Essential Building Blocks of Dark Energy (1304.4840v2)

Abstract: We propose a minimal description of single field dark energy/modified gravity within the effective field theory formalism for cosmological perturbations, which encompasses most existing models. We start from a generic Lagrangian given as an arbitrary function of the lapse and of the extrinsic and intrinsic curvature tensors of the time hypersurfaces in unitary gauge, i.e. choosing as time slicing the uniform scalar field hypersurfaces. Focusing on linear perturbations, we identify seven Lagrangian operators that lead to equations of motion containing at most two (space or time) derivatives, the background evolution being determined by the time dependent coefficients of only three of these operators. We then establish a dictionary that translates any existing or future model whose Lagrangian can be written in the above form into our parametrized framework. As an illustration, we study Horndeski's-or generalized Galileon-theories and show that they can be described, up to linear order, by only six of the seven operators mentioned above. This implies, remarkably, that the dynamics of linear perturbations can be more general than that of Horndeski while remaining second order. Finally, in order to make the link with observations, we provide the entire set of linear perturbation equations in Newtonian gauge, the effective Newton constant in the quasi-static approximation and the ratio of the two gravitational potentials, in terms of the time-dependent coefficients of our Lagrangian.

Summary of "Essential Building Blocks of Dark Energy"

This paper, authored by Jerome Gleyzes, David Langlois, Federico Piazza, and Filippo Vernizzi, provides a detailed framework for understanding single-field dark energy and its perturbative dynamics within the context of effective field theory (EFT). Adopting a method rooted in the EFT language, the authors streamline the treatment of cosmological perturbations in dark energy models, emphasizing the nuanced relationship between theoretical constructs and observational parameters.

The authors propose a minimalistic yet integral set of Lagrangian operators that ensure the resulting equations of motion remain second order in both time and spatial derivatives. This is accomplished by utilizing a 3 + 1 ADM decomposition where the lapse and curvature tensors serve as the primary elements of the Lagrangian framework. They emphasize the utility of their approach through an elaboration on Horndeski’s theories, which are effectively captured by six of the proposed operators.

Key contributions of the paper include:

1. Lagrangian Construction: The authors detail a generic Lagrangian in unitary gauge that can be expanded into a set of seven operators, which accommodate second-order equations of motion at the perturbative level. The focus is on the intrinsic and extrinsic curvature of time hypersurfaces minus any higher-order derivative terms.
2. Galileon Theories Examination: By exploring Horndeski's theories, also recognized as generalized Galileons, the authors illustrate that these can be described successfully within their proposed operator framework, thereby simplifying the covariant treatment of these models.
3. EFT Parameter Mapping: A systematic translation between specific theoretical models and the EFT language is established, providing a dictionary for converting Lagrangian descriptor terms into applied observational frameworks.
4. Cosmological Perturbations and Observables: The paper provides comprehensive formulations for linear cosmological perturbation equations in the Newtonian gauge. The effective Newtonian constant and the ratio of gravitational potentials are expressed in terms of time-variable coefficients, which link theoretical models with observational data.

Moreover, the implications of their findings are profound, extending theoretical comprehension of cosmological acceleration and offering a refined characterization of gravitational dynamics influenced by dark energy. The structural formulation provided invites further exploration within and beyond traditional parametric scales, suggesting potential domains for future theoretical and observational research.

This work is robustly situated within the established literature and pits its findings against a backdrop of prior theoretical advancements, eschewing higher-order spatial derivatives commonly encountered in many models. Future efforts could leverage this framework to refine models with observational data including Planck results, further elucidating the enigmatic properties of dark energy.

The insights presented in this paper have significant implications for both the theoretical development of cosmological models and the practical improvements in astrophysical observation methodologies. It not only solidifies the foundational understanding of single-field dark energy models but also sets a trajectory for future advancements in the modeling of the universe's accelerating expansion.