Modified Gravity and Cosmology: An Update by the CANTATA Network (2105.12582v2)

Abstract: General Relativity and the $\Lambda$CDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. All extended theories and scenarios are first examined under the light of theoretical consistency, and then are applied to various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology are able to offer recently. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature. This work is a Review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. Its realization was performed in the framework of the COST European Action ``Cosmology and Astrophysics Network for Theoretical Advances and Training Actions''.

• The paper presents updated numerical tests demonstrating that modified gravity theories can recover General Relativity in appropriate limits.
• The paper highlights scalar-tensor and teleparallel models that drive cosmic acceleration without invoking dark energy.
• The paper emphasizes how upcoming missions and advanced analytical methods will further differentiate these theories from ΛCDM cosmology.

Modified Gravity and Cosmology: An Update from the CANTATA Network

Modified gravity theories represent a departure from the traditional framework of General Relativity (GR), incorporating alterations that typically involve higher-order terms, additional fields, or a more intricate geometry. These adaptations are motivated by both theoretical considerations—like quantum gravity and the desire to unify gravity with the other fundamental interactions—and observational challenges, such as the need to account for cosmic acceleration without invoking dark energy or other exotic substances. This essay provides an overview of recent developments in modified gravity and cosmology, as highlighted by the CANTATA network.

Basics of Modified Gravity

Modified gravity theories extend GR by introducing terms into the gravitational Lagrangian that are functions of curvature invariants, such as in $f(R)$ gravity, or coupling with scalar fields, as seen in scalar-tensor theories. An example is the Horndeski theories, which are the most general scalar-tensor theories with second-order equations of motion, thus avoiding Ostrogradski instabilities. These theories allow for a more comprehensive exploration of gravitational phenomena beyond the standard model of cosmology.

In stark contrast, the Teleparallel Equivalent of General Relativity reframes gravity as a gauge theory of the translation group, attributing gravitational effects to torsion rather than curvature. This reformulation provides a different path to extend gravity, giving rise to $f(T)$ theories where $T$ is the torsion scalar.

Numerical Results and Viability

Several crucial results have emerged in recent years concerning the viability of these models. Theories of modified gravity are subjected to stringent constraints from both theoretical consistency and observational data. For instance, $f(R)$ theories must recover GR in the appropriate limits to ensure compliance with solar system tests and cosmological observations. These demands necessitate that such theories exhibit a viable Newtonian limit and exhibit no unstable dynamical behavior, such as ghost or tachyonic instabilities.

Observations from cosmic microwave background radiation, high-resolution surveys, and gravitational wave detections further constrain the parameters of these theories, particularly those that predict additional polarization modes in gravitational waves or affect the luminosity distance relation used in observing standard sirens.

Cosmological Implications and Theoretical Advances

One of the most striking consequences of modified gravity theories is their ability to naturally generate cosmic acceleration, potentially eliminating the need for dark energy. These models provide a fertile testing ground for understanding large-scale structure formation and cosmological perturbations. Scalar modes in these theories can impact the growth rate of cosmic structures and leave imprints on the matter power spectrum observable in galaxy surveys.

Moreover, in the context of early Universe cosmology, modified theories can drive inflationary dynamics. Certain $f(R)$ models can naturally lead to a de Sitter solution associated with the inflationary phase, paving the way to address traditional problems such as the horizon and flatness problems without invoking additional fields.

Future Directions in Modified Gravity

The field is moving towards not only verifying compatible models with current datasets but also making future predictions that distinguish these models from $\Lambda$CDM cosmology. For example, future missions like the LISA and Euclid, and improvements in gravitational wave astronomy, will probe the predictions of these theories at both cosmological and astrophysical scales.

The development of sophisticated analytical methods, such as Effective Field Theory approaches, extends the reach of theoretical frameworks like Horndeski and beyond Horndeski theories, capturing complex gravitational phenomenology. Additionally, numerical relativity simulations are becoming crucial tools for investigating the nonlinear dynamics of these theories.

Conclusion

Modified gravity offers a dynamic and robust framework to analyze the gravitational interaction beyond General Relativity. As observational techniques become increasingly refined, theories such as $f(R)$ gravity, scalar-tensor models, and teleparallel formulations provide promising avenues to explore fundamental questions in cosmology and astrophysics. Continued collaboration, like that of the CANTATA network, is vital for advancing our understanding of these theories and their implications on our Universe. Through rigorous testing against empirical data, we may refine these models to provide deeper insights into the fundamental nature of gravity and the evolution of the cosmos.