The big issue, even for cosmologists today, is whether or not that primordial state contained some of the information needed for the appearance and development of the cosmos.
Cosmologists have done the equivalent of measuring our Universe's triangles by looking at a picture of the early Universe, and studying the spatial relationship between different points on that picture.
Cosmologists should be able to spot the imprint of these gravitational waves by measuring the polarisation of the microwaves; this is the way the light is ordered together.
The second way to measure curvature is to measure the thing that causes space to curve in the first place: the density of energy and matter throughout the Universe. Which cosmologists have also measured.