Transcript Reconstruction of Scalar Tensor Theories

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L. Perivolaropoulos
http://leandros.physics.uoi.gr
Department of Physics
University of Ioannina
L.P.
accepted in JCAP (2005)
2
min
 171.7
2
LCDM
 177.1
Gold Dataset (157 SNeIa):
Riess et. al. 2004
What theory produces the features of best
parametrizations?
wDE
 z  0   1,
wDE
z
 0.4   1
dwDE
z
dz
 0
 0,
1 2
L     V  
2
+: Quintessence
-: Phantom
 Quint   1
1 2
   V  
p
 0
w  2

1
  1  2  V   Phant  < 1
 
2
To cross the w=-1 line the kinetic energy term
must change sign
(impossible for single phantom or quintessence field)
Generalization for k-essence:
Non-minimal Coupling
1
8 Geff
    1
F    , U  Φ
 F   1
F
G r 
 0
G0
F r 
Model U   Pr ediction H z   Comparewith Data
 d  z    Best Fit Parametrization  H  z  ,   z   
 Theoretical Model U    , F    ...
Data
L
i
 , p
'
d
dz
positive energy of gravitons
For U(z)=0 there is no acceptable F(z)>0 in 0<z<2 consistent with
the H(z) obtained even from a flat LCDM model.
1
0.75
0.5
F
0.25
0
0.25
0.5
0.75
0
0.2
0.4
0.6
z
0.8
1
Q.: Is there a set
Φ(z), F(z),U(z) consistent
with the constraints that
Can not be reproduced
predicts
the best
by any single
field fit w(z)
crossing
w=-1theory
line?
minimallythe
coupled
1
2
• Use trial Φ(z) to solve (2) for F(z) with F'(z=0)=0, F(z=0)=1.
• Select Φ(z) such that F(z)>0 for all z (need Φ'(z) small).
• Use the resulting f(z) and the best fit q(z) in (1) to find U(z).
• Invert Φ(z) to find z(Φ).
• Sustitute z(Φ) in F(z) and U(z) to find F(Φ) and U(Φ).
G(z)~1/F(z) decreases
at recent times thus boosting
accelerating expansion
Minimum: Generic feature
F(Φ)
U(Φ)
Minimum: Generic feature
Φ
Φ
(more data are needed eg δm(z))
(best fit H(z) must be rederived fiting M(z) with new parameters)
SnIa peak luminosity:
SnIa Absolute Magnitude Evolution:
SnIa Apparent Magnitude:
with:
Parametrizations:
a0
a0
a0
a0
Φ'2 changes sign!
• An observationally viable scalar tensor theory
that predicts an H(z)-w(z) crossing the w=-1
line was explicitly reconstructed.
• The reconstructed theory is not uniquely determined
from H(z).
• The SnIa data can be utilized to simulatneously fit
for both H(z) and the Newton's constant
G(z) in the context of scalar tensor theories.
This can lead to a uniquely defined
reconstruction process.