Gravitational Waves from Inflation

Gravitational waves (GW) are tensor perturbations of the metric of curved spacetime that propagate. The metric g is a matrix (or differential 2-form, to be specific) that fully describes the 4-dimensional manifold of a spacetime in general relativity. The components of the full metric gμν are the sum of an unperturbed metric and the perturbation hμν , which varies on a smaller scale (separated in Fourier transform) than the unperturbed metric, poetically like ripples moving on a pond surface. For example, on a sufficiently local scale or away from massive bodies, spacetime is not significantly curved, and the spacetime is described by the flat or Minkowski metric ημν = diag(−1, 1, 1, 1) of special relativity. In the linearized gravity approximation, a small perturbation to flat spacetime can be considered, by taking the metric: