and f = exp(α|p x |) with F (u) = (1 − e −|u| ) sign u used after Taylor expansion in [23,24] and all implying K ≈ 1/α and a ≈ α ≈ ℓ P .Coordinate space turns out to exhibit features of discreteness [25] and continuity at the same time like information does [26][27][28][29][30][31][32]. The main idea is that space can be thought of a differentiable manifold, but the physical

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We investigate a particle physics model for cosmic inflation based on the following assumptions:(i) there are at least two complex scalar fields; (ii) the scalar potential is bounded from below and remains perturbative up to the Planck scale; (iii) we assume slow-roll inflation with maximally correlated adiabatic and entropy fluctuations 50-60 e-folds before the end of inflation. The energy scale of the inflation is set automatically by the model. Assuming also at least one massive right handed neutrino, we explore the allowed parameter space of the scalar potential as a function of the Yukawa coupling of this neutrino.

The phase structure and the infrared behaviour of the Euclidean 3-dimensional O(2) symmetric ghost scalar field model with higher-order derivative term has been investigated in Wegner and Houghton's renormalization group framework. The symmetric phase in which no ghost condensation occurs and the phase with restored symmetry but with a transient presence of a ghost condensate have been identified. Finiteness of the correlation length at the phase boundary hints to a phase transition of first order. The results are compared with those for the ordinary O(2) symmetric scalar field model.

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