Imprints of anisotropy on the power spectrum in matter dominated bouncing universe as background

In this paper, we aim to investigate the effects of the anisotropy on the scale-invariant power spectrum considering the matter-dominated collapsing universe as background and look for the deviations from the scale invariance. Having set up this background, we consider a test massless scalar field and work out the correlations for the field, first by using the perturbative approach in which the anisotropic background is approximated with an effective isotropic metric represented by the metric of matter dominated collapsing universe, second by directly solving the field equation numerically, and then obtain the power spectrum for the range of modes which are of cosmological interest. Using both techniques, we get an upper bound on the deviation in the power spectrum from the scale invariance. We also work out the power spectrum for much smaller modes and look at whether it is possible to explain the observed anomalies in CMB via the matter bounce scenario.