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The Cosmological Constant as a Zero-Parameter Prediction of Asymptotic Safety with Standard Model Matter

Year: 2026
Type: preprint
Abstract: In the asymptotic safety approach to quantum gravity, the ultraviolet fixed point of the gravitational renormalisation group constrains all low-energy parameters, potentially making the cosmological constant Λ a calculable prediction rather than an input. We compute this fixed point in the f(R) truncation with full Standard Model matter content (Nₛ = 4, N_D = 45/2, N_V = 12), extending the polynomial expansion from order n = 3 to n = 6. The UV critical surface has dimension three, stable across all orders. Three UV constraints combined with two measured IR quantities — Newton's constant and the inflationary amplitude Aₛ = 2.1 × 10⁻⁹ — leave zero free parameters: Λ is uniquely determined. We identify and correct a factor-of-two error in the matter trace coefficients (confirmed by authors), and discover multiple non-Gaussian fixed points in the coupling space, selecting the physical branch by its eigenvalue structure. The polynomial truncation at n = 6 produces Aₛ ∼ O(1), confirming that the quantitative extraction of Λ requires the full non-perturbative f(R) flow equation. We note the potential complementarity with the topological protection of Λ via gravitational θ-vacua (Alexander, Bernardo, and Hui 2026). Series. This is Paper IV of a six-part series: Paper I (Salmond 2026, DOI: 10.5281/zenodo.20156389): The Cosmological Constant as a Feedback AttractorPaper II (Salmond 2026, DOI: https://doi.org/10.5281/zenodo.20222173): Testing a Connected-Singularity Mechanism for Gravitational Feedback CosmologyPaper III (Salmond 2026, DOI: 10.5281/zenodo.20222351): Two-Boundary Determination of the Cosmological Constant from Asymptotic Safety and Gravitational FeedbackPaper IV (Salmond 2026, DOI: 10.5281/zenodo.20284172): The Cosmological Constant as a Zero-Parameter Prediction of Asymptotic Safety with Standard Model MatterPaper V (Salmond 2026, DOI: 10.5281/zenodo.20286625): Resolving the Spin-2 Boundary Layer in f(R) Asymptotic Safety Paper VI (Salmond 2026, DOI: 10.5281/zenodo.20286761): Zero Crossing of the Cosmological Constant in f(R) Asymptotic Safety with Standard Model Matter
DOI: 10.5281/zenodo.20284172
Language: English
Open Access status: green
OpenAlex ID: W7161700977
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