Transient Parity Violation during Inflation: Implications for PTA Gravitational Waves

Author(s)

Tasinato, Gianmassimo

Abstract

We investigate the consequences of a transient phase of enhanced parity violation during inflation. Modeling this phase through a time-localized Chern--Simons-like coupling, we show that it amplifies primordial gravitational waves at small scales, producing a robust spectral shape with a blue growth of effective slope $n_T \simeq 2$, largely insensitive to microscopic details. This prediction lies in the range explored by recent pulsar timing array (PTA) analyses under cosmological power-law interpretations, while differing from the canonical supermassive black hole binary expectation. Our framework thus provides a predictive cosmological template to benchmark astrophysical versus primordial origins of the signal, consistent with cosmic microwave background bounds. The signal also exhibits large linear polarization and non-trivial Stokes correlations, corresponding to an almost maximally phase-coherent helicity state. Such features are difficult to realize in classical stochastic backgrounds, and their detection would provide circumstantial evidence for a primordial, coherently generated origin of the gravitational-wave background.

Figures

\small We represent the scale dependence of the tensor spectrum generated during inflation on our scenario. {\bf Left panel}: plot of Eq.~\eqref{def_pii} in the region of increasing tensor spectrum, from large towards small scales, for different values of $\beta$ and $\Delta \tau$. {\bf Right panel}: the corresponding spectral index $n_T$ of Eq.~\eqref{def_nT}, zooming around the inflection point of the spectral growth. Notice that, in the growing part of the spectrum in proximity of the inflection point, the spectral tilt lies in the range $n_T\simeq 2$.
Caption \small We represent the scale dependence of the tensor spectrum generated during inflation on our scenario. {\bf Left panel}: plot of Eq.~\eqref{def_pii} in the region of increasing tensor spectrum, from large towards small scales, for different values of $\beta$ and $\Delta \tau$. {\bf Right panel}: the corresponding spectral index $n_T$ of Eq.~\eqref{def_nT}, zooming around the inflection point of the spectral growth. Notice that, in the growing part of the spectrum in proximity of the inflection point, the spectral tilt lies in the range $n_T\simeq 2$.
\small We represent the scale dependence of the tensor spectrum generated during inflation on our scenario. {\bf Left panel}: plot of Eq.~\eqref{def_pii} in the region of increasing tensor spectrum, from large towards small scales, for different values of $\beta$ and $\Delta \tau$. {\bf Right panel}: the corresponding spectral index $n_T$ of Eq.~\eqref{def_nT}, zooming around the inflection point of the spectral growth. Notice that, in the growing part of the spectrum in proximity of the inflection point, the spectral tilt lies in the range $n_T\simeq 2$.
Caption \small We represent the scale dependence of the tensor spectrum generated during inflation on our scenario. {\bf Left panel}: plot of Eq.~\eqref{def_pii} in the region of increasing tensor spectrum, from large towards small scales, for different values of $\beta$ and $\Delta \tau$. {\bf Right panel}: the corresponding spectral index $n_T$ of Eq.~\eqref{def_nT}, zooming around the inflection point of the spectral growth. Notice that, in the growing part of the spectrum in proximity of the inflection point, the spectral tilt lies in the range $n_T\simeq 2$.
\small {\bf Left panel}: the region of increasing tensor spectrum according to Eq.~\eqref{finr_pik}, from large scales (where it is almost scale invariant) towards small scales. {\bf Right panel}: the corresponding spectral index, zooming at the inflection point at around $\kappa\simeq 1$.
Caption \small {\bf Left panel}: the region of increasing tensor spectrum according to Eq.~\eqref{finr_pik}, from large scales (where it is almost scale invariant) towards small scales. {\bf Right panel}: the corresponding spectral index, zooming at the inflection point at around $\kappa\simeq 1$.
\small {\bf Left panel}: the region of increasing tensor spectrum according to Eq.~\eqref{finr_pik}, from large scales (where it is almost scale invariant) towards small scales. {\bf Right panel}: the corresponding spectral index, zooming at the inflection point at around $\kappa\simeq 1$.
Caption \small {\bf Left panel}: the region of increasing tensor spectrum according to Eq.~\eqref{finr_pik}, from large scales (where it is almost scale invariant) towards small scales. {\bf Right panel}: the corresponding spectral index, zooming at the inflection point at around $\kappa\simeq 1$.
\small Our theoretical prediction for $h^2 \Omega_{\rm GW}^I$ as green line, with parameters discussed after Eq.~\eqref{comp_ogw_improved}, compared with the sensitivity curves of current CMB measurements \cite{BICEP2:2018kqh}, and of PTA experiments NANOGrav, IPTA, and SKA, taken from \cite{Schmitz:2020syl}.
Caption \small Our theoretical prediction for $h^2 \Omega_{\rm GW}^I$ as green line, with parameters discussed after Eq.~\eqref{comp_ogw_improved}, compared with the sensitivity curves of current CMB measurements \cite{BICEP2:2018kqh}, and of PTA experiments NANOGrav, IPTA, and SKA, taken from \cite{Schmitz:2020syl}.
\small The functions defined in Eq.~\eqref{eq_stpar} describing the scale dependence of the GW Stokes parameters in our setup. While circular polarization is generated, it remains suppressed, whereas the linear polarization reaches a sizeable amplitude comparable to intensity.
Caption \small The functions defined in Eq.~\eqref{eq_stpar} describing the scale dependence of the GW Stokes parameters in our setup. While circular polarization is generated, it remains suppressed, whereas the linear polarization reaches a sizeable amplitude comparable to intensity.
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