Inflation and Effective Shift Symmetries

Abstract

Cosmic inflation not only sets the initial conditions for the evolution of the universe but also provides the origin of structure formation. It is hence both from a theoretical and observational point of view a highly successful paradigm. Precision measurements of the cosmic microwave background constrain inflation to be effectively driven by a single scalar field whose potential maintains an approximate and continuous shift symmetry V ∼ const. sufficiently far from its minimum. In effective field theory, such a shift symmetry amounts to tuning an essentially infinite number of coefficients of all higher dimensional operators involved. Here, we study different realisations of shift-symmetric inflaton potentials to examine if the amount of fine tuning can be reduced. We begin by considering a UV example and find that underlying parameters do not evade tuning as the intrinsic suppressions do not suffice. Continuing to study non-canonical dynamics, we formulate a condition on the non-canonical kinetic term equivalent to the potential shift symmetry and provide expressions for universal corrections and phenomenological imprints resulting from a broken shift symmetry. Studying modified gravity, we derive all order expressions for broken shift symmetries that allow for observationally viable inflation to occur. Finally, we study scalar field dynamics non-minimally coupled to gravity. After developing an understanding of the phenomenological implications of different types of shift symmetry breaking, we propose a mechanism that realises a sufficient intermediate shift symmetry for inflation to occur by essentially only tuning one parameter. This parameter sets the spectral index as well as the normalisation of the cosmic microwave background temperature spectrum and is found to satisfy both observational constraints while at the same time pushing all higher order terms sufficiently far away in field space.