Cosmology in a braneinduced gravity model with traceanomaly terms

1
Cosmology in a brane-induced gravity modelwith
trace-anomaly terms
Mini Workshop on Brane World _at_ Tokyo Institute of
Technology
2003. 10. 30
1. Introduction
Shuntaro Mizuno
2. DGP model
Waseda University, Japan

• Brane induced gravity
• in 5D-AdS

Kei-ichi Maeda, S.M. , Takashi Torii

• Brane induced gravity
• with trace anomaly terms

Phys. Rev. D 68, 024033 (2003)
5. Summary and discussion
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1. Introduction
Cosmological scenario based on brane models
R-SII model
(simple and concrete)
homogeneous part
inhomogeneous part
quadratic term
(necessary for comparison with observations)
dark radiation
many discussions
modified by curvature corrections
1, induced gravity term on brane
4d gravity in infinite volume extradimension
2, trace anomaly term on brane
quantum fluctuation of matter fields on brane
3, Gauss-Bonnet term in bulk
non-singular warped compactification
new interesting phenomenology?
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2. D-G-P model
(Dvali, Gabadadze, Porrati, 00)
model
matter
gravity
a flat brane in 5D Minkowski bulk
quantum interaction between bulk gravity and
brane matter
graviton
( Sakharov 75, Akama 78 Adler 80 )
massive scalars/fermions
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Cosmological solutions in DGP model
( Deffayet 01)
( matching condition)
low energy
high energy
branch
5D cosmology
4D cosmology
branch
Inflationary solution
present cosmic acceleration even for
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Gravitational property in DGP model
(Dvali, Gabadadze, Porrati, 00)
Scalar property (gravitational potential)
Tensor property (tensor structure of graviton
propagator)
cf. 4D massless graviton
excluded for relativistic sources
van Dam-Veltman discontinuity
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3. Brane induced gravity in 5D-AdS
Maeda, S.M. , Torii (03)
confinement of the massless mode on the brane as
R-S model
field equation
cf. Shiromizu, Maeda, Sasaki (00)
5D Einstein eq., Gauss eq.
and Cadazzi eq.,
Israels junction condition
on the brane
( effective energy momentum tensor )
with
quadratic with respect to
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cosmological solutions
case 1
branch
(inflationary solution is the attractor in D-G-P
model even for )
effective Friedmann equation
with
present cosmological acceleration
confinement of the massless mode
effective gravitational constant changes
with
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case 2
(5D Friedmann solution is the attractor in D-G-P
model)
effective Friedmann equation
4d-like cosmology
case 3
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Further extension of the model
In addition to dark energy ( cosmological
constant problem), other interesting
cosmological consequences by other
curvature correction terms?
trace anomaly of matter field on brane
(free, massless, conformally invariant case)
U(N) super Yang-Mills theory
adding the counter term
In 4D theory, inflationary solution is obtained
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4. Brane induced gravity with trace anomaly
terms
S.M., Maeda , Torii (2003)
Model
Effective energy momentum tensor on the brane
Basic equation
with
deviation from 4D theory
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Cosmological scenario
value of the parameters
number of species
first inflation
creation
GUT scale
second inflation
first inflation
second inflation
present
Cf. Dvali et al
quintessential inflation driven by induced
curvature terms
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5. Summary and discussion
First, I review the cosmology based on DGP model.
natural explanation for zero vacuum energy
alternative to dark energy
tensor structure becomes 4d massive (problematic)
Next, for the relevant gravitational property on
brane, we consider generalized DGP model with
bulk cosmological constant and brane tension like
RS model.
effective gravitational constant on brane changes
effective cosmological constant on brane
suppressed
Last, for the early stage of inflationary
solution, we consider other curvature correction
term, trace anomaly.
creation
early inflation