{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-simple-prediction-of-the-non-linear-matter","title":"A simple prediction of the nonlinear matter power spectrum in Brans-Dicke gravity from linear theory","arxiv_id":"2403.03786","date":"2024-03-06","proceeding":null,"authors":["Herman Sletmoen","Hans A. Winther"],"abstract":"Brans-Dicke (BD), one of the first proposed scalar-tensor theories of gravity, effectively makes the gravitational constant of general relativity (GR) time-dependent. Constraints on the BD parameter $\\omega$ serve as a benchmark for testing GR, which is recovered in the limit $\\omega \\rightarrow \\infty$. Current small-scale astrophysical constraints $\\omega \\gtrsim 10^5$ are much tighter than large-scale cosmological constraints $\\omega \\gtrsim 10^3$, but the two decouple if the true theory of gravity features screening. On the largest cosmological scales, BD approximates the most general second-order scalar-tensor (Horndeski) theory, so constraints here have wider implications. These constraints will improve with upcoming large-scale structure and cosmic microwave background surveys. To constrain BD with weak gravitational lensing, one needs its nonlinear matter power spectrum $P_\\mathrm{BD}$. By comparing the boost $B = P_\\mathrm{BD}/P_\\mathrm{GR}$ from linear theory and nonlinear $N$-body simulations, we show that the nonlinear boost can simply be predicted from linear theory if the BD and GR universes are parameterized in a way that makes their early cosmological evolution and quasilinear power today similar. In particular, they need the same $H_0 / \\sqrt{\\smash[b]{G_{\\rm eff}(a=0)}}$ and $\\sigma_8$, where $G_{\\rm eff}$ is the (effective) gravitational strength. Our prediction is $1\\%$ accurate for $\\omega \\geq 100$, $z \\leq 3$, and $k \\leq 1\\,h/\\mathrm{Mpc}$; and $2\\%$ up to $k \\leq 5\\,h/\\mathrm{Mpc}$. It also holds for $G_\\mathrm{BD}$ that do not match Newton's constant today, so one can study GR with different gravitational constants $G_\\mathrm{GR}$ by sending $\\omega \\rightarrow \\infty$. We provide a code that computes $B$ with the linear Einstein-Boltzmann solver hi_class and multiplies it by the nonlinear $P_\\mathrm{GR}$ from EuclidEmulator2 to predict $P_\\mathrm{BD}$.","url_abs":"https://arxiv.org/abs/2403.03786v2","url_pdf":"https://arxiv.org/pdf/2403.03786v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-simple-prediction-of-the-non-linear-matter","repo_url":"https://github.com/hersle/jbd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}