In this paper, the λφ 4 scalar field effective action, in the one-loop approximation, is calculated by using the Krein space quantization. We show that the effective action is naturally finite and the singularity does not appear in the theory. The physical interaction mass, the running coupling constant and β-function are then calculated. The effective potential which is calculated in the Krein space quantization is different from the usual Hilbert space calculation, however we show that β-function is the same in the two different methods.

The one-loop effective action of QED is calculated by the Schwinger method in Krein space quantization. We show that the effective action is naturally fnite and regularized. It also coincides with the renormalized solution which was derived by Schwinger.Comment: 15 pages, Accepted for publication in Phys.Lett.

The behavior of a non-canonical scalar field within an anisotropic Bianchi type I, spatially homogeneous Universe in the framework of the intermediate inflation will be studied. It will be examined on the condition that both the anisotropy and non-canonical sources come together if there is any improvement in compatibility with the observational data originated from Planck 2015. Based on this investigation, it can be observed that automatically a steep potential which can manage inflation in a better way will be obtained. Additionally, as a common procedure for an inflationary study, we shall try to calculate the related inflationary observables such as the amplitude of the scalar perturbations, scalar and tensor spectral indices, tensor-to-scalar ratio, the running spectral index and the number of e-folds. As an exciting part of our results, we will find that our model has a good consistency compared to data resulting from CMB and different Planck results. To justify our claims, the well-known canonical inflationary scenario in an anisotropic Bianchi type I Universe will also be evaluated.