Anisotropies of cosmological gravitational wave backgrounds in non-flat spacetime

TL;DR

This paper introduces a new method to constrain the early Universe's flatness by analyzing anisotropies in the cosmological gravitational wave background, considering non-flat spacetime effects and their correlation with CMB data.

Contribution

It develops a generalized harmonic decomposition approach to study CGWB anisotropies in non-flat spacetime, revealing different behaviors of Sachs-Wolfe and Integrated Sachs-Wolfe effects based on spatial curvature.

Findings

CGWB anisotropies depend on spatial curvature through SW and ISW effects.

Cross-correlations between CGWB and CMB can indicate the sign of non-Gaussianity.

Different GW mechanisms show distinct ISW and SW contributions in non-flat spacetime.

Abstract

Recent reports of stochastic gravitational wave background from four independent pulsar-timing-array collaborations have renewed the interest in the cosmological gravitational wave background (CGWB), which is expected to open a new window into the early Universe. Although the early Universe is supposed to be extremely flat from an inflationary point of view, the cosmic microwave background (CMB) data alone from the Planck satellite measurement prefers an enhanced lensing amplitude that can be explained by a closed Universe. In this paper, we propose an independent method to constrain the early-universe flatness from the anisotropies of CGWB. Using the generalized harmonic decompositions in the non-flat spacetime, we find CGWBs from different physical mechanisms such as cosmic inflation and phase transitions share the same integrated Sachs-Wolfe (ISW) term but possess different SW terms, which would exhibit different behaviors when including the spatial curvature since the ISW effect is more sensitive to the spatial curvature than the SW effect. Furthermore, we provide the cross-correlations between CGWB and CMB, implying a positive or negative correlation between their SW effect terms depending on the GW mechanisms, which may hint at the sign of $f_{\mathrm{NL}}$ when considering non-Gaussianity contributions to anisotropies.