69,016 research outputs found

    A new approach on the stability analysis in ELKO cosmology

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    In this work it has been developed a new approach to study the stability of a system composed by an ELKO field interacting with dark matter, which could give some contribution in order to alleviate the cosmic coincidence problem. It is assumed that the potential which characterizes the ELKO field is not specified, but it is related to a constant parameter δ\delta. The strength of the interaction between matter and ELKO field is characterized by a constant parameter β\beta and it is also assumed that both ELKO field as matter energy density are related to their pressures by equations of state parameters ωϕ\omega_\phi and ωm\omega_m, respectively. The system of equations is analysed by a dynamical system approach. It has been found the conditions of stability between the parameters δ\delta and β\beta in order to have stable fixed points for the system for different values of the equation of state parameters ωϕ\omega_\phi and ωm\omega_m, and the results are presented in form of tables. The possibility of decay of ELKO field into dark matter or vice versa can be read directly from the tables, since the parameters δ\delta and β\beta satisfy some inequalities. It allows us to constrain the potential assuming that we have a stable system for different interactions terms between the ELKO field and dark matter. The cosmic coincidence problem can be alleviated for some specific relations between the parameters of the model.Comment: 16 pages, some new comments in the Introduction and at the begining of Section I

    Isotropization of the universe during inflation

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    A primordial inflationary phase allows one to erase any possible anisotropic expansion thanks to the cosmic no-hair theorem. If there is no global anisotropic stress, then the anisotropic expansion rate tends to decrease. What are the observational consequences of a possible early anisotropic phase? We first review the dynamics of anisotropic universes and report analytic approximations. We then discuss the structure of dynamical equations for perturbations and the statistical properties of observables, as well as the implication of a primordial anisotropy on the quantization of these perturbations during inflation. Finally we briefly review models based on primordial vector field which evade the cosmic no-hair theorem.Comment: 9 pages, 3 figures. Invited review article for the French Academy of Scienc

    A nonlinear elliptic problem with terms concentrating in the boundary

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    In this paper we investigate the behavior of a family of steady state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a ϵ\epsilon-neighborhood of a portion Γ\Gamma of the boundary. We assume that this ϵ\epsilon-neighborhood shrinks to Γ\Gamma as the small parameter ϵ\epsilon goes to zero. Also, we suppose the upper boundary of this ϵ\epsilon-strip presents a highly oscillatory behavior. Our main goal here is to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on Γ\Gamma, which depends on the oscillating neighborhood
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