1. Scalar perturbations in braneworld cosmology Takashi Hiramatsu Research Center for the Early Universe (RESCEU), School of Science, University of Tokyo Collaboration with A.Cardoso, K.Koyama, S.S.Seahra Institute of Cosmology and Gravitation, University of Portsmouth arxiv/0705.1685 [astro-ph] submitted to JCAP

2. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 2 / 18 Braneworld String theories imply 10/11 D space-time.  a simple description : Randall-Sundrum II model Cosmological perturbations in RSII model –Tensor perturbations During inflation After inflation –Scalar perturbations During inflation brane bulk5D anti de Sitter space-time Hiramatsu, Koyama, Taruya, PLB(2004) Ichiki, Nakamura, PRD(2004) Ichiki, Nakamura, astro-ph(2004) Kobayashi, Tanaka, JCAP(2004) Kobayashi, Tanaka, PRD(2005) Hiramatsu, Koyama, Taruya, PLB(2004) Hiramatsu, PRD(2006) Kobayashi, PRD(2006) Seahra, PRD(2006) Langlois, Maartens, Wands, PLB(2000) Gorbunov, Rubakov, Sibiryakov, JHEP(2001) Kobayashi, Kudoh, Tanaka, PRD(2003) Maartens, Wands, Bassett, Heard, PRD(2000) Calcagni, JCAP(2003) Liddle, Smith, PRD(2003) Tsujikawa, Liddle, JCAP(2004) Calcagni, JCAP(2004) Ramirez, Liddle, PRD(2004) Seery, Taylor, PRD(2005) Liddle, Taylor, PRD(2005) Koyama, Mizuno, Wands, JCAP(2005) Hiramatsu, Koyama, JCAP(2007) Koyama, Mennim, Rubakov, Wands, Hiramatsu, JCAP(2007) After inflation Randall, Sundrum, PRL (1999)

3. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 3 / 18 Scalar perturbations in RS model Observables – : curvature perturbations – : density perturbations  CMB anisotropy, large-scale structure, etc. High-energy corrections caused by extra-dimensions –Friedmann equation  slower expansion law –Interaction with the bulk metric perturbations

4. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 4 / 18 Evolution of primordial fluctuations High-energy effects appear above the critical wave number

5. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 5 / 18 Metric perturbations (bulk) 5D metric perturbations (5D-longitudinal gauge) Master variable No matter in the bulk

6. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 6 / 18 Density perturbations (brane) Perturbation of energy-momentum tensor Gauge-invariant density/velocity perturbation Evolution equation assumption Correction to Firedmann eq. Bulk metric perturbations

7. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 7 / 18 Junction conditions (brane) Perturbed effective Einstein equation

8. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 8 / 18 Growing / Decaying modes High-energy limit Junction condition Evolution equation 3 rd order equation for dominant growing mode : subdominant growing mode : decaying mode :

9. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 9 / 18 Curvature perturbations / consistency relations Two definitions for g.-i. curvature perturbations Consistency relations for the dominant growing mode on superhorizon scales –At high-energies, –In 4D GR, On subhorizon scales,

10. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 10 / 18 Numeric analysis Using two independent codes –Pseudo-spectral method (PS) –Characteristic integration method (CI) Hiramatsu, PRD(2006) Seahra, PRD(2006)

11. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 11 / 18 Initial conditions / critical wave number Initial condition –Only the dominant growing mode survived on the brane, –and bulk metric perturbations become negligible at very early time

12. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 12 / 18 Typical waveforms (high-frequencies) const

13. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 13 / 18 Large scale fluctuations

14. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 14 / 18 Enhancement factor (Comparing with GR) To separate out the two effects, …

15. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 15 / 18 Enhancement factor (Comparing with GR)

16. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 16 / 18 Enhancement factor (Comparing with GR) ~7.1 ~3.0 ~2.4

17. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 17 / 18 Summary / Implications EOMs and junction condition for scalar perturbations in RD epoch in RSII model. Analytic approximations (3 modes). Applied two numerical algorithms to solve EOMs. All consistency relations are satisfied, and GR results are recovered for low-frequency modes. Above critical wave number, amplitude of is enhanced, which leads to

18. 宇宙初期における時空と物質の進化, University of Tokyo, 28-30 May 2007 18 / 18 Summary / Implications Why is the amplitude enhanced ? The self-gravity of supercritical perturbative modes will be greater than subcritical ones (, or ?) Implications The enhancement is important on comoving scales 10AU.  too small to be relevant to CMB/galaxy observations  through predictions of PBH abundance, we can derive new limits on RS cosmology ? Gravitational force ～ Cf. Sendouda et al., PRD (2003); PRD (2005); JCAP (2006) Guedens et al., PRD (2006a); Majumdar, PRL (2003)