  We propose methods and present calculations that can be used to search for
evidence of cosmic fields by investigating the parity-violating effects,
including parity nonconservation amplitudes and electric dipole moments, that
they induce in atoms. The results are used to constrain important fundamental
parameters describing the strength of the interaction of various 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. Existing parity nonconservation
experiments in Cs, Dy, Yb, and Tl are combined with our calculations to
directly place limits on the interaction strength between the temporal
component, b_0, of a static pseudovector cosmic field and the atomic electrons,
with the most stringent limit of |b_0^e| < 7*10^(-15) GeV, in the laboratory
frame of reference, coming from Dy. From a measurement of the nuclear anapole
moment of Cs, and a limit on its value for Tl, we also extract limits on the
interaction strength between the temporal component of this cosmic field, as
well as a related tensor cosmic-field component d_00, with protons and
neutrons. The most stringent limits of |b_0^p| < 4*10^(-8) GeV and |d_00^p| <
5*10^(-8) for protons, and |b_0^n| < 2*10^(-7) GeV and |d_00^n| < 2*10^(-7) for
neutrons (in the laboratory frame) come from the results using Cs. Axions may
induce oscillating P- and T-violating effects in atoms and molecules through
the generation of oscillating nuclear magnetic quadrupole and Schiff moments,
which arise from P- and T-odd intranuclear forces and from the electric dipole
moments of constituent nucleons. Nuclear-spin-independent parity
nonconservation effects may be enhanced in diatomic molecules possessing close
pairs of opposite-parity levels in the presence of time-dependent interactions.
