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Solar System Experiments in the Search for Dark Energy and Dark Matter

Slava G. Turyshev

TL;DR

This work develops a concrete framework to connect cosmology-scale gravity signatures, encapsulated by linear-response functions $μ(z,k)$ and $Σ(z,k)$, to local Solar System residuals under environmental screening. By assuming a universal conformal coupling $A(φ)$ and applying chameleon or Vainshtein screening, the authors map cosmological posteriors into explicit local targets for $γ$, $β$, $η_{EEP}$, and potential Yukawa or ULDM signals, while enforcing the GW-speed bound $|c_T/c-1|<10^{-15}$. They advocate a two-branch program: (i) a detection-first approach where a verified local anomaly triggers joint cosmology-local modeling, and (ii) guardrails ensuring Solar System tests prune unscreened regions; they forecast concrete sensitivities such as $|γ-1| ext{ of a few }×10^{-6}$, $η_{EEP} ext{ of }(1$–$10)×10^{-17}$, and $| rac{ ext{d}G}{ ext{d}t}/G| ext{ of }(3$–$5)×10^{-15}$ yr$^{-1}$. The paper also outlines near-term portfolios leveraging existing radio/optical links, mm-LLR, clock networks, and ephemerides, with explicit triggers for dedicated missions if the microphysical model predicts detectable local signatures. Overall, Solar System experiments serve to enforce universal guardrails for DE/DM models while offering targeted discovery channels for ultralight fields and long-range forces, thereby complementing cosmology-driven probes.

Abstract

We reassess the realistic discovery reach of Solar-System experiments for dark energy (DE) and dark matter (DM), making explicit the bridge from cosmology-level linear responses to local, screened residuals. In scalar-tensor frameworks with a universal conformal coupling $A(φ)$ and chameleon/Vainshtein screening, we map cosmological responses $\{μ(z,k),Σ(z,k)\}$ inferred by DESI and \emph{Euclid} to thin-shell or Vainshtein residuals in deep Solar potentials $Φ_N$. We emphasize a two-branch strategy. In a detection-first branch, a verified local anomaly -- an Einstein equivalence principle (EEP) violation, a Shapiro-delay signal with $|γ-1|\sim\mathrm{few}\times 10^{-6}$, an AU-scale Yukawa tail, or a ultralight DM (ULDM) line in clocks/atom interferometers in space (AIS) -- triggers a joint refit of cosmology and Solar-System data under a common microphysical parameterization $\{V(φ),A(φ)\}$. In a guardrail branch, Solar-System tests enforce constraints (EEP; PPN parameters $γ,β$; and $\dot G/G$) and close unscreened or weakly screened corners indicated by cosmology. We forecast, per conjunction, $|γ-1|\lesssim (2-5)\times 10^{-6}$ (Ka-/X-band or optical Shapiro), $η_{EEP}\sim (1\mbox{--}10)\times 10^{-17}$ (drag-free AIS), $|\dot G/G|\sim(3-5)\times10^{-15}\,\mathrm{yr^{-1}}$ (sub-mm-class LLR), a uniform ~2x tightening of AU-scale Yukawa/DM-density bounds, and $(3-10)\times$ improved ULDM-coupling reach from clocks. For a conformal benchmark, $μ_{ lin,0}=0.10$ implies $χ\simeq \sqrt{μ_{lin,0}/2}$ and a Sun thin shell $ΔR/R\lesssim (1/3χ)\sqrt{|γ-1|/2}=2.4\times 10^{-3}$ at $|γ-1|=5\times 10^{-6}$; Vainshtein screening at 1 AU yields $|γ-1|\lesssim 10^{-11}$, naturally below near-term reach. We recommend a cost-effective guardrail+discovery portfolio with explicit triggers for escalation to dedicated missions.

Solar System Experiments in the Search for Dark Energy and Dark Matter

TL;DR

This work develops a concrete framework to connect cosmology-scale gravity signatures, encapsulated by linear-response functions and , to local Solar System residuals under environmental screening. By assuming a universal conformal coupling and applying chameleon or Vainshtein screening, the authors map cosmological posteriors into explicit local targets for , , , and potential Yukawa or ULDM signals, while enforcing the GW-speed bound . They advocate a two-branch program: (i) a detection-first approach where a verified local anomaly triggers joint cosmology-local modeling, and (ii) guardrails ensuring Solar System tests prune unscreened regions; they forecast concrete sensitivities such as , –, and – yr. The paper also outlines near-term portfolios leveraging existing radio/optical links, mm-LLR, clock networks, and ephemerides, with explicit triggers for dedicated missions if the microphysical model predicts detectable local signatures. Overall, Solar System experiments serve to enforce universal guardrails for DE/DM models while offering targeted discovery channels for ultralight fields and long-range forces, thereby complementing cosmology-driven probes.

Abstract

We reassess the realistic discovery reach of Solar-System experiments for dark energy (DE) and dark matter (DM), making explicit the bridge from cosmology-level linear responses to local, screened residuals. In scalar-tensor frameworks with a universal conformal coupling and chameleon/Vainshtein screening, we map cosmological responses inferred by DESI and \emph{Euclid} to thin-shell or Vainshtein residuals in deep Solar potentials . We emphasize a two-branch strategy. In a detection-first branch, a verified local anomaly -- an Einstein equivalence principle (EEP) violation, a Shapiro-delay signal with , an AU-scale Yukawa tail, or a ultralight DM (ULDM) line in clocks/atom interferometers in space (AIS) -- triggers a joint refit of cosmology and Solar-System data under a common microphysical parameterization . In a guardrail branch, Solar-System tests enforce constraints (EEP; PPN parameters ; and ) and close unscreened or weakly screened corners indicated by cosmology. We forecast, per conjunction, (Ka-/X-band or optical Shapiro), (drag-free AIS), (sub-mm-class LLR), a uniform ~2x tightening of AU-scale Yukawa/DM-density bounds, and improved ULDM-coupling reach from clocks. For a conformal benchmark, implies and a Sun thin shell at ; Vainshtein screening at 1 AU yields , naturally below near-term reach. We recommend a cost-effective guardrail+discovery portfolio with explicit triggers for escalation to dedicated missions.

Paper Structure

This paper contains 42 sections, 79 equations, 4 figures, 12 tables.

Table of Contents

  1. Introduction and scope
  2. Recent cosmology results and modified gravity
  3. Cosmological probes and linear response
  4. DESI
  5. Euclid
  6. Theory and screening regimes
  7. From cosmology to local residuals: screening map and targets
  8. Illustrative $\gamma$ mapping
  9. Earth thin shell and EEP guardrails
  10. Considering ULDM examples
  11. Solar System observables: status and credible improvements
  12. Einstein equivalence principle and composition dependence
  13. Parameterized post-Newtonian gravity: $\gamma$ and $\beta$
  14. Time variation of $G$ and the strong-equivalence principle
  15. Solar System dark-matter density and Yukawa tails
  16. ...and 27 more sections

Figures (4)

  • Figure 1: Solar System sensitivities with advanced links and analysis. (a) Residual plasma time (group) delay, normalized to X-band (8.4 GHz), versus $f$ [Hz], following the $f^{-2}$ law in \ref{['eq:plasma-delay']}. (b) $1\sigma$ sensitivity to $|\gamma-1|$ versus solar impact parameter $b/R_\odot$, with Cassini ($2.3\times10^{-5}$) and a $10^{-6}$ target for reference. Curves assume a post-calibration residual time-delay budget $\le 0.1\,$ns for $b\gtrsim 5\,R_\odot$ (40 ps plasma/turbulence, 30 ps non-gravitational, 30 ps timing/transfer). (c) Maximum solar thin-shell fraction $\Delta R/R$ implied by a null $|\gamma-1|$ bound, as a function of the cosmology response $\mu_{\rm lin,0}$, using \ref{['eq:chi_from_mu']}--\ref{['eq:thin-shell-bound']}. (d) Normalized clock sensitivity to a fine‑structure‑constant-$\alpha$-coupled coefficient $d_e$ vs $m_\phi$ from the coherence-time/bandwidth scalings, (\ref{['eq:clock-dm']})--\ref{['eq:tc-correct']}.
  • Figure 2: Consolidated Yukawa-strength limits $|\alpha_Y|$ versus range $\lambda$. The solid curve is a smooth envelope anchored to representative ephemeris/small-body bounds $|\alpha_{\tt Y}|=10^{-9}$ at $\lambda=10^{9}\,\mathrm{m}$ and $|\alpha_{\tt Y}|=10^{-10}$ at $\lambda=10^{13}\,\mathrm{m}$; the dashed curve is a uniform factor-of-two tightening consistent with DSN reprocessing and improved asteroid catalogs (Tables \ref{['tab:mass-range']} and \ref{['tab:benchmarks']}). The upper axis shows $m=\hbar c/\lambda \simeq 1.97327\times 10^{-7}\,{\rm eV\cdot m}/\lambda$.
  • Figure 3: Thin-shell requirement for the Sun implied by a null detection of solar-conjunction PPN $\gamma$ at sensitivity $|\gamma-1|_{\max}$ as a function of the cosmology-level linear response $\mu_{\rm lin,0}$ in the conformal scalar benchmark (adopts $k\simeq 0.1\,h\,\mathrm{Mpc}^{-1}$ for $\mu_{\rm lin,0}$; see Sec. \ref{['sec:theory']}.) For $\mu_{\rm lin,0}\simeq 0.10$, the $|\gamma-1| \lesssim 5\times10^{-6}$ target implies $\Delta R/R \lesssim 2.4\times 10^{-3}$ [Eqs. (\ref{['eq:chi_from_mu']})--(\ref{['eq:phi_contrast_bound']})]. (See Appendix \ref{['sec:recipe']}.)
  • Figure 4: Null $\eta~\Rightarrow$ Earth thin-shell bound. Uses the AIS/EEP relation \ref{['eq:eta-AIS']} with the thin-shell expression \ref{['eq:thin-shell']} and the cosmology bridge $\chi=\sqrt{\mu_{\rm lin,0}/2}$ from \ref{['eq:chi_from_mu']}. In the screened-source limit, $\Delta R_\oplus/R_\oplus \le \eta_{\max}/(6\,\chi\,|\Delta K_{\rm eff}|)$ [cf. \ref{['eq:eta-EEP-worked']}], so stronger $\eta_{\max}$ and larger $|\Delta K_{\rm eff}|$ push the required thin shell lower.