Dark Energy and Alternative Gravity

The accelerated expansion of our Universe implies that we currently have incomplete knowledge about the energy content of the Universe or the true nature of gravity. The standard paradigm, LCDM, assumes that this accelerated expansion is caused by a cosmological constant; while this model fits most observational data to date well, its validity has been challenged from both the theoretical and the observational sides, and over the last two decades alternative theories have attracted significant research interest. A modification to the law of gravity is modified is likely to affect not only the Hubble expansion rate but also inter-particle interactions, both of which can change the evolution of large-scale cosmic structures.

Current and future cosmological data have the power of constraining and distinguishing between different classes of dark energy and modified gravity theories. However, the most interesting aspects of those theories often lie deep in the nonlinear regime of structure formation, and consequently the ideal places to test them are scales relevant for galaxies and galaxy clusters. Reliable quantitative theoretical predictions on such scales can only be made using numerical simulations, not only because the density field is highly nonlinear, but also because of the intrinsic nonlinearity of the theories themselves (i.e., the screening mechanism).

Thanks to its supercomputing resources and expertise in numerical simulation techniques, such as the modified gravity versions of N-body codes RAMSES (Li et al. 2012, Li et al. 2013a, Barreira et al. 2013, Li et al. 2013b, Becker et al. 2021), Arepo (Arnold et al. 2019, Hernandez-Aguayo et al. 2021) and GLAM (Ruan et al. 2022, Hernandez-Aguayo et al. 2022), the ICC has been a leading group in performing large and high-resolution simulations to study the structure formation in dark energy and modified gravity theories. More recently we have implemented the generic class of effective field theories of dark energy (EFTofDE) into RAMSES and the code, EFT-RAMSES, is now publicly available (Woodcock et al. 2026). Some recent research highlights are:

• Realistic simulations of galaxies and galaxy clusters in modified gravity: we have developed an efficient version of modified Arepo (Arnold et al. 2019), which implements some of the leading modified gravity models such as f(R) gravity and the DGP braneworld model, to study galaxy formation in such models using the state-of-the-art subgrid baryonic physics model from the Illustrious-TNG and the Auriga projects. A recalibrated subgrid model based on Illustris-TNG, specifically designed for large-box cosmological simulations, has been developed (Mitchell et al. 2022) too. These allow us to fully resolve the details of Milky-Way-sized galaxies up to large galaxy clusters, and quantify how stars form and distribute, how gas cools and gets heated, and how the modified gravitational force behave, in such objects (see Fig. 1).

  Fig. 1: Four selected galaxies from the SHYBONE galaxy formation simulations in f(R) gravity. In each panel, the left column shows the distribution of stars on top of gas, the central column shows the spatial profile of the fifth force to gravity ratio, and the right column shows the spatial profile of the scalar field. The top and bottom rows in each panel are respectively the galaxy viewed edge on and face on.

• Galaxy clustering and galaxy-halo connection in modified gravity: Using full cosmological hydrodynamical simulations of modified gravity, we studied the clustering of galaxies in detail. Contrary to naive expectations, and depending on how galaxies are selected, the effect of gravity on their clustering strength does not monotonically change with gravity strength (Collier et al. 2024). Assembly bias is non-negligible in theoretical modelling of galaxy clustering, with an effect of order 10 per cent, and this can be largely captured by a simple model of environmental dependence of galaxy-halo connection, for both standard and modified gravity ((Collier et al. 2026).
• Constraining cosmological models using small-scale redshift-space distortions: RSD is a powerful cosmological probe of the cosmic density and velocity fields, capable of placing stringent constraints on dark energy and modified gravity theories where structure growth is enhanced. Based on a very-high resolution simulation of f(R) gravity (Shi et al. 2015), He et al. (2018), extending earlier study of He et al. (2016), placed a strong constraint on this model using RSD on small scales (see Fig. 2). We developed an improved "halo streaming" model to model RSD accurately down to the 1-halo regime (Cuesta-Lazaro et al. 2020, Cuesta-Lazaro et al. 2022, Ruan et al. 2024, Ruan et al. 2026). The halo streaming model is built upon accurately emulated dark matter halo properties and an analytical model of galaxy-halo connection, allowing the latter to be flexibly varied by users or to include higher order effects such as assembly bias.

  Fig. 2: Left Panel: the 2D redshift space galaxy correlation functions from SDSS observations (coloured contours) and predictions for LCDM (dashed contours). Right Panel: the corresponding multipole moments of redshift space galaxy correlation, respectively shown as symbols with error bars and black solid lines; the red solid lines are the predictions of a f(R) gravity model with f_R0=-1e-6.

• Cosmological emulators: We have developed the FORGE-BRIDGE emulators for cosmologicdal quantities in modified gravity theories (Arnold et al. 2022). One of the applications of these simulations was the development of MGLenS mock weak lensing maps (Haronis-Deraps et al. 2023).
• Constraining gravity using novel weak lensing statisics: Weak lensing is a key probe in modern cosmology and people have mostly used its two-point and one-point statistics to test cosmologicdal models. We have developed other lensing statistics such as weak lensing peak count and clustering, weak lensing voids, to complement these standard probes (Davies et al. 2019a, Davies et al. 2019b, Davies et al. 2020, Davies et al. 2021, Davies et al. 2022, Davies et al. 2024).
• Constraining gravity using galaxy clusters: Mitchell et al. (2018, 2019, 2020, 2021a, 2021b), based on earlier work of He & Li (2016), developed a framework to consistently use the number counts of galaxy clusters to test one of the leading modified gravity theories, f(R) gravity, or chameleon theory. Despite the complicated effect of a chameleon-screened modified gravity on the formation and evolution of structures, it was found that the modified gravity effects on important properties of dark matter haloes, such as their dynamical mass and concentration-mass relation, can be modelled in an exceedingly simple way.
• Constraining gravity using cosmic voids: the leading modified gravity models, such as f(R) gravity and DGP model, employ screening mechanisms to suppress deviation from General Relativity in high-density regions, which makes low-density regions, or cosmic voids, an ideal place to find their signatures and test them, as found by a series of studies (Barreira et al. 2015, 2017; Cautun et al. 2018; Paillas et al. 2019).