I will talk about various topics related to primordial gravitational waves. First I will explore the robustness of tensor consistency relations and their relation with the Higuchi bound in de Sitter. Then I will describe models of inflation with a different symmetry pattern (solid inflation) and the emergence of new consistency relations after angular average. Finally I will expose a no-go theorem on non-inflationary primordial cosmology, where there is no sizeable production of GWs.

ICTP