Environmental Engineering Reference
In-Depth Information
where the subscript
d
stands for
dark
.Giving
c
s
=
/
ˁ
=
dP
d
0 one obtains that
P
0
ˁ
d
,
w
d
=
P
d
=
P
0
,
(33)
obtaining that the pressure is constant. For cold dark matter, this pressure is equal
to zero, but astronomical observations allow this pressure to be non vanishing, and
in fact, it could be as large as the critical density of the Universe (
3
H
0
/
G
).
For example, a recent analysis of rotation curves in LSB galaxies has shown that
|
ˁ
c
≡
8
ˀ
10
−
6
at the center of the galaxies (Barranco et al.
2013
). This allows us to
think the pressure as a source of the cosmic accelerated expansion. To see how this
is possible, consider the continuity equation for the background evolution
w
dm
|
<
3
˙
a
a
(ˁ
d
+
ˁ
d
+
P
0
)
=
0
.
(34)
This equation can be integrated to give
1
ˁ
d
0
+
a
3
ˁ
d
(
a
)
=
,
(35)
1
+
K
where
K
=−
(ˁ
d
0
+
P
0
)/
P
0
is an integration constant fitted such that
ˁ
d
0
is the
value of the dark fluid energy density at a scale factor
a
1. Equation (
35
)
is what one expects for a unified dark sector fluid, that is, a component that decays
with the third power of the scale factor plus a component that remains constant.
In order for the energy density to be positive at all times,
(
t
0
)
≡
a
0
=
K
must be positive and
therefore the pressure is negative and lies in the interval
0, allowing
the dark fluid to accelerate the Universe. Equation (
35
) shows that the dark fluid
model gives the same phenomenology as the
−
ˁ
d
0
≤
P
0
≤
ʛ
CDM at the background cosmology.
Its EoS parameter can be written as
1
w
d
(
a
)
=−
a
−
3
,
(36)
1
+
K
which should be compared to the corresponding for the dark sector of the standard
model of Cosmology,
1
w
(
a
)
=−
a
−
3
.
(37)
ʛ
+
dm
+
ʩ
dm
ʩ
ʛ
1
One can go back and forth between the two models with the identifications
K
=
ʩ
dm
ʩ
ʛ
,
and
d
=
dm
+
ʛ
.
(38)
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