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- 3. What is a gravitaBonal wave? • Ripple in the fabric of space-Bme • Traveling disturbance in the gravitaBonal field ds2 = c2 dt2 + ( ij + hij)dxi dxj
- 5. About Gravita-onal Waves A traveling disturbance in the gravitaBonal field, in the fabric of space+me Analogy with E&M: propagaBng E displaces charges; moving charges make propagaBng E ~E(t, ~x) = 1 4⇡ @ @t Z d3 x0 ~J(t, ~x0 ) |~x ~x0| |ret General RelaBvity: propagaBng GW (h) displaces masses; moving masses make propagaBng h
- 7. Stokes Parameters I = |h+|2 + |h⇥|2 Q = |h+|2 |h⇥|2 U = h⇤ ⇥h+ + h⇤ +h⇥ V = i(h⇤ ⇥h+ h⇤ +h⇥) Consider the paSerns of burst and conBnuous sources of gravitaBonal radiaBon on the sky
- 8. Tremendous Discoveries! Black Holes: 25, 31M ! 53M + radiation Violent Collisions in Distant Space produce displacements on Earth Smaller than the width of a proton
- 9. What LIGO Saw Laser Interferometer GravitaBonal Wave Observatory Hanford, WA and Livingston, LA L=4 km long interferometer arms Frequency range: ∼100Hz Strain: h∼10-21 h = 2 L/L L ⇠ 2 ⇥ 10 18 m Image: Science News
- 12. Cosmic Origins
- 16. d⇢GW = 2~! ✓ !2 d! 2⇡2c3 ◆ n! d⇢GW = ~ 4⇡2c3 H2 0 H2 inf d! ! RadiaBon… …from inflaBon Spectral density ⌦GW = ! ⇢c d⇢GW d! = 16 9 ~G2 c7 ⇢inf Cosmic InflaBon
- 18. ds2 = dt2 + ( ij + ✏ hij)dxi dxj How to detect: a quick calculaBon h
- 19. if d~x dt |i = 0 then d2 ~x dt2 = 0 test masses: d2 xi dt2 + ( i µ⌫ t µ⌫)dxµ dt dx⌫ dt = 0 k · k = 0 ! q0 = 1 2 ˆ`i 12 ˆ`j 12 hij ˆ`i 12qi light: kµ = dxµ d = pµ + ✏ qµ ' = 2⇡⌫ R dt = R d ⇣ 1 + 1 2 ✏ ˆ`i 12 ˆ`j 12hij ⌘ ds2 = dt2 + ( ij + ✏ hij)dxi dxj masses remain at fixed coordinates accumulated phase of light depends on h How to detect: a quick calculaBon
- 20. for each interferometer pair s1(t) = '12 '13 + n1 How to detect: a quick calculaBon 1 2 3
- 21. for each interferometer pair correlate pairs measure the power s1(t) = '12 '13 + n1 S = R dt dt0 s1(t) s4(t0 ) Q(t t0 ) How to detect a stochasBc background I = |h+|2 + |h⇥|2 µ = hSi = 3T 10⇡2 H2 0 R df ⌦GW (f) R(f) ˜Q(f)/f3 for the expected signal stochastic background ⌦GW = f ⇢c d⇢GW df ⇢GW = 1 32⇡G h˙hij ˙hij i
- 26. Novel Geometries ⌦I,GW |min = 1.3 ⇥ 10 14 ⌦V,GW |min = 5.2 ⇥ 10 14 ⌦I,GW |min = 2.8 ⇥ 10 12 ⌦V,GW |min = 1.3 ⇥ 10 10
- 29. To detect ultra-long wavelength GWs from inflation: Use the CMB surface of last scattering as a test body!
- 34. T+ B+ TR BR