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In its first moments, the Universe expanded faster than light could cross it. This process, inflation, left behind ripples — tiny density fluctuations from which galaxies later grew. The spectrum of these ripples is usually described by a number: if it is exactly 1, then all fluctuations, large and small, were equally strong.

Observations give a value slightly less than 1, but recent attempts to settle the debate over the expansion rate require exactly 1. The authors propose a simple way out: let inflation end not smoothly but with a sharp drop, like a ball rolling down a hill suddenly falling off a cliff. Then even in the simplest models, such as chaotic inflation or the Starobinsky model, the desired spectrum emerges.

This scenario requires no complicated additions and stays within a single scalar field. If future observations confirm the value of exactly 1, it would be a strong argument for models with a sudden stop of inflation.

Original abstract

as written by the authors arXiv:2604.02823

The early dark energy resolution of Hubble tension seems to be suggesting a scale-invariant Harrison-Zeldovich spectrum of primordial scalar perturbation, i.e. $$n_s=1$$ ($$|n_s-1|\sim {\cal O}(0.001)$$) for $$H_0\sim 73$$km/s/Mpc. In this work, we propose a possibility to acquire $$n_s=1$$ in single field slow-roll models of inflation. In our consideration, the potential of inflaton during inflation still preserve the shape of well-known single field inflation models in deep slow-roll region, but inflation ends suddenly due to a large step of inflaton potential. In particular, we investigate the implication of our scheme for chaotic inflation and Starobinski inflation, and show how they can be compatible with the observation for $$n_s=1$$.