Quantum Cosmological Perturbations: Predictions and Observations

TL;DR

This paper argues that quantum cosmological perturbations yield robust, model-independent predictions when inflation is described via a hydrodynamical framework with a decaying cosmological constant. It derives a two-parameter description, $1+\frac{p}{\varepsilon}=\frac{\beta}{(N+1)^{\alpha}}$, and shows consistent, testable outcomes: a flat universe for sufficient e-folds, adiabatic and nearly Gaussian perturbations with a red tilt, and a nonzero lower bound on gravitational waves linked to the measured spectral index $n_s$. By explicitly connecting to slow-roll and k-inflation scenarios, the work maps the parameter space to specific potentials and behaviors of $n_s$ and $r$, highlighting cases like chaotic inflation ($\alpha=1$), Starobinsky-like models ($\alpha=2$), and small-field cases ($\alpha=3$). It also demonstrates how non-Gaussianity constrains the sound speed in k-inflation, capping how small $r$ can be. Overall, the paper shows that precision measurements of $n_s$, $f_{NL}$, and $r$ can exclude large classes of inflationary models while reinforcing the quantum origin of cosmic structure.

Abstract

I consider the generic model independent predictions of the theory of quantum cosmological perturbations. To describe the stage of cosmic inflation, where these perturbations are amplified, the hydrodynamical approch is used. The inflationary stage is completely characterized by the deviation of the equation of state from cosmological constant which is a smooth function of the number of e-folds until the end of inflation. It is shown that in this case the spectral index should deviate from the flat one at least by 3 percent irrespective of any particular scenario. Given the value of the spectral index the lower bound on the amount of the gravitational waves produced is derived. Finally the relation between effective hydrodynamical description of inflation and inflationary scenarios is discussed.