The physics of the early universe is encoded in the correlations of cosmological perturbations. While the Cosmic Microwave Background (CMB) provides precise constraints of the power spectrum and bispectrum of perturbations, over scales from gigaparsec to megaparsec, the recent signal of stochastic gravitational wave (GW) claimed by Pulsar Timing Arrays (PTA) opens a new window into primordial cosmology over scales of few parsecs. Future interferometric missions promise to extend this window to even smaller scales. The theory of inflation explains the generation of perturbations, and its dynamics has been constrained primarily by CMB over large scales. Today, efforts are underway to test inflationary models against the GW signal seen in PTA and forecasts of future interferometers. In this talk, I will first discuss the generation of perturbations and relate the structure of their correlations to the physics of inflation. 

I will then focus on production of primordial GWs, specifically arising from the interaction of tensor perturbations with scalar and vector perturbations at early times. Because they originate from these interactions, such induced GWs serve as unique probes of primordial correlations. I will demonstrate how the spectral density of induced GWs, when analyzed along with CMB constraints, reveals the magnitude and shape of primordial non-Gaussianity at the level of the bispectrum and trispectrum. I will also illustrate how the chirality of induced GWs serves a novel test of parity violation in the early universe. In summary, I shall aim to convey how GWs complement CMB, enabling a comprehensive examination of primordial correlations across a vast range of scales.