Multi-Field Dilaton Screening Beyond the Thin-Shell Mechanism

Abstract

We analyse screening in multi-field scalar-tensor theories, focusing on systems with a dilaton coupled to matter and an axion with a dilaton-dependent kinetic term, in the presence of both planetary and stellar density profiles. Using analytic arguments and fully coupled numerical solutions, we identify a regime in which full screening for a dark-energy-light, effectively unpinned string-dilaton, can occur without fine-tuning. The backreaction of the dilaton's partnered axion field can suppress the exterior scalar charge by selecting a minimum-energy configuration (the BBQ mechanism), yielding robust screening for generic axion gradients. In this regime screening is achieved by cancelling the dilaton's gradient rather than localising it. This reduces the exterior scalar charge and allows for gravity tests in the solar system to be passed. We then show that the more familiar thin-shell intuition need not apply in the multi-field setting. Axion surface gradients can drastically reshape the dilaton profile and drive a more localised transition without generically suppressing the fifth force. The exterior charge can remain essentially unchanged or even be enhanced as the shell is made thinner by a kinetically coupled field. Multi-field two-derivative dynamics therefore decouple localisation in thin shells from screening, evade single-field no-go arguments, and reopen viable parameter space for cosmologically light dilaton-like scalars with strong couplings to matter.

Figures (16)

• Figure 1: Axion--dilaton profiles illustrating the scale hierarchy underlying the thin--shell approximation. Top: dilaton displacement; middle: axion; bottom: conserved density profile. The dashed line marks the surface $r=R_s$. The two curves correspond to the cut-off scale in \ref{['eq:U_ax']} being $\Lambda_{\mathfrak a}=10^{-3}M_{\rm pl}$ (broad axion transition) and $\Lambda_{\mathfrak a}=10^{-5}M_{\rm pl}$ (surface--localised axion transition), showing how a macroscopic axion gradient drives $\chi$ well inside the object. In both cases, $W_0 = 1$, $\zeta = \sqrt{2}$, and the vacuum axion mass is taken to be $m_{\mathfrak a} = 5\times10^{-17}\rm eV$.
• Figure 2: Radial profiles (First: dilaton, Second: axion, Third: density, Fourth: dilaton charge) for different axion boundary jumps $\Delta{\mathfrak a}={\mathfrak a}_{+}-{\mathfrak a}_{-}$ and a wide axion gradient using the flux conserving treatment for the axion described in \ref{['app:methodology']} instead of solving the full equations of motion, with $\ell_{\mathfrak a} = 0.15$. Here we took $\beta = 0.2$, $\zeta = \sqrt{2}$ and $W_0 = 1$. We also took boundary conditions for the dilaton field $\chi'(0) = 0$, $\chi(0) = \chi_c$ corresponding to the pinned regime. Crucially for numerical stability in the presence of exponential factors of the dilaton field, we choose an Earth--like density $\rho_c\simeq 10^{-9}M_{\rm pl}^2/R_s^2$, with $V_0=0.5\,\rho_c$ and $\rho_{\rm env}=0.1\,\rho_c$ (an unrealistically small hierarchy).
• Figure 3: Radial profiles for the same parameters as in \ref{['fig:thick_ramp_profiles']} except for $\rho_{\rm env} = 10^{-8} \rho_c$ and a star-like object density profile described in \ref{['app:methodology']}. In this case we solve the full multi-field equations using the microphysical parameters $\Lambda_{\mathfrak a} = 3\times10^{-6}M_{\rm pl}$ and $m_{\mathfrak a} = 3\times10^{-16}\,\text{eV}$.
• Figure 4: Radial profiles for an unpinned dilaton with axion boundary jumps $\Delta{\mathfrak a}={\mathfrak a}_+-{\mathfrak a}_-$. We used the same parameters as \ref{['fig:thick_ramp_profiles']} but swapped a boundary condition at $\chi(0) = \chi_c$ with an asymptotic boundary condition $\chi(r_{\rm max}) = \chi_{\rm env}$. No parametrically thin rolling layer forms, consistent with $m_\chi R_s\ll1$. Axion gradients modify the global profile rather than suppressing the exterior scalar charge.
• Figure 5: Field profiles and dilaton charge evaluated for a pinned scalar in the presence of a suppressing coupling to the axion in a stellar density profile outlined in \ref{['app:methodology']}. Here we took $W_0 = 1$, $V_0 = 10^{-5}\rho_c$ and $\rho_{\rm env} = 10^{-15}\rho_c$. We solve the full coupled two-field system using the microphysical axion potentials \ref{['eq:U_ax']} and \ref{['eq:V_ax']} with $\Lambda_{\mathfrak a} = 3\times10^{-7}M_{\rm pl}$ and $m_{\mathfrak a} = 3\times10^{-16}\,\text{eV}$.