Beyond the Cosmological Standard Model

TL;DR

This review surveys theories and tests of gravity beyond the cosmological standard model, emphasizing screening mechanisms that hide new light degrees of freedom in high-density environments. It frames modified gravity within an effective field theory context and classifies screening into deep-potential, derivative, and Vainshtein categories, with f(R), chameleon, symmetron, galileon, and Horndeski theories discussed in depth. The paper then maps experimental tests from lab to Solar System to astrophysical and cosmological scales, highlighting how current data generally align with GR yet leave room for percent-level MG signatures in specific regimes. It provides a roadmap for upcoming decade tests, including novel astrophysical probes and refined cosmological analyses, to robustly distinguish MG effects from dark energy or systematics.

Abstract

After a decade and a half of research motivated by the accelerating universe, theory and experiment have a reached a certain level of maturity. The development of theoretical models beyond Λ, or smooth dark energy, often called modified gravity, has led to broader insights into a path forward, and a host of observational and experimental tests have been developed. In this review we present the current state of the field and describe a framework for anticipating developments in the next decade. We identify the guiding principles for rigorous and consistent modifications of the standard model, and discuss the prospects for empirical tests. We begin by reviewing attempts to consistently modify Einstein gravity in the infrared, focusing on the notion that additional degrees of freedom introduced by the modification must screen themselves from local tests of gravity. We categorize screening mechanisms into three broad classes: mechanisms which become active in regions of high Newtonian potential, those in which first derivatives become important, and those for which second derivatives are important. Examples of the first class, such as f(R) gravity, employ the familiar chameleon or symmetron mechanisms, whereas examples of the last class are galileon and massive gravity theories, employing the Vainshtein mechanism. In each case, we describe the theories as effective theories. We describe experimental tests, summarizing laboratory and solar system tests and describing in some detail astrophysical and cosmological tests. We discuss future tests which will be sensitive to different signatures of new physics in the gravitational sector. Parts that are more relevant to theorists vs. observers/experimentalists are clearly indicated, in the hope that this will serve as a useful reference for both audiences, as well as helping those interested in bridging the gap between them.

Figures (24)

• Figure 1: If additional scalars are to neutralize the Standard Model vacuum energy contribution, the tadpole diagram (left) involving the scalar field (dotted line) attached to Standard Model fields (solid line) running in the loop is necessary. By unitarity, the tree-level diagram (right) with a scalar exchanged by Standard Model fields is also allowed, implying that the scalar field mediates a $5^{\rm th}$ force that must therefore be screened in the local environment.
• Figure 2: This 1-loop diagram with Standard Model fields (solid) running in the loop renormalizes the mass of the scalar field (dashed line).
• Figure 3: Sketch of the effective potential felt by a chameleon field (solid line). The effective potential is a sum of the bare potential of runaway form, $V(\phi)$ (dashed line) and a density-dependent piece, from coupling to matter (dotted line). Reproduced from Jain:2010ka.
• Figure 4: Comparison of chameleon effective potential in regions of low and high density. In regions of low density, the curvature of the potential is much shallower, corresponding to a light scalar that mediates a long range force. In regions of high density, the scalar acquires a large mass, and the force shuts off.
• Figure 5: Setup for the computation of the thin-shell effect of Section \ref{['thinshellsec']}.