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Scalar perturbations in braneworld cosmology

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.

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Scalar perturbations in braneworld cosmology

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  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. 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 Randall, Sundrum, PRL (1999) bulk 5D anti de Sitter space-time brane 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) Langlois, Maartens, Wands, PLB(2000) Gorbunov, Rubakov, Sibiryakov, JHEP(2001) Kobayashi, Kudoh, Tanaka, PRD(2003) 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) • After inflation

  3. 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. Evolution of primordial fluctuations • High-energy effects appear above the critical wave number

  5. Metric perturbations (bulk) • 5D metric perturbations (5D-longitudinal gauge) • Master variable No matter in the bulk

  6. Density perturbations (brane) • Perturbation of energy-momentum tensor • Gauge-invariant density/velocity perturbation • Evolution equation assumption Correction to Firedmann eq. Bulk metric perturbations

  7. Junction conditions (brane) • Perturbed effective Einstein equation

  8. Growing / Decaying modes • High-energy limit Evolution equation 3rd order equation for Junction condition dominant growing mode : subdominant growing mode : decaying mode :

  9. 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. Numeric analysis • Using two independent codes • Pseudo-spectral method (PS) • Characteristic integration method (CI) Hiramatsu, PRD(2006) Seahra, PRD(2006)

  11. 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. const Typical waveforms (high-frequencies)

  13. Large scale fluctuations

  14. Enhancement factor (Comparing with GR) • To separate out the two effects, …

  15. Enhancement factor (Comparing with GR)

  16. Enhancement factor (Comparing with GR) ~7.1 ~3.0 ~2.4

  17. 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. 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)

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