# Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity

**Authors:** Emilio Bellini, Ignacy Sawicki  
**arXiv:** [1404.3713](https://arxiv.org/abs/1404.3713)  
**Date:** 2014-04-14  
**Summary page:** https://www.summarizepaper.com/en/paper/1404.3713v1/

## Key points

- Emilio Bellini and Ignacy Sawicki's paper focuses on studying linear structure formation in scalar-tensor models with a single universally coupled scalar field.
- The authors demonstrate that five independent functions of time and one constant can efficiently represent all cosmological information related to the gravitational sector without redundancy.
- These functions capture important aspects of the universe such as background expansion history, current fractional matter density, and four time-dependent properties of dark energy.
- Two of the dark energy properties govern anisotropic stress, while the other two influence dark energy clustering, with potential scale-dependence and measurability.
- The framework presented does not provide insights into the underlying theory of acceleration beyond these properties.
- Bellini and Sawicki offer a translation to their formulation for easy comparison with existing models of late-time acceleration and effective field theory frameworks.
- Researchers can use this numerical formulation as a versatile tool to systematically test various proposed models of late-time acceleration, providing insights into the dynamics and characteristics of dark energy in cosmology.

## Summary

In their paper "Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity," Emilio Bellini and Ignacy Sawicki present a comprehensive solution for studying linear structure formation in scalar-tensor models with a single universally coupled scalar field. They demonstrate that all cosmological information related to the gravitational sector can be efficiently represented by five independent functions of time and one constant, without any redundancy. These functions encapsulate crucial aspects of the universe such as the observable background expansion history, current fractional matter density, and four time-dependent properties of dark energy. The authors highlight that two of these dark energy properties govern the presence of anisotropic stress while the other two influence dark energy clustering. Both may exhibit scale-dependence and have potential measurability. However, they caution that this framework cannot provide insights into the underlying theory of acceleration beyond these properties. To facilitate comparisons with existing models of late-time acceleration (e.g., perfect fluids, f(R) gravity, kinetic gravity braiding, galileons), as well as the effective field theory framework, Bellini and Sawicki provide a translation to their formulation. By implementing this numerical formulation, researchers gain a versatile tool capable of systematically testing various proposed models of late-time acceleration. This approach offers a streamlined method for investigating the behavior of linear large-scale structures within different gravitational modifications while providing valuable insights into the dynamics and characteristics of dark energy in cosmology.