avoiding the phantom menace júlio c. fabris departamento de física – ufes barcelona - 2006
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AVOIDING THE PHANTOM MENACE
Júlio C. Fabris
Departamento de Física – UFES
Barcelona - 2006
Inflation requires:
0a 3 0p
Strong energy condition is violated!
However, the null energy condition
does not need to be violated:
0T k k
0k k
0p
A phantom field (or fluid) is characterized by
p
1
All energy conditions are violated!
The phantom case became quite fashion due to the recent observational results
Of course, the predictions depend on which data are taken into account and how the statistics is made
Combining CMB (WMAP), matter clustering (SDSS e 2dFGRS) and supernovae:
13 . 010 . 0 93 . 0
Matts Roos, astrop-ph/0509089
Other estimations:
CMB, SNIa, large scale structures
79.039.1
S. Nannestad e E. Mortsell, JCAP 0409, 001(2004)
Including X-Rays 24.028.020,1
S.W. Allen et al., Mon. Not. R. Astron. Soc. 353, 457(2004)
22
3
8'a
G
a
a
0)1('
3' a
a
)1(30
a
)31(
2
0 aa
addt
3
1
13
1 0
1 0
a
0
a
0
a
Inevitable consequence for a Universe dominated by an exotic fluid where all the energy conditions are
violated:
A “big rip”: a curvature singularity in a future finite proper time
This requires, however, homogeneity and isotropy
Some remarks on the perturbative behaviour of the phantom fields
Considering a barotropic equation of state
p
The following equation governing the gravitational potential is found:
0)31('2')1(3'' 22 HHqH
J.C.F and S.V.B. Gonçalves, PRD, 2006
The scale factor behaves as
)31/(2 a
The equation for the potential becomes
0'
) 3 1(
) 1(6 ' '
2
q
The solution depends on the sign of the pressure:
0
)()( 21 qJcqJc
0
)()( 21 qKcqIc
Asymptotic behaviour
0
0q 2
21 cc
q
qcos)31(
)1(3
)31(2
35
0
0q 221
cc
q
qe
)31(
)1(3
The instability at small scale may be solved using a field representation:
)(2
1
2
1 ,,,,
VggRgR
)31(
2
a
ln31
)1(32
)1(3
2)1(
)1(
3
2)(
eV
The perturbed equation is
0'
'''2'
'
''2'' 2
HHqH
Using the background solution,
0'
31
)1(32'' 2
q
The solution is:
)()( 21 qJcqJc
)31(2
35
Asymptotic behaviour:
0q 221
cc
q )cos()31(
)1(6
q
0 0q
t
0 q
t
03
1 0q
t
q 03
1
t
3
11 0q
t
3
11 q
t
13
5 0q
t
13
5 q
t
3
5 0q
t
3
5 q
t
The Hubble horizon is given by
3(1 ) /(1 3 )Hl
It grows for normal fields, but it decreases when the phanton field dominates the matter content of the universe
Considering now local configurations:
22 2 2 2( ) ( )
( )
dds A dt r d
A
2 2
2
2 2
( ' ) ' 2 ( )
''2 '
( ) '' '' 2
A r r V
r
r
A r r A
0
An “anomalous” scalar field0
A “normal” scalar field
K.A. Bronnikov e J.C.F, PRL(2006)
0
0
The horizon can be the border between regular regions
A horizon
A static region
An expanding non-singular universe
Phantom inflation may be very attractive today
And it may not be so dangerous!
Moreover, local configurations are very attractive
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