Gravitational Waves from primordial density perturbations PRD 75

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

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?

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

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

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

Linear modes - II • The radiation solutions

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

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

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

The delta function case

The power-law case - I

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

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 Ge. V. – BBO could constrain A~1 at Tent ~100 Te. V

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

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.