Constraining low energy effective field theories via high energy axioms

Abstract

Low energy effective field theories (EFTs) allow us to predict low energy (macroscopic) observables without specifying the high energy (microscopic) details of a system. This is useful across many areas in physics, and particularly in situations where the high energy is unknown or difficult to measure. However, the EFT is not blind to all aspects of the high energy microphysics—certain consistency conditions on very small scales are inherited as conditions on the large scale dynamics. Physically, the high energy consistency conditions we wish to impose correspond to locality, causality, unitarity and crossing symmetry. By exploiting the resulting analytic structure of scattering amplitudes (S matrix elements), these translate into rigorous constraints on the EFT. Failure to satisfy these constraints indicates that no local, causal, unitary, Lorentz-invariant high energy completion of the low energy theory can ever exist—the microphysics must be inherently incompatible with this kind of quantum field theory. Here, such constraints are derived at nearly every order in the EFT expansion, for massive particles of any spin with any kinematics. To illustrate the power of these techniques, specific applications to various cosmological field theories are presented—including the scalar, vector and massive gravity theories used in the early Universe for inflation and the late Universe for dark energy, as well as non-singular bouncing cosmologies and gravitational waves. Exploiting relations between high and low energy in order to better constrain effective field theories with fewer experimental data therefore proves itself to be a useful tool in a variety of applications, and will guide our future efforts to construct both fundamental and phenomenological models of the Universe in which we live.