What question did this study set out to answer?

This research aims to compute the renormalization group trajectory of the cosmological constant in f(R) gravity while incorporating Standard Model matter.

May 25, 2026Open Access

Zero Crossing of the Cosmological Constant in f(R) Asymptotic Safety with Standard Model Matter

Puntos clave

This research aims to compute the renormalization group trajectory of the cosmological constant in f(R) gravity while incorporating Standard Model matter.
Computed renormalization group trajectories at polynomial orders n = 3–6.
Utilized Radau IIA integration to analyze the crossing of the cosmological constant.
Conducted consistency checks against Friedmann equation with Λ-independent inputs.
The cosmological constant crosses zero at t_cross = −1.57 ± 0.01, transitioning from anti-de Sitter to de Sitter.
The trajectory demonstrates that the fixed point value of Λ̃ is O(1) at the UV fixed point.
Λ calculated as 1.09 × 10^−52 m^−2 aligns within 1.3% of the Planck 2018 value.

Resumen

Note: This has been amended with improved combined with Paper III's observation that λ (H₀) = 3 Ω_Λ ≈ 2. 06 is also O (1) at the Hubble scale, the 122-order hierarchy between Λₒbs and MPl⁴ arises as the squared ratio of these two boundary scales. It is not a fine-tuning. Combined with Paper I's feedback attractor as the infrared boundary condition and Paper III's two-boundary framework, the trajectory addresses all three aspects of the cosmological constant problem: the old problem (why Λ ≪ MPl⁴), the coincidence problem (why Ω_Λ ∼ Ωₘ), and the determination problem (what fixes Λ). A consistency check against the Friedmann equation with Λ-independent inputs yields Λ = 1. 09 × 10^−52 m^−2, within 1. 3% of the Planck 2018 value. Paper V's spatial ODE method achieves Aₛ within 0. 5 decades of the Planck target at n = 6; closing this gap at higher truncation order (Paper VII) would enable the direct extraction of Λ from the trajectory endpoint. --This is Paper VI of a six-part series, no more papers are planned. 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

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