  We propose methods for extracting limits on the strength of P-odd
interactions of pseudoscalar and pseudovector cosmic fields with electrons,
protons and neutrons. Candidates for such fields are dark matter (including
axions) and dark energy, as well as several more exotic sources described by
standard-model extensions. Calculations of parity nonconserving amplitudes and
atomic electric dipole moments induced by these fields are performed for H, Li,
Na, K, Rb, Cs, Ba+, Tl, Dy, Fr, and Ra+. From these calculations and existing
measurements in Dy, Cs and Tl, we constrain the interaction strengths of the
parity-violating static pseudovector cosmic field to be 7*10^(-15) GeV with an
electron, and 3*10^(-8) GeV with a proton.
