Tuning the Mass of Chameleon Fields in Casimir Force Experiments

We have calculated the chameleon pressure between two parallel plates in the presence of an intervening medium that affects the mass of the chameleon field. As intuitively expected, the gas in the gap weakens the chameleon interaction mechanism with a screening effect that increases with the plate separation and with the density of the intervening medium. This phenomenon might open up new directions in the search of chameleon particles with future long-range Casimir force experiments.

Figure 1

Continuous and dashed lines (left $y$ axis): chameleon pressure between two parallel plates as a function of separation for two configurations: in vacuum (continuous line) and in a gas with density $\rho \approx 5\mathrm{g}/\mathrm{l}$. The calculations were performed fixing the exponent that describes the chameleon potential to $n=4$ and the coupling constant to $\beta =10000$. Symbols (right $y$ axis): Decrease of the chameleon pressure (in percentage) between two parallel plates induced by the screening effect, plotted as a function of separation. The different symbols correspond to the different values of $\beta \rho$ indicated in the legend, where $\rho$ is expressed in $\mathrm{g}/\mathrm{l}$.

Figure 2

Expected chameleon pressure between two parallel plates kept at $30\mu \mathrm{m}$ separation as a function of $\beta \rho$, where $\beta$ is the coupling constant and $\rho$ is the density of the gas in the gap, expressed in $\mathrm{g}/\mathrm{l}$. Different symbols correspond to different values of the exponent $n$, corresponding to different slopes of the chameleon potential.

Figure 3

Symbols: Expected change of the chameleon pressure between two parallel plates kept at $30\mu \mathrm{m}$ separation when the gap is filled with gaseous Xe at room temperature and pressure $P$. Different symbols correspond to different values of the coupling constant $\beta$. Line: expected change of the electrostatic force in the same experimental configuration.

Figure 4

Expected change of the total pressure between two parallel plates kept at $30\mu \mathrm{m}$ separation when the gap is filled with gaseous Xe at room temperature and pressure $P$. Different symbols correspond to different values of the coupling constant $\beta$. The line represents the result expected in the absence of chameleon interaction.