Les Houches Lectures on Physics Beyond the Standard Model of Cosmology

TL;DR

This work analyzes extensions of $\Lambda$CDM that introduce light scalars in the dark sector and must satisfy gravitational tests through screening. It classifies three primary screening paradigms—Chameleon, k-mouflage, and Vainshtein—and develops concrete models (notably chameleon potentials and Galileon theories) to show how environmental dependence suppresses fifth forces while leaving cosmology testable. The text surveys theoretical properties, including effective potentials, thin-shell effects, derivative interactions, and non-renormalization features, and surveys experimental constraints from laboratory tests, Lunar Laser Ranging, and planned space-based gravity experiments. Overall, local gravity remains GR-like due to screening, while cosmological signatures persist on large scales, offering multiple avenues for near-term experimental probes of physics beyond the Standard Model of cosmology.

Abstract

In these Lectures, I review various extensions of the Lambda-Cold Dark Matter model, characterized by additional light degrees of freedom in the dark sector. In order to reproduce the successful phenomenology of GR in the solar system, these fields must effectively decouple from matter on solar system/laboratory scales. This is achieved through screening mechanisms, which rely on the interplay between self-interactions and coupling to matter to suppress deviations from standard gravity. The manifestation of the new degrees of freedom depends sensitively on their environment, which in turn leads to striking experimental signatures.

Figures (5)

• Figure 1.1: The tadpole diagram (on the left) involving the scalar field (dotted line) attached to Standard Model fields (solid line) running in the loop is necessary in order to neutralize the Standard Model vacuum energy contribution. By unitarity, the tree-level diagram (on the 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.
• Figure 3.2: Schematic 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).
• Figure 3.3: Effective potential for $a)$ low ambient matter density and $b)$ high ambient density. As the density increases, the minimum of the effective potential, $\phi_{\rm min}$, shifts to smaller values, while the mass of small fluctuations, $m_\phi$, increases.
• Figure 3.4: Sketch of the set-up for thin-shell calculation.
• Figure 4.5: Different regimes for $a)$ Galileons and $b)$ GR. In both case, the far region ($r\gg r_{\rm V}$ for Galileons; $r \gg r_{\rm Sch}$ for GR) corresponds to the weak-field regime, where the description is both weakly-coupled and classical. In the intermediate region ($\Lambda_{\rm s}^{-1}\ll r\ll r_{\rm V}$ for Galileons; $M_{\rm Pl}^{-1} \ll r \ll r_{\rm Sch}$ for GR), the description is still classical but strongly non-linear. Below the strong coupling scale ($r \ll \Lambda_{\rm s}^{-1}$ for Galileons; $r \ll M_{\rm Pl}^{-1}$ for GR), the description becomes fully quantum.