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Recent observational data have shown two important results about cosmicinflation: First, the primordial power spectrum is approximately scaleinvariant. Secondly, the space-time geometry during inflation is quasi-deSitter. In this paper, we study the background field method and the concept ofnegative norm states in the framework of Krein space to use in early universecosmology. For the inflaton field equation, based on the observations andtaking into account our studies, we suggest an alternative proposal. We willtake the quasi-de Sitter solutions as the physical geometry with the positivenorm and the pure de Sitter solutions as the background geometry with thenegative norm. In the following, we review the consequences of applying theproposal to calculate some cosmological quantities.

Quasi-de Sitter Solution, Negative Norm State and Krein Space in Cosmology