  Pseudoscalar or pseudovector cosmic fields, that serve as a source of parity
($\mathcal{P}$) violation, are invoked in different models for cold dark matter
or in the standard model extension that allows for Lorentz invariance
violation. A direct detection of the timelike-component of such fields requires
a direct measurement of $\mathcal{P}$-odd potentials or their evolution over
time. Herein, advantageous properties of chiral molecules, in which
$\mathcal{P}$-odd potentials lead to resonance frequency differences between
enantiomers, for direct detection of such $\mathcal{P}$-odd cosmic fields are
demonstrated. Scaling behavior of electronic structure enhancements of such
interactions with respect to nuclear charge number and the fine-structure
constant is derived analytically. This allows a simple estimate of the effect
sizes for arbitrary molecules. The analytical derivation is supported by
quasi-relativistic numerical calculations in the molecules H$_2$X$_2$ and
H$_2$XO with X $=$ O, S, Se, Te, Po. Parity violating effects due to cosmic
fields on the C--F stretching mode in CHBrClF are compared to electroweak
parity violation and influences of non-separable anharmonic vibrational
corrections are discussed. On this basis it was estimated from a twenty year
old experiment with CHBrClF that bounds on Lorentz invariance violation as
characterized by the parameter $|b^\mathrm{e}_0|$ can be pushed down to the
order of $10^{-17}\,\mathrm{GeV}$ in modern experiments with suitably selected
molecular system, which will be an improvement of the current best limits by at
least two orders of magnitude. This serves to highlight the particular
opportunities that precision spectroscopy of chiral molecules provides in the
search for new physics beyond the standard model.
