  According to inflationary cosmology, the CMB anisotropy gives an opportunity
to test predictions of new physics hypotheses. The initial state of quantum
fluctuations is one of the important options at high energy scale, as it can
affect observables such as the CMB power spectrum. In this study a quasi-de
Sitter inflationary background with approximate de Sitter mode function built
over the Bunch-Davies mode is applied to investigate the scale-dependency of
the CMB anisotropy. The recent Planck constraint on spectral index motivated us
to examine the effect of a new excited mode function (instead of pure de Sitter
mode) on the CMB anisotropy at large angular scales. In so doing, it is found
that the angular scale-invariance in the CMB temperature fluctuations is broken
and in the limit $ \ell<200 $ a tiny deviation appears. Also, it is shown that
the power spectrum of CMB anisotropy is dependent on a free parameter with mass
dimension $H<<M_{*}<M_{p}$ and on the slow-roll parameter $\epsilon $.
