Complementary signatures of α−attractor inflation in CMB and cosmic string Gravitational Waves

Abstract

When cosmic strings are formed during inflation, they regrow to reach a scaling regime, leaving distinct imprints on the stochastic gravitational wave background (SGWB). Such signatures, associated with specific primordial features, could be detectable by upcoming gravitational wave observatories like LISA, Einstein Telescope (ET), and others. Our analysis explores scenarios where cosmic strings form either before or during inflation. We examine how the number of e-folds experienced by the cosmic strings during inflation correlates with the predictions of inflationary models observable in CMB measurements. This correlation provides a testable link between inflationary physics and associated gravitational wave signals in a complementary manner. Focusing on α-attractor models of inflation,with the Polynomial α-attractor serving as an illustrative example, we find constraints, for instance, on the spectral index ns to 0.962 ≲ ns ≲ 0.972 for n = 1, 0.956 ≲ ns ≲ 0.968 for n = 2, 0.954 ≲ ns ≲ 0.965 for n = 3 and 0.963 ≲ ns ≲ 0.964 for n = 4 which along with the GW signals from LISA are capable of detecting local cosmic strings that have suffered ∼ 34 − 47 e-folds of inflation consistent with current Planck data and also testable in the upcoming CMB experiments like LiteBIRD and CMB-S4.