Scale-invariance and the strong coupling problem

The effective theory of adiabatic fluctuations around arbitrary Friedmann-Robertson-Walker backgrounds — both expanding and contracting — allows for more than one way to obtain scale-invariant two-point correlations. However, as we show in this paper, it is challenging to produce scale-invariant fluctuations that are weakly coupled over the range of wavelengths accessible to cosmological observations. In particular, requiring the background to be a dynamical attractor, the curvature fluctuations are scale-invariant and weakly coupled for at least 10 e-folds only if the background is close to de Sitter space. In this case, the time-translation invariance of the background guarantees time-independent n-point functions. For non-attractor solutions, any predictions depend on assumptions about the evolution of the background even when the perturbations are outside of the horizon. For the simplest such scenario we identify the regions of the parameter space that avoid both classical and quantum mechanical strong coupling problems. Finally, we present extensions of our results to backgrounds in which higher-derivative terms play a significant role