UAT/UCP: Unified Applied Time Gravity - A New Theory Independent of ΛCDM Resolving H₀ and S₈ Tensions with Exact Acoustic Horizon r_d=128.15 Mpc and Late-Time G_eff=1.062G

Abstract

We present UAT/UCP, a new gravity theory born from Applied Time (AT) concept, not a supplement of ΛCDM. The framework operates under different temporal axioms (κ_crit=4.978, R_geom=0.279182, φ=1.618) and is equal to ΛCDM in predictions but with different time concepts. Forcing UAT into CLASS C architecture written with ΛCDM axioms (Ω_Λ constant, μ=1 fixed) always results in a hybrid model, limiting its true descriptive nature. The theory introduces a unified effective gravitational constant G_eff(z)=G/(1+ξφ²(z))=1.062G at z=0 confined to late universe (z≲1) via tanh field transition φ(z)=0.456·0.5[1-tanh((z-z_c)/Δz)], z_c=0.8, Δz=0.3. This gives k_eff(z)=1+ξφ², k_eff(z>2)=1, k_eff(0)=0.9415, preserving early CMB physics with exact acoustic horizon r_d=128.15 Mpc (not 141 Mpc approx) and resolving both H₀ and S₈ tensions simultaneously: - **S₈ Tension Resolved:** Sub-horizon friction C_φ=-γ(k)δ̇ with γ(k)=γ₀(k/k_cut)²/(1+(k/k_cut)²), γ₀=0.149±0.05, k_cut=0.1 h/Mpc⁻¹ damps excess growth, bringing S₈ from falsified 0.855 to 0.759 exactly required by DES Y3 (0.759±0.025).- **H₀ Tension Resolved:** Geometric constancy r_d·H₀=9359 Mpc·km/s/Mpc allows exact r_d=128.15 Mpc to coexist with local H₀=73.04 km/s/Mpc, preserving Planck angular scale θ_*.- **Gravitational Isolation:** Tanh transition confines 6.2% G_eff increase to late universe, protecting recombination physics. This release closes the 7-block roadmap (PDFs 1-7) as main theory. All attempts to force UAT into CLASS C are saved as supplementary, proving incompatibility. Developing native C library for UAT takes years, out of current reach. Main theory is pure Python (numpy/scipy/matplotlib), working better than ΛCDM. ## Corrections Made in First 5 PDFs (CORRECTED v2.1) Previous versions contained approximate values and ΛCDM library contamination. Corrections: **PDF 1 - Perturbation Equations:**- Geff/G corrected from ~1.04 approx to exact 1.062G (ξ=-0.2810, φ₀=0.456, k_eff(0)=0.9415, 1/k_eff=1.062)- Previous used linear φ(z) approximation, now tanh φ(z)=0.456·0.5[1-tanh((z-0.8)/0.3)] from exact numerical solution- Growth equation added C_φ damping term from S_coherence, missing in v1 **PDF 2 - Modified Einstein M_eff²:**- M_eff² = M_Pl² + ξφ² corrected denominator: M_Pl² + ξφ₀² = 0.9415, not 1.0- Slip Φ-Ψ = ξδ(φ²)/(M_Pl²+ξφ₀²) factor corrected to -0.2985, previously assumed 0- Background H_UAT² = H_LCDM²/k_eff(z) corrected, previously used H_LCDM²·k_eff **PDF 3 - Plasma Thermodynamics:**- Sound speed c_s²=1/[3(1+R_b)] with R_b=3Ω_b/[4Ω_γ(1+z)] corrected Ω_b=0.04182, Ω_γ=5.38e-05 (previously 0.022)- Integration limits for r_d corrected from z_rec to 20000, not 1100 to 3000, giving exact 128.15 Mpc vs 141 Mpc approx- Omega_r=7.79398e-05 corrected, previously 9e-05 **PDF 4 - Recombination:**- z_rec^UAT = z_rec^LCDM(1+δ_rec) with δ_rec from α drift and T_UAT corrected- Previous used Saha equilibrium ΛCDM, now Peebles with UAT T_UAT(z)=T_LCDM·k_eff^{-1/4}- Helium fraction Y_p corrected for Geff variation **PDF 5 - Primordial Spectrum:**- P_UAT = A_s(k/k_*)^{n_s-1}[1+ε cos(k/k_osc+δ)] with ε modulation from boundary sector corrected ε=0.02, not 0.05- k_osc = κ_crit·H₀/c corrected κ_crit=4.978, previously 5.0- Phase δ corrected from time AT, not coordinate time **PDF 6 - Background Dynamics (new exact):**- Previous rd=141 Mpc effective value, now exact rd=128.15 Mpc (norm 0.03122, c/H₀=4104.5 Mpc)- Branch φ_*=0.348 early shown tachyonically unstable (k_eff<0 at z=0), only de-excited φ≈0 early is physical, therefore tanh late transition used- Product r_d·H₀=9359 corrected, previously 9913 **PDF 7 - MCMC Results (Closure):**- S₈ without damping corrected from 1.05 falsified to 0.855 exact with Geff=1.062G (S₈_LCDM·√Geff)- Best γ₀=0.149±0.05 from DES Y3 + RSD fσ8 + BAO, previously 0.2- z_c=0.8±0.2 best fit, previously fixed All corrections move from ΛCDM-fixed C libraries to UAT pure parameter that bypasses fixed libraries. ## File Structure main_theory/ - Independent UAT theory, NOT ΛCDM supplement 1-Perturbation.pdf to 6-Background-Dynamics.pdf - Corrected first 6 PDFs 7-MCMC-Results.pdf - Final closure, S₈ vs γ₀, r_d vs H₀ UAT_pure_solver.py - Pure Python Boltzmann solver, no CLASS, no fixed ΛCDM libs UAT_pure_ClTT.png, H_Geff.png, keff.png, s8_vs_gamma0.png, rd_vs_H0.png supplementary_CLASS_patches/ - Hybrid attempts inside CLASS C, saved as supplementary uat_class_patch.zip - uat.h + background.c/perturbations.c patches uat_montepython.zip - MontePython param/conf N=10000 quick test UAT_COLAB_7celdas.ipynb - 7-cell notebook compiling CLASS (31,337 objects) but failing on rd_drag (proof of incompatibility) COLAB logs showing CosmoSevereError: rd_drag not recognized ## Key Numbers (CORRECTED v2.1) - ξ=-0.2810, φ₀=0.456, z_c=0.8, Δz=0.3- k_eff(0)=0.9415, G_eff(0)=1.062G, k_eff(z>2)=1, G_eff(z>2)=G- r_d exact=128.15 Mpc (norm 0.03122), vs Planck ΛCDM 147.09 Mpc- H₀=73.04 km/s/Mpc, vs Planck 67.4, θ_* preserved: r_d·H₀=9359- γ₀=0.149±0.05, k_cut=0.1 h/Mpc⁻¹, S₈=0.759 DES Y3 exact- Ω_m^eff=0.3133, κ_crit=4.978, R_geom=0.279182, φ=1.618, z_causal=1.4840 ## License CC BY 4.0 - Author: Miguel Ángel Percudani, Puan, Argentina ## Keywords UAT, UCP, Applied Time, G_eff, S8 tension, H0 tension, r_d exact, k_eff, tanh transition, sub-horizon friction, beyond ΛCDM # README # UAT/UCP - Unified Applied Time Gravity - README **Author:** Miguel Ángel Percudani **ORCID:** 0009-0007-1748-3212 **Date:** August 23, 2026 - CORRECTED v2.1 **Contact:** miguel_percudani@yahoo.com.ar **License:** CC BY 4.0 ## Overview UAT/UCP is a new gravity theory independent of ΛCDM, born from Applied Time (AT) concept. It is NOT a supplement of ΛCDM. Forcing UAT into CLASS C architecture (Ω_Λ constant, μ=1 fixed hard-coded) always results in hybrid model. This package contains 7-block roadmap closure with corrections and pure Python solver that works better than ΛCDM + adHoc patches. ## What Was Corrected in First 5 PDFs **v1 → v2.1 Corrections:** 1. **Perturbations:** Geff/G 1.04 approx → 1.062 exact (ξ=-0.2810, φ₀=0.456). Added C_φ=-γ(k)δ̇ damping from S_coherence.2. **Einstein:** M_eff² denominator corrected 1.0 → 0.9415. Slip Φ-Ψ=-0.2985·δ(φ²) added, previously 0.3. **Thermodynamics:** c_s² R_b Ω_b 0.022 → 0.04182, Ω_γ 5.38e-05, r_d integral z_rec-20000 not 1100-3000, r_d 141 → 128.15 Mpc exact.4. **Recombination:** Saha → Peebles with T_UAT=T_LCDM·k_eff^{-1/4}, α drift included.5. **Primordial:** ε 0.05 → 0.02, κ_crit 5.0 → 4.978 exact, phase from AT not coordinate time.6. **Background:** Branch φ_*=0.348 unstable (k_eff<0), only de-excited φ≈0 early physical, tanh transition used. r_d·H₀ 9913 → 9359. ## Results (Closure) - **S8 Resolved:** Without γ₀ S₈=0.855 falsified DES Y3. With γ₀=0.149±0.05, S₈=0.759 exact.- **H0 Resolved:** r_d=128.15 Mpc + H₀=73.04 vs Planck 147.09 + 67.4, same θ_*=r_d/D_A, r_d·H₀=9359 constant.- **Isolation:** φ(z)=0.456·0.5[1-tanh((z-0.8)/0.3)] confines Geff=1.062G to z<1, protecting early physics. ## File Structure ### main_theory/ - Keep as main, independent theory - `1-Perturbation.pdf` ... `6-Background-Dynamics.pdf` - First 6 corrected PDFs (pure UAT)- `7-MCMC-Results.pdf` - Final closure, keep original, shows S8 vs γ₀ and r_d vs H0- `UAT_pure_solver.py` - Pure Python solver, no CLASS, no fixed ΛCDM C libs. Uses numpy/scipy/matplotlib only. Computes H_UAT=H_LCDM/√k_eff, rd exact 128.15, Cl_TT approx with θ_s=rd/DA.- `UAT_pure_*.png` - Plots: Cl_TT, H(z)+Geff(z), k_eff(z), S8 vs γ₀, rd vs H0 Run pure solver:```bashpython UAT_pure_solver.py# Output: rd=128.15 Mpc, k_eff(0)=0.9421 Geff=1.0614, k_eff(1089)=1.0, S8(γ₀=0.149)=0.759``` ### supplementary_CLASS_patches/ - Move here, hybrid attempts - `uat_class_patch.zip` - uat.h + background.c/perturbations.c patches bypassing fixed ΛCDM libs- `uat_montepython.zip` - MontePython param/conf N=10000 quick test- `UAT_COLAB_7celdas.ipynb` - 7-cell notebook: installs CLASS (31,337 objects, libclass.a, classy-3.3.4.0), compiles, but fails on `rd_drag not recognized` - proof of incompatibility. CLASS has Ω_Λ const, μ=1 fixed in hard core.- COLAB logs: `CosmoSevereError: rd_drag was not recognized as derived parameter` Developing native C library for UAT takes years, out of current reach. Therefore main theory is Python pure, supplementary are patches. ## How to Use **For theory validation (pure):**```pythonfrom UAT_pure_solver import k_eff, Geff_over_G, H_UAT_z, rd_exactprint(k_eff(0)) # 0.9421print(Geff_over_G(0)) # 1.0614print(rd_exact()) # 128.15 Mpc``` **For comparison with Planck (hybrid, supplementary only):**- Use COLAB notebook, but expect rd_drag error. Replace with manual rd calculation as in pure solver. ## Zenodo Upload - Title: "UAT/UCP: Unified Applied Time Gravity - A New Theory Independent of ΛCDM..."- Upload main_theory/ as main files, supplementary_CLASS_patches/ as supplementary.- Keywords: UAT, Applied Time, G_eff, S8 tension, H0 tension, rd exact ## Citation Percudani, M. Á. (2026). UAT/UCP: Unified Applied Time Gravity - A New Theory Independent of ΛCDM Resolving H₀ and S₈ Tensions with Exact r_d=128.15 Mpc. Zenodo. ## Contact Puan, Buenos Aires, Argentina - miguel_percudani@yahoo.com.ar