72,516 research outputs found
Nearly Scale-Invariant Spectrum of Adiabatic Fluctuations May be from a Very Slowly Expanding Phase of the Universe
In this paper we construct an expanding phase with phantom matter, in which
the scale factor expands very slowly but the Hubble parameter increases
gradually, and assume that this expanding phase could be matched to our late
observational cosmology by the proper mechanism. We obtain the nearly
scale-invariant spectrum of adiabatic fluctuations in this scenario, different
from the simplest inflation and usual ekpyrotic/cyclic scenario, the tilt of
nearly scale-invariant spectrum in this scenario is blue. Although there exists
an uncertainty surrounding the way in which the perturbations propagate through
the transition in our scenario, which is dependent on the detail of possible
"bounce" physics, compared with inflation and ekpyrotic/cyclic scenario, our
work may provide another feasible cosmological scenario generating the nearly
scale-invariant perturbation spectrum.Comment: 4 pages, no figures, to appear in Phys. Rev. D. Many thanks for
referee's kind comments and criticism
Schr\"odinger-Poisson equations with singular potentials in
The existence and estimate of positive solutions are discussed
for the following Schr\"{o}dinger-Poisson system {ll} -\Delta u
+(\lambda+\frac{1}{|y|^\alpha})u+\phi (x) u =|u|^{p-1}u, x=(y,z)\in
\mathbb{R}^2\times\mathbb{R}, -\Delta\phi = u^2,\ \lim\limits_{|x|\rightarrow
+\infty}\phi(x)=0, \hfill y=(x_1,x_2) \in \mathbb{R}^2 with
|y|=\sqrt{x_1^2+x_2^2}, where , and
.Comment: 23page
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