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

We establish a method in asymptotic safety with full Standard Model matter content that makes it possible to calculate the cosmological constant Λ with zero free parameters, using only Newton's constant and the inflationary amplitude as inputs. Computing the non-Gaussian fixed point (NGFP) of the gravitational renormalisation group in the f(R) truncation (N_S = 4, N_D = 45/2, N_V = 12) at polynomial orders n = 3 through 6, we find that the UV critical surface has dimension three, stable across all orders. Three UV constraints from the fixed point, combined with two measured quantities — Newton's constant G_N and the inflationary amplitude A_s = 2.1 × 10⁻⁹ — uniquely determine all couplings, leaving Λ as a prediction rather than an input. Along the way we identify and correct a factor-of-two error in the matter trace coefficients (confirmed by the authors of CPR (2009), private communication), and discover multiple non-Gaussian fixed points in the coupling space, selecting the physical branch by its eigenvalue hierarchy θ₁ ≈ 4.0 > θ₂ ≈ 2.3 > θ₃ ≈ 0.5 > 0. The polynomial truncation at n = 6 produces A_s ~ O(1), 8.8 orders of magnitude above the observed value, confirming that the quantitative extraction of Λ requires the full non-perturbative f(R) flow equation — a defined computation whose inputs are established here. 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