Abstract
According to the theoretical results obtained in usual quantum cosmology in which the field operator is constructed on the Hilbert space, the power spectrum of the scalar field fluctuations is scale invariant in the inflationary epoch. On the other hand, the observational data predict some deviation from scale-invariance in the power spectrum. It has been shown previously that by using Krein quantization method for constructing field operator, the power spectrum is obtained scale dependent (Mohsenzadeh et al. IJTP 48, 755, 2009). The main goal in this work is to investigate the effect of Krein quantization method on the matter density perturbation at present. The results show if one uses covariant two point function for mass-less minimally coupled scalar field in de Sitter space-time which is calculated via Krein quantization method, the power spectrum of primordial gravitational potential set up during inflation and the power spectrum of matter density perturbation at present deviate from scale-invariant result.
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