  We calculate the 1-loop effect in super-Yang-Mills which preserves
1/4-supersymmetries and is holographically dual to the null-like cosmology with
a big-bang singularity. Though the bosonic and fermionic spectra do not agree
precisely, we do obtain vanishing 1-loop vacuum energy for generic warped
plane-wave type backgrounds with a big-bang singularity. Moreover, we find that
the cosmological "constant" contributed either by bosons or fermions is
time-dependent. The issues about the particle production of some background and
about the UV structure are also commented. We argue that the effective higher
derivative interactions are suppressed as long as the Fourier transform of the
time-dependent coupling is UV-finite. Our result holds for scalar
configurations that are BPS but with arbitrary time-dependence. This suggests
the existence of non-renormalization theorem for such a new class of
time-dependent theories. Altogether, it implies that such a super-Yang-Mills is
scale-invariant, and that its dual bulk quantum gravity might behave regularly
near the big bang.
