A Class of Effective Field Theory Models of Cosmic Acceleration

Abstract

We explore a class of effective field theory models of cosmic acceleration involving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy the weak equivalence principle, assuming that one boson is lighter than all the others, and integrating out the heavier fields. The result is a quintessence model with matter coupling, together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients. After eliminating higher derivative terms and exploiting the field redefinition freedom, we show that the resulting theory contains nine independent free functions of the scalar field when truncated at four derivatives. This is in contrast to the four free functions found in similar theories of single-field inflation, where matter is not present. We discuss several different representations of the theory that can be obtained using the field redefinition freedom. For perturbations to the quintessence field today on subhorizon lengthscales larger than the Compton wavelength of the heavy fields, the theory is weakly coupled and natural in the sense of t'Hooft. The theory admits a regime where the perturbations become modestly nonlinear, but very strong nonlinearities lie outside its domain of validity.

Figures (2)

• Figure 1: The parameter space of fractional density perturbation $\delta \rho/\rho$ for perturbations to the quintessence field, and cutoff scale $M$ for the effective field theory, illustrating the constraint (\ref{['eq:ddd']}) on the domain of validity. Near the boundary of the domain of validity the higher derivative terms in the action are potentially observable, this is labeled the "interesting regime". Further away from the boundary the higher derivative terms are negligible and the theory reduces to a standard quintessence model with a matter coupling.
• Figure 2: The domain of validity of the effective field theory in the two dimensional parameter space of energy $E$ per quantum of a mode of the quintessence field, and mode occupation number $N$. The cutoff scale $M$ must be larger than the Hubble parameter $H_0$ in order that the background cosmology lie within the domain of validity. Perturbation modes on length-scales that are small compared to $H_0^{-1}$ but large compared to $M^{-1}$ can be described, but only if the mode occupation number and fractional density perturbation are sufficiently small. See Sec. \ref{['sec:validity']} for details.