Mp = 1 and Mpl is the planks mass (reduced). %3D Assuming natural units where 8rG
Mp = 1 and Mpl is the planks mass (reduced). %3D Assuming natural units where 8rG
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Transcribed Image Text:Assuming natural units where 8TG = M = 1 and Mpl is the planks mass (reduced).
Considering a flat homogonous isotropic universe that has a scalar field P() and potential
energy density V9) and fluid with density PF(a)
Friedmann eg : 3H =
= Pola) +
+ PF(a)
H is Hubble parameter
Scalar field density Pe = 0*/2 + V(4)
p2/2 – V(4)
We
62/2 + V(v)
Eq of state
2n
V
1. Assuming
-n' giving rise to eq of state We = n/3 – 1 where n is constant, rising
30. and V(o) = (1-) P.
an assumption of
. And a Simplified Friedmann eq
3H? = PF.oa¯ + P„,oa¯"
from eq state of WF = m/3–1 and continuity eq
where PF.0 is fluid and Po.0 scalar field energy densities.
p+ 3H(p + P) = 0
%3D
Vn
da av1+ Ca"-m
do
C = PF.0/P.0
Show
where
V(9) = Vo exp (-Ap)
2. Now assume n=m Show the potential
for constant A and Vo
SOLVE NUMBER 2
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