Cosmology in a brane-induced gravity model with trace-anomaly terms

1. Mini Workshop on Brane World @ Tokyo Institute of Technology 2003. 10. 30 Cosmology in a brane-induced gravity modelwith 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, 024033 (2003) 5. Summary and discussion

2. 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?

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. Gravitational property in DGP model (small scale) (4D gravity) for (5D gravity) for (large scale) (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

6. 3. Brane induced gravity in 5D-AdS cf. Tanaka (`03) tensor structure model 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., 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 cosmological constant for suppressed!! for cosmological constant problem SUSY case 2: (5D Friedmann solution is the attractor in D-G-P model) effective Friedmann equation 4d-like cosmology case 3:

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