Particle Creation Amplification in Curved Space due to Thermal Effects

A physical system composed by a scalar field minimally coupled to gravity and a thermal reservoir, as in thermo field dynamics, all of them in curved space time, is considered. When the formalism of thermo field dynamics is generalized to the above mentioned case, an amplification in the number of created particles is predicted.Comment: 7 pages; Plain Te

An intermediate framework between WIMP, FIMP, and EWIP dark matter

WIMP (Weakly Interacting Massive Particle), FIMP (Feebly interacting Massive Particle) and EWIP (Extremely Weakly Interacting Particle) dark matter are different theoretical frameworks that have been postulated to explain the dark matter. In this paper we examine an intermediate scenario that combines features from these three frameworks. It consists of a weakly interacting particle --a la WIMP-- that does not reach thermal equilibrium in the early Universe --a la FIMP-- and whose relic density is determined by the reheating temperature of the Universe --a la EWIP. As an example, an explicit realization of this framework, based on the singlet scalar model of dark matter, is analyzed in detail. In particular, the relic density is studied as a function of the parameters of the model, and the new viable region within this intermediate scenario is determined. Finally, it is shown that this alternative framework of dark matter allows for arbitrarily heavy dark matter particles and that it suggests a connection between dark matter and inflation.Comment: 14 pages, 6 figure

Small clique number graphs with three trivial critical ideals

The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. In this article we provide a set of minimal forbidden graphs for the set of graphs with at most three trivial critical ideals. Then we use these forbidden graphs to characterize the graphs with at most three trivial critical ideals and clique number equal to 2 and 3.Comment: 33 pages, 3 figure

Computation of the unipotent radical of the differential Galois group for a parameterized second-order linear differential equation

We propose a new method to compute the unipotent radical $R_u(H)$ of the differential Galois group $H$ associated to a parameterized second-order homogeneous linear differential equation of the form $$\tfrac{\partial^2}{\partial x^2}Y-qY=0,$$ where $q \in F(x)$ is a rational function in $x$ with coefficients in a $\Pi$-field $F$ of characteristic zero, and $\Pi$ is a commuting set of parametric derivations. The procedure developed by Dreyfus reduces the computation of $R_u(H)$ to solving a creative telescoping problem, whose effective solution requires the assumption that the maximal reductive quotient $H / R_u(H)$ is a $\Pi$-constant linear differential algebraic group. When this condition is not satisfied, we compute a new set of parametric derivations $\Pi'$ such that the associated differential Galois group $H'$ has the property that $H'/ R_u(H')$ is $\Pi'$-constant, and such that $R_u(H)$ is defined by the same differential equations as $R_u(H')$. Thus the computation of $R_u(H)$ is reduced to the effective computation of $R_u(H')$. We expect that an elaboration of this method will be successful in extending the applicability of some recent algorithms developed by Minchenko, Ovchinnikov, and Singer to compute unipotent radicals for higher order equations.Comment: 12 page