In this work, we use recent data on the Hubble expansion rate H(z), the quantity f σ 8 (z) from redshift space distortions and the statistic E g from clustering and lensing observables to constrain in a model-independent way the linear anisotropic stress parameter η. This estimate is free of assumptions about initial conditions, bias, the abundance of dark matter and the background expansion. We denote this observable estimator as η obs . If η obs turns out to be different from unity, it would imply either a modification of gravity or a non-perfect fluid form of dark energy clustering at sub-horizon scales. Using three different methods to reconstruct the underlying model from data, we report the value of η obs at three redshift values, z = 0.29, 0.58, 0.86. Using the method of polynomial regression, we find η obs = 0.57 ± 1.05, η obs = 0.48 ± 0.96, and η obs = −0.11 ± 3.21, respectively. Assuming a constant η obs in this range, we find η obs = 0.49 ± 0.69. We consider this method as our fiducial result, for reasons clarified in the text. The other two methods give for a constant anisotropic stress η obs = 0.15 ± 0.27 (binning) and η obs = 0.53 ± 0.19 (Gaussian Process). We find that all three estimates are compatible with each other within their 1σ error bars. While the polynomial regression method is compatible with standard gravity, the other two methods are in tension with it.

Astrophysical tests of the stability of fundamental couplings, such as the finestructure constant α, are becoming an increasingly powerful probe of new physics. Here we discuss how these measurements, combined with local atomic clock tests and Type Ia supernova and Hubble parameter data, constrain the simplest class of dynamical dark energy models where the same degree of freedom is assumed to provide both the dark energy and (through a dimensionless coupling, ζ, to the electromagnetic sector) the α variation. Specifically, current data tightly constrains a combination of ζ and the present dark energy equation of state w 0 . Moreover, in these models the new degree of freedom inevitably couples to nucleons (through the α dependence of their masses) and leads to violations of the Weak Equivalence Principle. We obtain indirect bounds on the Eötvös parameter η that are typically stronger than the current direct ones. We discuss the model-dependence of our results and briefly comment on how the forthcoming generation of high-resolution ultra-stable spectrographs will enable significantly tighter constraints.

We use astrophysical and atomic clock tests of the stability of the fine-structure constant $\alpha$, together with Type Ia supernova and Hubble parameter data, to constrain the simplest class of dynamical dark energy models where the same degree of freedom is assumed to provide both the dark energy and (through a dimensionless coupling, $\zeta$, to the electromagnetic sector) the $\alpha$ variation. We show how current data tightly constrains a combination of $\zeta$ and the dark energy equation of state $w_0$. At the $95\%$ confidence level and marginalizing over $w_0$ we find $|\zeta|<5\times10^{-6}$, with the atomic clock tests dominating the constraints. The forthcoming generation of high-resolution ultra-stable spectrographs will enable significantly tighter constraints.Comment: 5 pages, 3 figure