We calculate the 1-loop effect in super-Yang-Mills which preserves 1/4supersymmetries 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 timedependent 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.Keywords: M(atrix) Theories, AdS-CFT Correspondence, Penrose limit and pp-wave background.1 Though the conformal invariance of N=4 SYM is broken, as shown in [10], there is still a residual scale-invariance that guarantees the power-law structure of the SYM correlators.2 We thank C. Bachas for pointing this out to us.