A unifying description of dark energy (1411.3712v2)

Abstract: We review and extend a novel approach that we introduced recently, to describe general dark energy or scalar-tensor models. Our approach relies on an ADM formulation based on the hypersurfaces where the underlying scalar field is uniform. The advantage of this approach is that it can describe in the same language and in a minimal way a vast number of existing models, such as quintessence models, $F(R)$ theories, scalar tensor theories, their Horndeski extensions and beyond. It also naturally includes Horava-Lifshitz theories. As summarized in this review, our approach provides a unified treatment of the linear cosmological perturbations about a FLRW universe, obtained by a systematic expansion of our general action up to quadratic order. This shows that the behaviour of these linear perturbations is generically characterized by five time-dependent functions. We derive the full equations of motion in the Newtonian gauge, and obtain in particular the equation of state for dark energy perturbations, in the Horndeski case, in terms of these functions. Our unifying description thus provides the simplest and most systematic way to confront theoretical models with current and future cosmological observations.

• The paper introduces a unified formalism that uses ADM decomposition and EFT to integrate diverse dark energy models.
• It derives five time-dependent functions that capture deviations from general relativity and control cosmological perturbations.
• It facilitates model comparison, integration with cosmological codes, and precision testing of dark energy theories.

A Unifying Description of Dark Energy

The paper "A Unifying Description of Dark Energy" by J. Gleyzes, D. Langlois, and F. Vernizzi provides a comprehensive framework for modeling various dark energy or scalar-tensor models within a single formalism. The approach is anchored in the Arnowitt-Deser-Misner (ADM) decomposition and extends the applicability of the effective field theory (EFT) formalism for gravitational theories, allowing for a unified treatment of linear cosmological perturbations across a wide range of models. This includes quintessence models, F(R) theories, scalar-tensor theories, their Horndeski extensions, and even Hořava-Lifshitz theories.

Central to the paper is the characterization of cosmological perturbations through five time-dependent functions derived from the ADM Lagrangian. These functions correspond to physical quantities that deviate from General Relativity (GR), such as the Planck mass evolution and the speed of gravitational waves. A significant advantage of this approach is its versatility—it not only facilitates comparison and identification of degeneracies among various dark energy models but also simplifies the confrontation of these models with observational data.

The authors highlight the observational ramifications of their framework through an examination of linear perturbation evolution equations. Importantly, the theory is presented in both Newtonian and synchronous gauges, covering relevant observables, and allowing for its incorporation into cosmological codes that are designed to handle a diverse range of gravitational theories. The theoretical development here is poised to aid in constraining dark energy models with precision cosmology datasets.

For researchers in the field, this work serves as a bridge between theoretical model development and empirical constraint. The ability to express a variety of dark energy models within a single theoretical structure opens pathways for novel explorations and optimizations in both model-building and observational testing.

Scientifically, the work emphasizes the importance of the EFT framework as a unifying language in cosmology, capable of handling both linear and nonlinear gravitational dynamics. It addresses ghosts and stability conditions, thereby extending the landscape of viable models beyond traditional Horndeski theories, to include those without Ostrogradski instabilities.

In considering future developments, the paper suggests that the inclusion of matter fields and their interactions within this framework could further enhance our understanding of dark energy dynamics. The derivations and formulations also provide a platform upon which novel gravitational theories can be proposed and analyzed systematically, potentially addressing outstanding questions in cosmology such as the Hubble tension and the nature of initial cosmological conditions.

In summary, this paper provides a critical tool for modern cosmologists seeking to develop and constrain theories of dark energy within a coherent and robust theoretical framework. It exemplifies a significant step towards a more comprehensive understanding of late-time cosmic acceleration and its underlying physics.