Abstract
We investigate radiative corrections to the inflaton potential from heavy fields undergoing a fast-roll phase transition. We find that a logarithmic one-loop correction to the inflaton potential involving this field can induce a temporary running of the spectral index. The induced running can be a short burst of strong running, which may be related to the observed anomalies on large scales in the cosmic microwave spectrum, or extend over many e-folds, sustaining an effectively constant running to be searched for in the future. We implement this in a general class of models, where effects are mediated through a heavy messenger field sitting in its minimum. Interestingly, within the present framework it is a generic outcome that a large running implies a small field model with a vanishing tensor-to-scalar ratio, circumventing the normal expectation that small field models typically lead to an unobservably small running of the spectral index. An observable level of tensor modes can also be accommodated, but, surprisingly, this requires running to be induced by a curvaton. If upcoming observations are consistent with a small tensor-to-scalar ratio as predicted by small field models of inflation, then the present study serves as an explicit example contrary to the general expectation that the running will be unobservable.
Highlights
Over the past few decades, cosmic inflation [1, 2] has emerged as the dominant explanation for the dynamics of the early universe, bearing many successful predictions
We find that a logarithmic one-loop correction to the inflaton potential involving this field can induce a temporary running of the spectral index
Within the present framework it is a generic outcome that a large running implies a small field model with a vanishing tensorto-scalar ratio, circumventing the normal expectation that small field models typically lead to an unobservably small running of the spectral index
Summary
Over the past few decades, cosmic inflation [1, 2] has emerged as the dominant explanation for the dynamics of the early universe, bearing many successful predictions. A non-vanishing running of the spectral index is a strong indication of non-trivial new physics in the inflationary sector It makes us ask the more precise question: what kind of new physics could lead to an observable running in a small field model?. Where f and g can be chosen to be simple renormalizable functions, to arrive at the desired form of the one loop potential without spoiling an otherwise single field slow roll dynamics Though models of this form yield a positive running, which is disfavored by data, we explicitly write two generalizations that naturally lead to negative running, namely that the messenger fields are fermions, and by using Ratra-Peebles type potentials.
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