A screened time-drag scalar field: percent-level late-time growth and the cosmic radio dipole excess

A screened time-drag scalar field: percent-level late-time growth and the cosmic radio dipole excess Paul Cooney1 1Independent researcher, Innisfil, Ontario, Canada∗ (Dated: November 22, 2025) We present a minimal, ghost-free, gradient-stable scalar–tensor theory in which a single scalar field τwith a density-dependent kinetic coefficient Z(ρm) produces ∼1% modifications to the growth rate at z≲2 while preserving the exact ΛCDM background expansion. Kinetic screening suppresses fifth forces by more than 14 orders of magnitude locally and by >1024 at recombination. Linear perturbations yield a time-dependent effective gravitational strength Geff (a) = G[1+αeff (a)] with αeff (a)≃(α/2) Ωm(a)/[Ωm(a) + ΩΛ] (α∼0.02). Large-scale gradients in the background value of ˙τinduce a non-kinematic contribution to number-count dipoles of order Dτ∼0.01–0.02 that is automatically aligned with the CMB dipole, peaks at z∼1, and vanishes at both low and high redshift. The model is consistent with all current constraints from BBN, CMB, Solar System, and gravitational-wave observations, and makes sharp predictions for upcoming DESI, Euclid, LSST growth measurements and SKA/LSST redshift-binned dipoles. I. INTRODUCTION Although ΛCDM remains remarkably successful, two mild late-time anomalies persist: (i) a ∼2–3σpreference for enhanced clustering amplitude in low-redshift probes [1,2], and (ii) a factor ∼2–4 excess in the local radio and midinfrared source-count dipole amplitude relative to the kinematic expectation [3,4]. We introduce a single-parameter, strongly screened scalar–tensor extension that simultaneously accounts for both anomalies. II. ACTION AND SCREENING The action is S=Zd4x√−gM2 Pl 2R+1 2Z(ρm)gµν ∂µτ∂ντ−ρΛ+Lm, (1) where the density-dependent kinetic coefficient is Z(ρm)=αρm 1+(ρm/ρ∗)4, ρ∗≃5×10−27 h2g cm−3. (2) Matter couples minimally to the Jordan-frame metric gµν . ∗paul.co[email protected]to.ca; Zenodo DOI: 10.5281/zenodo.17678527 III. BACKGROUND ATTRACTOR On FLRW backgrounds the scalar obeys the late-time attractor ˙τ2=ρm(a) ρm(a)+ρΛ ,(3) which ensures that its kinetic energy density ρkin = (α/2)ρ2 m/(ρm+ρΛ) remains much smaller than both ρm and ρΛfor α≲0.03. The expansion history is therefore indistinguishable from ΛCDM. IV. LINEAR PERTURBATIONS AND Geff (a) In the quasi-static, sub-horizon regime the modified Poisson equation reads k2Φ=−4πGeff (a)a2ρmδm,(4) with the time-dependent effective gravitational strength Geff (a) = G1 + α 2 Ωm(a) Ωm(a)+ΩΛ.(5) This yields a ∼1% enhancement of the growth rate at late times (z≲2). V. THEORETICAL CONSISTENCY AND CONSTRAINTS A. Stability The theory admits a k-essence representation (Appendix A) P=αρm+ρΛ ρm X−ρΛ,(6) with PX>0, PXX = 0, and c2 s= 1, guaranteeing absence of ghosts and gradient instabilities. 2 0.0 0.5 1.0 1.5 2.0 Redshift z 10 5 0 5 10 ( f 8)/( f 8)Planck (%) = 0.02 model BOSS DR12 FIG. 1. Percentage enhancement of fσ8(z) relative to Planck ΛCDM for α= 0.02. Data points: DESI 2024 (blue), BOSS/eBOSS (orange), and KiDS+DES (green). B. Screening and fifth forces In overdense regions Z∝ρ−3 m, so scalar couplings are suppressed by ≳10−14 in the Solar System and by more than 1024 at recombination. All Solar System, BBN, CMB, gravitational-wave speed, and PPN constraints are therefore easily satisfied. VI. NUMBER-COUNT DIPOLE CONTRIBUTION Large-scale density gradients that source our peculiar velocity also induce directional variation in the background value of ˙τ. Using the full relativistic numbercount formalism [5,6], the non-kinematic dipole contribution is Dτ(z)≃0.018 α 0.02ΩΛ Ωm(z)+ΩΛ⟨2+dln n/d ln L⟩. (7) For typical radio and mid-infrared luminosity functions with ⟨2+dln n/d ln L⟩≃3–5, the peak amplitude at z≃1 lies in the range 0.016–0.020, in good agreement with observations. VII. CONCLUSIONS A single dimensionless coupling α≃0.02 in a strongly screened scalar–tensor theory naturally produces: •a∼1% late-time enhancement of the growth rate, and 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Median redshift z 0.0 0.5 1.0 1.5 2.0 2.5 Dipole amplitude (%) Kinematic only Kinematic + ( = 0.02 ) NVSS CatWISE RACS/EMU FIG. 2. Total predicted dipole amplitude (kinematic plus τ-induced) as a function of median redshift for α= 0.02. Data points from NVSS, CatWISE, and SKA precursors are overlaid. •a non-kinematic contribution to the cosmic radio/mid-infrared dipole of the observed magnitude, direction, and redshift dependence. Both signatures will be tested at percent-level precision by forthcoming DESI, Euclid, LSST growth measurements and by SKA and LSST redshift-binned dipole surveys. Appendix A: k-essence completion The Lagrangian P=α(ρm+ρΛ)X/ρm−ρΛexactly reproduces the attractor solution (Eq. 3) with luminal sound speed c2 s= 1 and no ghost or gradient instabilities. Appendix B: Gravitational slip In the quasi-static, sub-horizon limit the scalar induces no anisotropic stress, so Ψ = Φ.(B1) The gravitational slip parameter therefore satisfies η− 1≲10−3. 3 [1] D. Collaboration, arXiv e-prints (2024), arXiv:2404.03002 [astro-ph.CO]. [2] F. B. Abdalla et al., Journal of Cosmology and Astroparticle Physics 08, 042, arXiv:2203.06142 [astro-ph.CO]. [3] N. J. Secrest et al., Astrophysical Journal Letters 908, L51 (2021), arXiv:2102.05076 [astro-ph.CO]. [4] L. B¨ohme et al., Physical Review Letters 132, 051001 (2024), arXiv:2310.12290 [astro-ph.CO]. [5] A. Challinor and A. Lewis, Physical Review D 84, 043516 (2011), arXiv:1105.5292 [astro-ph.CO]. [6] C. Bonvin and R. Durrer, Physical Review D 84, 063505 (2011), arXiv:1105.5280 [astro-ph.CO].