1. Cosmology in a brane-induced gravity model with trace-anomaly terms
Mini Workshop on Brane Tokyo Institute of Technology
Cosmology in a brane-induced gravity model with trace-anomaly terms
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, (2003)
5. Summary and discussion

2. 1. Introduction R-SII model
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?

3. 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

4. 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

5. excluded for relativistic sources
Gravitational property in DGP model
(Dvali, Gabadadze, Porrati, `00)
Scalar property (gravitational potential)
(4D gravity)
for
(small scale)
(5D gravity)
for
(large scale)
Tensor property (tensor structure of graviton propagator)
cf. 4D massless graviton
excluded for relativistic sources
van Dam-Veltman discontinuity

6. 3. Brane induced gravity in 5D-AdS
Maeda, S.M. , Torii (`03)
confinement of the massless mode on the brane as R-S model
cf. Tanaka (`03)
tensor structure
model
field equation
cf. Shiromizu, Maeda, Sasaki (`00)
5D Einstein eq., Gauss eq.
and Cadazzi eq.,
Israel’s junction condition
on the brane
with
( effective energy momentum tensor )
quadratic with respect to

7. 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

8. effective Friedmann equation
case 2:
(5D Friedmann solution is the attractor in D-G-P model)
effective Friedmann equation
4d-like cosmology
case 3:
effective cosmological constant
for
suppressed!!
for cosmological constant problem
SUSY

9. 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

10. 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

11. Cosmological scenario
value of the parameters
number of species
creation
first inflation
GUT scale
second
inflation
first
inflation
second inflation
present
Cf. Dvali et al
quintessential inflation driven by induced curvature terms

12. 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