Minimal cut-off vacuum state constraints from CMB bispectrum statistics

In this short note we translate the best available observational bounds on the CMB bispectrum amplitudes into constraints on a specific scale-invariant New Physics Hypersurface (NPH) model of vacuum state modifications, as first proposed by Danielsson, in general models of single-field inflation. As compared to the power spectrum the bispectrum constraints are less ambiguous and provide an interesting upper bound on the cut-off scale in general models of single-field inflation with a small speed of sound. This upper bound is incompatible with the power spectrum constraint for most of the parameter domain, leaving very little room for minimal cut-off vacuum state modifications in general single-field models with a small speed of sound.Comment: 9 pages, 1 figur

Relativistic Dissipative Hydrodynamic Equations at the Second Order for Multi-Component Systems with Multiple Conserved Currents

We derive the second order hydrodynamic equations for the relativistic system of multi-components with multiple conserved currents by generalizing the Israel-Stewart theory and Grad's moment method. We find that, in addition to the conventional moment equations, extra moment equations associated with conserved currents should be introduced to consistently match the number of equations with that of unknowns and to satisfy the Onsager reciprocal relations. Consistent expansion of the entropy current leads to constitutive equations which involve the terms not appearing in the original Israel-Stewart theory even in the single component limit. We also find several terms which exhibit thermal diffusion such as Soret and Dufour effects. We finally compare our results with those of other existing formalisms.Comment: 18 pages, no figures; title changed, to appear in Nucl. Phys.

The unification of inflation and late-time acceleration in the frame of kk-essence

By using the formulation of the reconstruction, we explicitly construct models of $k$-essence, which unify the inflation in the early universe and the late accelerating expansion of the present universe by a single scalar field. Due to the higher derivative terms, the solution describing the unification can be stable in the space of solutions, which makes the restriction for the initial condition relaxed. The higher derivative terms also eliminate tachyon. Therefore we can construct a model describing the time development, which cannot be realized by a usual inflaton or quintessence models of the canonical scalar field due to the instability or the existence of tachyon. We also propose a mechanism of the reheating by the quantum effects coming from the variation of the energy density of the scalar field.Comment: LaTeX, 13 pages, 10 figure

Energy Density in Expanding Universes as Seen by Unruh's Detector

We consider the response of an Unruh detector to scalar fields in an expanding space-time. When combining transition elements of the scalar field Hamiltonian with the interaction operator of detector and field, one finds at second order in time-dependent perturbation theory a transition amplitude, which actually dominates in the ultraviolet over the first order contribution. In particular, the detector response faithfully reproduces the particle number implied by the stress-energy of a minimally coupled scalar field, which is inversely proportional to the energy of a scalar mode. This finding disagrees with the contention that in de Sitter space, the response of the detector drops exponentially with particle energy and therefore indicates a thermal spectrum.Comment: 15 pages, 1 figur