A Unified Approach to Cosmic Acceleration

TL;DR

The paper addresses the problem of cosmic acceleration without a cosmological constant by formulating a scalar-tensor effective field theory (EFT) that includes all leading four-derivative operators allowed by symmetry. It derives the master action $S = \int d^4x \sqrt{-g} \{ \frac{m_p^2}{2} \Omega^2(\varphi) R - \tfrac{1}{2} Z(\varphi) (\partial \varphi)^2 - U(\varphi) + \tfrac{\alpha(\varphi)}{\Lambda^4} (\partial \varphi)^4 \} + S_m$ and shows how special choices reproduce Quintessence, $f(R)$, and DGP-like behaviors, demonstrating a unifying framework for dark energy and modified gravity. It connects background evolution and linear perturbations in the Jordan frame, illustrating how $H(z)$ can mimic $\Lambda$CDM while $G_{\rm eff}$ and anisotropic stress provide additional observational handles. The work highlights that expansion history alone cannot distinguish models and emphasizes the role of structure growth and lensing in constraining EFT coefficients, while outlining future work on non-linear regimes, screening mechanisms, and super-horizon behavior. Overall, the EFT offers a systematic, testable route to unify and constrain late-time cosmic acceleration theories with data.

Abstract

We present a unified framework for the study of late time cosmic acceleration. Using methods of effective field theory, we show that existing proposals for late time acceleration can be subsumed in a single framework, rather than many compartmentalized theories. We construct the most general action consistent with symmetry principles, derive the background and perturbation evolution equations, and demonstrate that for special choices of our parameters we can reproduce results already existing in the literature. Lastly, we lay the foundation for future work placing phenomenological constraints on the parameters of the effective theory. Although in this paper we focus on late time acceleration, our construction also generalizes the effective field theory of inflation to the scalar-tensor and multi-field case for perturbatively constructed backgrounds.

Figures (1)

• Figure 1: In DGP gravity it is posited that our universe is a 3-brane embedded in a higher dimensional Minkowski space-time. It is then argued that a weakening of gravity on large scales in our $3+1$ dimensional world could offer an alternative explanation for observations of cosmic acceleration. For scales smaller than the cosmological horizon, but larger than around $1000$ km, one finds that the physics is described by a scalar-tensor theory. The Goldstone boson discussed in the text is geometrically realized as the so-called 'brane bending mode'. Although this effective description in terms of a scalar-tensor theory is valid cosmologically, for locally bound objects of higher than average density, classical non-linearities can become important before reaching the strong coupling scale $\Lambda_{UV}$ -- this is the Vainshtein effect Vainshtein:1972sx.