We introduce two non-minimal interactions in the gravitational sector: pseudoscalar couplings to the Pontryagin density (Chern-Simons term) and the Nieh-Yan topological invariant. In the presence of these terms, the rolling pseudoscalar sources non-trivial torsional fields during inflation. We show that pathological gradient and ghost instabilities limit the strength of the coupling to the Pontryagin density during inflation. Furthermore, we show that the interaction with the Nieh-Yan term induces a new contribution to the pseudoscalar kinetic term, which parametrically increases its decay constant and allows for inflation on steep potentials. The torsion field generated by the background is parity violating, which is manifest in the resulting chiral gravitational wave spectrum. We find that the scalar sector is largely unaffected beyond the remapping of the axion decay constant to a larger value. Consequently, we show that while natural inflation with a cosine potential remains inconsistent with observations, the squared quartic hilltop potential can be made consistent with Planck 2018 data even for sub-Planckian decay constants by coupling to the Nieh-Yan term.

Figures (5)

• Figure 1: Tensor powerspectrum, $P_{T}$, and chirality parameter, $\chi$ as a function of $e$-folding number for natural inflation (eq. \ref{['cosine natural inflation']}). Here, $N_e$ is the number of $e$-folds before inflation ends, $f/M_{\rm Pl} = 0.1$, $n = 90$, $\Lambda = 0.6\times10^{-3}M_{\rm Pl}$.
• Figure 2: (Left panel) Tensor powerspectrum, $P_{T}$, and chirality parameter, $\chi$, at $N_e = 60$$e$-folds before the end of inflation as $n$ is varied, $n \space \in \space \{50,99\}$, and fixed axion decay constant $f/M_{\rm Pl} = 0.1$. (Right panel) Tensor powerspectrum, $P_{T}$, and chirality parameter, $\chi$, as the axion decay constant $f$ is varied, $f/M_{\rm Pl} \space \in \space \{1,3\}$, with a fixed $n= 0.1$. We fix the energy scale, $\Lambda = 10^{-8}-10^{-3} M_{\rm Pl}$, such that the scalar amplitude $A_{s} (N_e = 60) \simeq 2.1\times 10^{-9}$ (see section \ref{['results']}). For both panels, the potential is given by eq. \ref{['cosine natural inflation']}.
• Figure 3: $P_{\mathcal{R}}$ vs $N_e$ for CNI model, where $N_e$ is the number of $e$-folds before inflation ends, $M_{\rm Pl} = 1$, $f = 0.1$, $n = 90$, $\Lambda = 0.6\times10^{-3}$
• Figure 4: $r$ vs $n_s$ for HSI$22$, GNI$0.1$ and DB$2$ model, $M_{\rm Pl} = 1$.
• Figure 5: $n_s$ and $r$ vs $\chi$ for HSI$22$, GNI$0.1$ and DB$2$ model, $M_{\rm Pl} = 1$