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It is known that modeling uncertainties and astrophysical
foregrounds can potentially introduce appreciable bias in the deduced
values of cosmological parameters. While it is commonly assumed that these
uncertainties will be accounted for to a sufficient level of precision,
the level of bias has not been properly quantified in most cases of
interest. We show that the requirement that the bias in derived values of
cosmological parameters does not surpass nominal statistical error,
translates into a maximal level of overall error $O(N^{-1/2})$ on $|Delta
P(k)|/P(k)$ and $|Delta C_{l}|/C_{l}$, where $P(k)$, $C_{l}$, and $N$ are
the matter power spectrum, angular power spectrum, and number of
(independent Fourier) modes at a given scale $l$ or $k$ probed by the
cosmological survey, respectively. For example, future
redshifted-21-cm observations, projected to sample $sim 10^{14}$ modes,
will require knowledge of the matter power spectrum to a fantastic
$10^{-7}$ precision level; realizing the expected potential of future
cosmological surveys, which aim at detecting $10^{6}-10^{14}$ modes,
sets the formidable challenge of reducing the overall level of
uncertainty to $10^{-3}-10^{-7}$.

In a “standard model”, filamentation of femtosecond laser pulses in atmospheric-pressure gases results from dynamic balance of self-focusing via Kerr lensing and defocusing due to ionization-generated plasma. Regarding both of these effects, recent developments cast doubts on the basic model assumptions, which become overstretched as the filamenting laser pulse shortens and increases in intensity. Attempts at revising the role of higher-order Kerr effects lead to a controversy being currently hotly debated. The scenario of plasma emergence has also come under scrutiny. We discuss modifications of these basic effects on microscopic level and show how essentially new features arise in the nonlinear optical response of the medium and call for re-evaluation of the currently accepted picture of filament formation. Further, we consider nonlinear optics of the filament wake channels, which is indicative of the excited system evolution in the channel. Specifically, we discuss four-wave mixing in the nonequilibrium electron gas and dynamic Rabi sidebands originating from the excited atoms.