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Non-Flat Power Spectra in the CDM Model

Standard inflation with one scalar field produces primordial perturbations with a nearly flat ('Harrison-Zeldovich') power spectrum. Here we consider first, a double inflation spectrum, and second, a massive scalar field with an interaction potential which mimics an early quartic interaction, but fading away at a characteristic scale. We solve numerically the linear perturbation equations with initial conditions due to scalar field quantum fluctuations at the initial horizon crossing. The resulting power spectra are shown to be non-flat, exhibiting either a break or a valley. Using the transfer function of cold dark matter model we study the influence of the shape of primordial power spectra on observations of large scale structure in the universe. We compare the power spectra in redshift space with reconstructed power spectra from the IRAS catalogue. Further we discuss the variances of galaxy counts in cells, and the mass function of galaxy clusters. Comparison with standard CDM demonstrates the advantages and benefits of the more complicated initial spectra.