1、Scalar perturbations in braneworld cosmology,Takashi HiramatsuResearch Center for the Early Universe (RESCEU),School of Science, University of TokyoCollaboration with A.Cardoso, K.Koyama, S.S.SeahraInstitute of Cosmology and Gravitation, University of Portsmouth,arxiv/0705.1685 astro-phsubmitted to
2、JCAP,宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,2 / 18,Braneworld,String theories imply 10/11 D space-time. a simple description : Randall-Sundrum II modelCosmological perturbations in RSII modelTensor perturbationsDuring inflation After inflation Scalar perturbationsDuring inflation,brane,bulk
3、,5D 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, Wand
4、s, 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)K
5、oyama, Mizuno, Wands, JCAP(2005)Hiramatsu, Koyama, JCAP(2007)Koyama, Mennim, Rubakov, Wands, Hiramatsu, JCAP(2007),After inflation,Randall, Sundrum, PRL (1999),宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,3 / 18,Scalar perturbations in RS model,Observables : curvature perturbations : density pert
6、urbations CMB anisotropy, large-scale structure, etc.High-energy corrections caused by extra-dimensionsFriedmann equation slower expansion lawInteraction with the bulk metric perturbations,宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,4 / 18,Evolution of primordial fluctuations,High-energy effects
7、 appear above the critical wave number,宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,5 / 18,Metric perturbations (bulk),5D metric perturbations (5D-longitudinal gauge)Master variable,No matterin the bulk,宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,6 / 18,Density perturbations (brane),Perturbat
8、ion of energy-momentum tensorGauge-invariant density/velocity perturbationEvolution equation,assumption,Correction toFiredmann eq.,Bulk metricperturbations,宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,7 / 18,Junction conditions (brane),Perturbed effective Einstein equation,宇宙初期時空物質進化, University
9、of Tokyo, 28-30 May 2007,8 / 18,Growing / Decaying modes,High-energy limit,Junctioncondition,Evolutionequation,3rd order equation for,dominant growing mode :,subdominant growing mode :,decaying mode :,宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,9 / 18,Curvature perturbations / consistency relati
10、ons,Two definitions for g.-i. curvature perturbationsConsistency relations for the dominant growing mode on superhorizon scalesAt high-energies,In 4D GR,On subhorizon scales,宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,10 / 18,Numeric analysis,Using two independent codesPseudo-spectral method (PS
11、)Characteristic integration method (CI),Hiramatsu, PRD(2006),Seahra, PRD(2006),宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,11 / 18,Initial conditions / critical wave number,Initial conditionOnly the dominant growing mode survived on the brane, and bulk metric perturbations become negligible at v
12、ery early time,宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,12 / 18,Typical waveforms (high-frequencies),宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,13 / 18,Large scale fluctuations,宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,14 / 18,Enhancement factor (Comparing with GR),To separate out
13、the two effects, ,宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,15 / 18,Enhancement factor (Comparing with GR),宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,16 / 18,Enhancement factor (Comparing with GR),7.1,3.0,2.4,宇宙初期時空物質進化, University of Tokyo, 28-30 May 2007,17 / 18,Summary / Implications,E
14、OMs 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 enh
15、anced, which leads to,宇宙初期時空物質進化, 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 ?) ImplicationsThe 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),
