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Gravitational Waves from primordial density perturbations

Gravitational Waves from primordial density perturbations. PRD 75 123518 (2007) arXiv:gr-qc/0612013. Kishore N. Ananda University of Cape Town In collaboration with Chris Clarkson and David Wands. Cosmo 07, 22 nd August 2007. TexPoint fonts used in EMF.

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Gravitational Waves from primordial density perturbations

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  1. Gravitational Waves from primordial density perturbations PRD 75 123518 (2007) arXiv:gr-qc/0612013 Kishore N. Ananda University of Cape Town In collaboration with Chris Clarkson and David Wands Cosmo 07, 22nd August 2007 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.:

  2. The cosmological standard model • GW’s are inevitable consequence of GR. • Studying linear perturbations during Inflation: • Large-scale GW’s are produced • Amplitude depends on the energy scale. • Current observations allow power up to 30% of scalars • What is the minimum (guaranteed) background of tensor modes? • Density perturbations do exist. • Density perturbations will produce GW’s via non-linear evolution. • We have detailed information on scalars. • What does the power spectrum look like? • What about in the frequency range of direct detectors?

  3. Calculation overview - I • Calculate the GW’s produced non-linearly during radiation era. • Compute as power series in  (perturbation parameter) • Carryout the standard SVT decomposition • Work in Fourier space. • Calculate EFE’s at each order • Linear order - modes decouple and evolve independently • Higher order – mode-mode coupling

  4. Calculation overview - II • The metric can be written as (longitudinal gauge) • The EMT – perfect fluid description of radiation.

  5. Linear modes - I • The background equations are • The standard first order equations for scalars

  6. Linear modes - II • The radiation solutions

  7. Linear modes - III • The power spectra definition • The curvature perturbation

  8. Tensor modes - I • The tensor wave equation • The source • The solution is given via Green’s function method

  9. Tensor modes - II • The solution is given via Green’s function method • Calculate the tensor power spectrum • After much simplification • The input PS • Delta function • Power-law

  10. The delta function case

  11. The power-law case - I

  12. The power-law case - II Baumann, Ichiki, Steinhardt, & Takahashi, hep-th/0703290

  13. The GW spectrum today • For the power-law case • For the delta function case, the amplitude of the resonance peak • Advance LIGO could constrain A~100 at Tent~108 GeV. • BBO could constrain A~1 at Tent ~100 TeV

  14. The GW spectrum today III Baumann, Ichiki, Steinhardt, & Takahashi, hep-th/0703290

  15. Conclusions • Calculated the background of GW’s generated from the scalar power spectrum during the radiation era. • Exists independently of the inflationary model. • Spectrum is scale-invariant at small scales with r~10-6. • GW’s can be used to look for features in scalar PS at scales much smaller than those probed by CMB+LSS.

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