Imprints of screened dark energy on nonlocal quantum correlations

TL;DR

This work proposes using quantum nonlocality as a novel probe of screened dark energy by analyzing how curved space-time and scalar-tensor screening mechanisms modify CHSH violations for entangled spins. By developing a general spin-evolution framework on curved backgrounds and applying it to the chameleon, symmetron, and dilaton mechanisms, the authors show that the CHSH violation is degraded by a curvature-induced Wigner rotation, quantified by $\mathscr{S}=2\sqrt{2}\cos^2\Delta$ where $\Delta$ encodes GR and screening effects through $\mathcal{G}(\epsilon)$, $\gamma(\epsilon)$ and $\beta(\epsilon)$. They identify open regions in parameter space where screening contributions are comparable to GR, thus providing a proof-of-principle for testing screened DE via quantum nonlocality, though experimental detectability remains challenging with present CHSH precision. The study highlights a promising interdisciplinary avenue bridging gravity and quantum information, with suggested extensions to massless particles and frame distinctions to sharpen observational prospects.

Abstract

We investigate how screening mechanisms, reconciling light scalar fields driving cosmic acceleration with local fifth force constraints, can be probed via their impact on non-local quantum correlations between entangled spin pairs, whose evolution on a curved background is affected by General Relativity (GR) and screened modified gravity effects. We consider a gedankenexperiment featuring a pair of massive, spin-1/2 particles orbiting the Earth, evaluating their non-local correlations through spin observables associated to the Clauser-Horne-Shimony-Holt (CHSH) inequality. Using a general formalism developed earlier for curved space-time spin evolution, we compute the effects of screening on the CHSH inequality, finding its degree of violation to be suppressed relative to the flat space-time case. Applying this formalism to the chameleon, symmetron, and dilaton mechanisms, we identify currently unconstrained regions of parameter space where the screening contribution is comparable to that of GR. While detecting these effects will be challenging, our work provides a proof-of-principle for testing screened dark energy through quantum non-locality.

Figures (3)

• Figure 1: Contour plot of $\log_{10}(\Delta_{\text{cham}}/\Delta_{\text{GR}})$ as a function of $n$ and $\beta_m$, where $n$ is the index determining the power-law behavior of the chameleon potential, and $\beta_m$ is the strength of the chameleon coupling to matter. $\Delta_{\text{cham}}$ and $\Delta_{\text{GR}}$ are the chameleon and pure General Relativity contributions to the parameter $\Delta$, respectively, with $\cos^2\Delta$ controlling the degree of violation of the CHSH inequality in our gedankenexperiment. For what concerns the parameters of our gedankenexperiment, as discussed in the main text, we set $\rho_{\infty}\sim 10^{-6}\,\text{eV}^4$, $\Lambda=2.4\,\text{meV}$, and $\zeta\simeq 5 \times 10^{-5}$. The dark blue shaded region of the plot represents the area excluded by the Cassini probe Zhang:2016njn. We see that there is a narrow region of parameter space where the chameleon contribution is significant compared to that of GR.
• Figure 2: As in Fig. \ref{['fig:deltaratiochameleon']}, but for $\log_{10}(\Delta_{\text{sym}}/\Delta_{\text{GR}})$ as a function of $\log_{10}(M_{\text{sym}}/{\text{GeV}})$ and $\log_{10}\lambda$, where $M_{\text{sym}}$ is the scale of the symmetron coupling to matter and $\lambda$ is the dimensionless symmetron self-coupling. The four panels correspond to different representative values of the tachyonic mass: $\mu=1\,{\text{meV}}$ (upper left panel), $1\,{\text{eV}}$ (upper right panel), $1\,{\text{keV}}$ (lower left panel), and $1\,{\text{MeV}}$ (lower right panel). For $\mu=1\,{\text{meV}}$, there is a narrow region of parameter space where the symmetron contribution is significant compared to that of GR. The dark blue shaded region represents the area excluded by Mercury perihelionZhang:2016njn.
• Figure 3: As in Fig. \ref{['fig:deltaratiochameleon']}, but for $\log_{10}(\Delta_{\text{dil}}/\Delta_{\text{GR}})$ as a function of $\log_{10}\lambda_{\text{dil}}$ and $\log_{10}A_2$, the two dimensionless parameters determining the effects of dilaton screening. The two panels correspond to different representative values of the potential scale: $V_0=1\,{\text{MeV}}^4$ (left panel) and $10\,{\text{MeV}}^4$ (right panel). For $V_0=1\,{\text{MeV}}^4$, there is a narrow region of parameter space where the dilaton contribution is significant compared to that of GR. The dark blue shaded region represents the area excluded by Mercury perihelionZhang:2016njn.