113 research outputs found

    Rock 'n' Roll Solutions to the Hubble Tension

    Full text link
    Local measurements of the Hubble parameter are increasingly in tension with the value inferred from a Λ\LambdaCDM fit to the cosmic microwave background (CMB) data. In this paper, we construct scenarios in which evolving scalar fields significantly ease this tension by adding energy to the Universe around recombination in a narrow redshift window. We identify solutions of Vϕ2nV \propto \phi^{2 n} with simple asymptotic behavior, both oscillatory (rocking) and rolling. These are the first solutions of this kind in which the field evolution and fluctuations are consistently implemented using the equations of motion. Our findings differ qualitatively from those of the existing literature, which rely upon a coarse-grained fluid description. Combining CMB data with low-redshift measurements, the best fit model has n=2n=2 and increases the allowed value of H0H_0 from 69.2 km/s/Mpc in Λ\LambdaCDM to 72.3 km/s/Mpc at 2σ2\sigma. Future measurements of the late-time amplitude of matter fluctuations and of the reionization history could help distinguish these models from competing solutions.Comment: 19 pages, 9 figures + appendi

    Oscillation of Certain Emden-Fowler Dynamic Equations on Time Scales

    Get PDF
    The theory of time scales has attracted a great deal of attention since it was first introduced by Hilger [1] in order to unify continuous and discrete analysis. For completeness, we recall the following concepts related to the notion of time scales; see [2, 3] for more details. A time scale T is an arbitrary nonempty closed subset of the real numbers R. In this paper, since we shall be concerned with the oscillatory behavior of solutions, we shall also assume that sup T = ∞.We define the time scale interval [0,∞)T by [0,∞)T := [0,∞)∩T.The forward and backward jump operators are defined b

    Asymptotic solutions of forced nonlinear second order differential equations and their extensions

    Full text link
    Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction between superlinear, sublinear, and linear differential equations that is normally found in the literature. An update of papers, past and present, in the theory of Volterra-Stieltjes integral equations is also presented

    On super-linear Emden–Fowler type differential equations

    Get PDF
    We study the second order Emden–Fowler type differential equation in the super-linear case. Using a Holder-type inequality, we resolve the open problem on the possible coexistence on three possible types of nononscillatory solutions (subdominant, intermediate, and dominant solutions). Jointly with this, sufficient conditions for the existence of globally positive intermediate solutions are established. Some of our results are new also for the Emden–Fowler equation
    corecore