The Cosmological Constant from an AdS-to-de Sitter f(R) Renormalisation-Group Trajectory with Standard Model Matter
Year: 2026
Type: preprint
Abstract: Note: This has been amended with improved and clearer claims and re-titled as suchWe compute the first renormalisation group trajectory of the cosmological constant in f(R) gravity with full Standard Model matter content (N_S = 4, N_D = 45/2, N_V = 12) at polynomial orders n = 3–6. The ultraviolet non-Gaussian fixed point established in Papers IV and V has Λ̃* ≈ −1.10 (anti–de Sitter) and a three-dimensional critical surface, making Λ calculable once G_N and A_s are measured. We show that this negative UV value is not pathological but expected: Bonanno, Platania & Saueressig (2018) demonstrated that Standard Model matter generically requires λ* < 0 for compatibility with Planck-era inflation. The physical cosmological constant is determined by the trajectory, not the fixed point. Using Radau IIA integration with real eigenvectors, we demonstrate that Λ̃(k) crosses zero at a converged scale t_cross = −1.57 ± 0.01 (k ≈ 0.21 M_Pl), transitioning from anti–de Sitter to de Sitter. The crossing is confirmed at all truncation orders, with Δt_cross = 0.008 across n = 3–6, and Newton's constant remains positive throughout. This is the first demonstration that the Standard Model f(R) NGFP produces a de Sitter infrared through its RG flow. The trajectory confirms that Λ̃ is O(1) at the UV fixed point; combined with Paper III's observation that λ(H₀) = 3Ω_Λ ≈ 2.07 is also O(1) at the Hubble scale, the 122-order hierarchy between Λ_obs and M_Pl⁴ is explained 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 ≪ M_Pl⁴), the coincidence problem (why Ω_Λ ~ Ω_m), 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; the direct extraction of Λ from the trajectory endpoint requires the non-polynomial f(R) solver and is the target of Paper VII.
Author: Salmond, Peter
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161722555
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