Initial conditions of the universe: Decaying tensor modes

Abstract

Many models of the early universe predict that there should be primordial tensor perturbations. These leave an imprint into the temperature and polarisation anisotropies of the cosmic microwave background (CMB). The differential equation describing the primordial tensor perturbations is a second order differential equation and thus has two solutions. Canonically, the decaying solution of this equation in radiation domination is dropped as it diverges at early times and on superhorizon scales while it is then suppressed at late times. Furthermore, if there is an inflationary phase prior to the radiation domination phase, the amplitude of the decaying mode will also be highly suppressed as it enters the radiation phase, thus its effect will be negligible. In this study we remain agnostic to the early universe models describing pre-radiation domination physics and allow this mode to be present and see what effect it has on the CMB anisotropies. We find that the decaying mode, if normalised at the same time on subhorizon scales as the growing mode leaves an imprint on the CMB anisotropies that is identical to the growing mode. Contrary to expectation, on large scales both modes are poorly constrained for a scale invariant spectrum, and the apparent divergence of the decaying mode does not lead to a divergent physical observable. Quantitatively, the decaying mode can be more constrained both from temperature and polarisation anisotropies. We use a model independent, non-parametric, approach to constrain both of these primordial tensor perturbations using the temperature and polarisation anisotropies. We find that both modes are best constrained at the reionisation and recombination bumps and crucially, at the reionisation bump the decaying mode can be distinguished from the growing mode.