Cosmological correlators beyond the de-Sitter invariance

Cosmological correlators serve as powerful probes of the physics that governed the Universe in its earliest moments. Yet analytic calculations of correlators involving massive spinning fields are highly challenging. Recent progress in the cosmological bootstrap program has greatly deepened our understanding of these correlators. In this talk, we will show how to extend the bootstrap program beyond exact de Sitter invariance by studying two types of symmetry breaking: explicit scale-invariance breaking and boost breaking. We will present the boundary differential equations that characterise correlators in these settings and highlight the rich phenomenology that emerges.
Finally, we will also show recent developments in approximation methods, based on the combination of exact WKB and saddle-point method, which provide a precise, efficient, and physically transparent way to capture and classify the non-analytic features of correlators.