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We point out that in models of macroscopic topological defects composed ofone or more scalar fields that interact with standard-model fields viascalar-type couplings, the back-action of ambient matter on the scalar field(s)produces an environmental dependence of the fundamental constants of nature, aswell as spatial variations of the fundamental constants in the vicinity ofdense bodies such as Earth due to the formation of a "bubble-like" defectstructure surrounding the dense body. In sufficiently dense environments,spontaneous symmetry breaking may be inhibited altogether for $\phi^2$interactions, potentially delaying the cosmological production of topologicaldefects. We derive bounds on non-transient variations of the fundamentalconstants from torsion-pendulum experiments that search forequivalence-principle-violating forces, experiments comparing the frequenciesof ground- and space-based atomic clocks, as well as ground-based clocks atdifferent heights in the recent Tokyo Skytree experiment, and measurementscomparing atomic and molecular transition frequencies in terrestrial andlow-density astrophysical environments. Our results constrain the present-daymass-energy fraction of the Universe due to a network of infinite domain wallsproduced shortly after the BBN or CMB epochs to be $\Omega_{\textrm{walls},0}\ll 10^{-10}$ for the symmetron model with a $\phi^4$ potential and $\phi^2$interactions, improving over CMB quadrupolar temperature anisotropy bounds byat least 5 orders of magnitude. Our newly derived bounds on domain walls with$\phi^2$ interactions via their effects of non-transient variations of thefundamental constants are significantly more stringent than previously reportedclock- and cavity-based limits on passing domain walls via transient signaturesand previous bounds from different types of non-transient signatures, under thesame set of assumptions.

physical review. d/physical review. d.

New bounds on macroscopic scalar-field topological defects from  non-transient signatures due to environmental dependence and spatial  variations of the fundamental constants