Casimir, gravitational, and neutron tests of dark energy

We investigate laboratory tests of dark energy theories which modify gravity in a way generalizing the inverse power law chameleon models. We make use of the tomographic description of such theories which captures $f(R)$ models in the large curvature limit, the dilaton and the symmetron. We consider their effects in various experiments where the presence of a new scalar interaction may be uncovered. More precisely, we focus on the Casimir, Eötvös-Washington and neutron experiments. We show that dilatons, symmetrons and generalized chameleon models are efficiently testable in the laboratory. For generalized chameleons, we revise their status in the light of forthcoming Casimir experiments like CANNEX in Amsterdam and show that they are within reach of detection.

Figure 1

The phase diagram of symmetron models for $\mu =\mathrm{\Lambda }=2.4\times 10^{-3}\mathrm{eV}$ as an example where $d<d_c$ and the field vanishes between the plates. The Eötvös-Washington experiment is sensitive to symmetrons for small values of $\lambda$ to the left of the vertical line. For values of $M_{\star }$ larger than the top horizontal line, the symmetron is in its vacuum phase and no constraints apply. Below the bottom curve the symmetron is not excluded while it is excluded between the bottom curve and the horizontal line.

Figure 2

Chameleons are such that the plates are not screened below the bottom curve (brown) and quantum effects are strong for values of the coupling larger than the top curve (green). The middle curve (red) is the limit below which the field is constant between the plates.

Figure 3

The top curve (green) represents the Eötvös-Washington limit. It is in the quantum corrected part of the phase diagram of chameleons which corresponds to $\beta$ being larger than values on the middle curve (red) where quantum effects start being relevant. The lower curve (blue) represents the limit below which the plates are not screened and the torque vanishes. This implies that chameleons are not excluded for very low couplings. The ascending curve (brown) is the Eötvös-Washington limit when the field between the plates is constant and equal to the values inside the plates for $m_{c}d\lesssim 1$. The triangular region between these three curves (red, blue, brown) is excluded by the Eötvös-Washington experiment. For large values of $n\gtrsim 20$, no constraints from Eötvös-Washington apply. Notice that the top part of the exclusion zone is in the quantum corrected region of the parameter space and therefore cannot be trusted.

Figure 4

For large values of ${\beta }_0$ higher than the top curve (green), the chameleons are in their strongly coupled phase and the quantum corrections which are present for values larger than the lower curve (red) are not important anymore.

Figure 5

The distance below which new Casimir experiments with plates of surface areas $1{\mathrm{cm}}^2$ would feel a scalar Casimir force of respectively from top to bottom 0.1 pN, 0.5 pN and 1 pN. At distances $2d=10\mu \mathrm{m}$, the new Casimir experiments with a sensitivity of 0.1 pN would cover most of the chameleon cases.