Small-field and scale-free: inflation and ekpyrosis at their extremes

Abstract

There is increasing evidence from string theory that effective field theories are only reliable over approximately sub-Planckian field excursions. The two most promising effective models for early universe cosmology, inflation and ekpyrosis, are mechanisms that, in order to address cosmological puzzles, must operate over vast expansion/energy ranges. This suggests that it might be appropriate to describe them using scaling laws. Here we combine these two ideas and demonstrate that they drive inflation and ekpyrosis to their extremes: inflation must start at ultra-slow-roll, and ekpyrosis at ultra-fast-roll. At face value, the implied spectra are overly tilted to the red, although in both cases minor departures from pure scale freedom bring the spectral indices within current observational bounds. These models predict a significant spectral running at a level detectable in the near future (αs ≈ −10−3). Ekpyrotic models with minimal coupling are nevertheless ruled out, as they lead to levels of non-Gaussianity that are at least an order of magnitude too large. No such restrictions apply to models with a kinetic coupling between the two ekpyrotic scalar fields, and these remain the most promising ekpyrotic models. An additional swampland criterion that was recently proposed for the slope of the scalar field potential would however rule out all ultra-slow-roll models of inflation. Finally, we speculate on the existence of corresponding restrictions on the slope at negative potential values, which might lead to similarly severe constraints on ekpyrotic models.