  In this Letter we compute analytically the effect of conformal symmetry on
the radiative corrections to the amplitude ratios for O($N$) $\lambda\phi^{4}$
massless scalar field theories in curved spacetime for probing the
two-scale-factor universality hypothesis. For that we employ three distinct and
independent field-theoretic renormalization group methods. The amplitude ratios
values obtained are identical when computed through the three distinct methods,
thus showing their universal character. Furthermore, they are the same as that
obtained in flat spacetime, then satisfying the two-scale-factor universality
hypothesis.
