Suppose you wanted to "pull an Einstein," and create a static universe  in which the gravitational attraction of matter is exac
tly balanced by the gravitational repulsion of dark energy with equation-of-state parameter − 1/ 3 < wq < − 1 and energy density εq.
What is the necessary matter density (εm) required to produce a static universe, expressed in terms of εq and wq?
Will the curvature of this static universe be negative or positive?
What will be its radius of curvature, expressed in terms of εq and wq?
What is the necessary matter density (εm) required to produce a static universe, expressed in terms of εq and wq?
Will the curvature of this static universe be negative or positive?
What will be its radius of curvature, expressed in terms of εq and wq?
2 answers:
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Answer:
and
Explanation:
See attached figure.
E due to sphere
E due to particule
(1)
according to the law of gauss and superposition Law:
; electric field due to the small sphere with r1=R/4
then: (2)
on the other hand, for the particule:
⇒
(3)
We replace (2) y (3) in (1):
--------------------
if R<x<2R AND
remember that
then:
solving:
but: R<x<2R
so :
