113 research outputs found
Rock 'n' Roll Solutions to the Hubble Tension
Local measurements of the Hubble parameter are increasingly in tension with
the value inferred from a CDM 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 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 and increases
the allowed value of from 69.2 km/s/Mpc in CDM to 72.3 km/s/Mpc
at . 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
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
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
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
- …