Tensor Perturbation

A tensor perturbation is a fluctuation in the metric of spacetime itself, as opposed to a scalar perturbation, which is a fluctuation in the energy density of matter. In cosmology, tensor perturbations are the direct source of primordial gravitational waves: during cosmic inflation, quantum fluctuations in the gravitational field are stretched to cosmological scales and freeze out as classical tensor modes.

The physics is governed by the same wave equation that describes gravitational waves in the weak-field limit of general relativity, but with the crucial difference that the source is not a localized mass distribution but the dynamics of the inflationary vacuum itself. The amplitude of tensor perturbations is parameterized by the tensor-to-scalar ratio r, which measures the relative power in tensor versus scalar modes. In single-field slow-roll inflation, r is determined by the Hubble parameter during inflation, making it a direct probe of the inflationary energy scale.

Tensor perturbations produce a distinctive signature in the cosmic microwave background: B-mode polarization, a curl-like pattern in the polarization of CMB photons that cannot be generated by scalar density fluctuations. This makes B-modes the smoking gun for tensor perturbations — and, by extension, for inflation.

The detection of tensor perturbations would be more than a confirmation of inflation. It would be the first direct observation of quantum gravity in action: the quantization of the gravitational field, stretched by cosmic expansion into a classical observable. In this sense, tensor perturbations are the bridge between the quantum and the classical, between the Planck epoch and the present day.