Cosmological Tests of Modified Gravity (1504.04623v2)

Abstract: We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein's theory of General Relativity (GR) has been tested accurately within the local universe i.e. the Solar System, but this leaves the possibility open that it is not a good description of gravity at the largest scales in the Universe. This being said, the standard model of cosmology assumes GR on all scales. In 1998, astronomers made the surprising discovery that the expansion of the Universe is accelerating, not slowing down. This late-time acceleration of the Universe has become the most challenging problem in theoretical physics. Within the framework of GR, the acceleration would originate from an unknown dark energy. Alternatively, it could be that there is no dark energy and GR itself is in error on cosmological scales. In this review, we first give an overview of recent developments in modified gravity theories including $f(R)$ gravity, braneworld gravity, Horndeski theory and massive/bigravity theory. We then focus on common properties these models share, such as screening mechanisms they use to evade the stringent Solar System tests. Once armed with a theoretical knowledge of modified gravity models, we move on to discuss how we can test modifications of gravity on cosmological scales. We present tests of gravity using linear cosmological perturbations and review the latest constraints on deviations from the standard $\Lambda$CDM model. Since screening mechanisms leave distinct signatures in the non-linear structure formation, we also review novel astrophysical tests of gravity using clusters, dwarf galaxies and stars.

• The paper reviews how modified gravity theories can explain cosmic acceleration without invoking dark energy.
• It examines various models—including f(R), braneworld, and Horndeski theories—and highlights screening mechanisms like chameleon and Vainshtein to satisfy local gravitational tests.
• The analysis outlines future observational opportunities with surveys such as DES, Euclid, and LSST to probe deviations from General Relativity.

Overview of Cosmological Tests of Modified Gravity

The paper entitled "Cosmological Tests of Modified Gravity" by Kazuya Koyama offers a comprehensive review of the current state of research regarding alternatives to dark energy and the process of testing gravitational theories on a cosmological level. The paper addresses the ongoing debate surrounding the sufficiency of Einstein's General Relativity (GR) as a description of gravity, especially in the context of the universe's accelerating expansion.

Motivation for Modified Gravity

One of the principal motivations for examining modifications to GR stems from the discovery in 1998 that the universe's expansion is accelerating. This observation has fundamentally challenged our understanding of cosmological dynamics. Within the GR framework, this acceleration necessitates the existence of dark energy, an unknown energy component driving the expansion. However, modified gravity offers an alternative explanation, suggesting that GR might not be valid on cosmological scales, thus potentially eliminating the need for dark energy.

Review of Modified Gravity Theories

The paper provides a detailed review of several modified gravity theories, each offering unique insights into the large-scale behavior of gravity:

• $f(R)$ Gravity: This theory extends the Einstein-Hilbert action by incorporating a function of the Ricci scalar, which aims to reproduce the accelerated expansion without dark energy. The chameleon mechanism is essential here for addressing Solar System scale constraints.
• Braneworld Gravity: The concept that our universe is a 4D membrane existing in a higher-dimensional space provides solutions where the cosmological constant does not gravitate. This theory offers insight into the cosmological constant problem.
• Horndeski Theory and Beyond: These encompass the most general scalar-tensor theories that yield second-order equations of motion. They include a broad range of scalar-tensor theories and provide frameworks for exploring interactions that could mimic dark energy.
• Massive and Bigravity Theories: Introducing a mass for the graviton or considering two interacting metrics could account for late-time acceleration. However, constructing a theoretically consistent model free of instabilities remains challenging.

Screening Mechanisms

A significant focus of the paper is on the need for screening mechanisms, which allow modified gravity theories to evade stringent local tests of gravity. Several mechanisms are considered:

• Chameleon Mechanism: It relies on the environment-dependent mass of the scalar field to suppress modifications locally while allowing significant changes on cosmological scales.
• Vainshtein Mechanism: Utilizes non-linear kinetic terms to recover GR at small scales, especially in high-density environments, which is characteristic of galileon and massive gravity models.

Implications and Future Directions

The implications of these theories are profound, potentially impacting our understanding of the universe's composition and the fundamental laws of physics. Practically, the ability to distinguish between dark energy and modified gravity through cosmological observations could provide insights into fundamental questions about the constituents of the universe.

The paper emphasizes the growing capabilities to test these ideas through cosmological observations. Surveys including DES, Euclid, and LSST have the potential to probe variations in cosmic structure formation that could signify departures from GR predictions. Key observables include weak gravitational lensing, galaxy clustering, and peculiar velocities, all of which can reveal how structure grows differently under modified gravity compared to GR with dark energy.

Additionally, the paper discusses future challenges, including:

• Developing model-independent parameterizations to efficiently test the consistency of modified theories.
• Exploring the rich non-linear regime of cosmic structures to find distinctive signatures of gravity modifications.
• Utilizing observational data to refine or refute theoretical models, ultimately converging towards a deeper understanding of the universe's accelerated expansion.

Conclusion

This review underscores that, while we have made significant strides in understanding these theoretical models and developing observational tests, the field remains open with many unresolved questions. The ongoing and future surveys hold promise for delivering the data necessary to potentially revolutionize our understanding of gravity on cosmological scales. Whether these modifications represent the correct path forward, only rigorous theoretical work combined with meticulous observations will tell.