What question did this study set out to answer?

This research aims to calculate the cosmological constant using a method in asymptotic safety with standard model matter, without any free parameters.

May 25, 2026Open Access

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

Key Points

This research aims to calculate the cosmological constant using a method in asymptotic safety with standard model matter, without any free parameters.
Utilized Newton's constant and inflationary amplitude as inputs for calculations.
Computed the non-Gaussian fixed point (NGFP) in the gravitational renormalization group within the f(R) truncation.
Identified and corrected a factor-of-two error in matter trace coefficients.
The cosmological constant Λ is uniquely predicted when using Newton's constant (G_N) and inflationary amplitude (A_s = 2.1 × 10⁻⁹).
Found a UV critical surface dimension of three that remains stable across polynomial truncations from n = 3 to 6.
The polynomial truncation produced results significantly above the observed cosmological constant, indicating the need for non-perturbative methods.

Abstract

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 (NS = 4, ND = 45/2, NV = 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 GN and the inflationary amplitude Aₛ = 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 Aₛ ~ 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

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

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