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Caldwellcolloquium

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Caldwellcolloquium

  1. 1. Primordial Gravita-onal Waves Robert Caldwell / Dartmouth College
  2. 2. Nobel Prize 2017? Kip Thorne (Caltech) and Rai Weiss (MIT), and ? For the direct detec+on of gravita+onal waves by LIGO.
  3. 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
  4. 4. Source of gravitaBonal waves Analogy to electromagneBsm: The “abrupt” moBon of charges produces a kink in the fields EM: Ai(t, ~x) GR: hij(t, ~x)
  5. 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
  6. 6. PolarizaBon h+ hL
  7. 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. 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. 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
  10. 10. What LIGO/VIRGO Saw arXiv:1709.09660 (LIGO/VIRGO)
  11. 11. Cosmic Origins
  12. 12. Cosmic Origins Phase transiBons: Bubble Collisions, Topological Defects Both scenarios would produce a broad spectrum of gravitaBonal radiaBon
  13. 13. Cosmic InflaBon A speculaBve early epoch in the history of the Universe, during which the scale of the cosmos grows exponenBally.
  14. 14. Cosmic InflaBon A speculaBve early epoch in the history of the Universe, during which the scale of the cosmos grows exponenBally. In this process, Bny quantum fluctuaBons are amplified and stretched to macroscopic scales
  15. 15. 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
  16. 16. Gravita-onal Wave Cosmology “GravitaBonal-wave cosmology across 29 decades in frequency,” Lasky et al, PRX 2016
  17. 17. ds2 = dt2 + ( ij + ✏ hij)dxi dxj How to detect: a quick calculaBon h
  18. 18. 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
  19. 19. for each interferometer pair s1(t) = '12 '13 + n1 How to detect: a quick calculaBon 1 2 3
  20. 20. 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
  21. 21. LISA: Laser Interferometer Space Antenna See sci.esa.int/lisa
  22. 22. LISA: Laser Interferometer Space Antenna See sci.esa.int/lisa L=16.7cs
  23. 23. BBO: Big Bang Observer Seto 2006 Seto & Taruya 2007 Crowder et al 2013 Smith & RC 2016 Uncorrelated detectors help to see primordial gravitaBonal waves. Need two planes to disBnguish V polarizaBon.
  24. 24. Platonic Solids as GravitaBonal Wave Detectors Tristan Smith & RC 2017
  25. 25. 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
  26. 26. Angular SensiBvity ABC-ABC (I) ABC-DEF (I) ABC-FEB (V) A mulBfaceted detector has greater angular resoluBon than a single pane
  27. 27. Gravita-onal Wave Cosmology “GravitaBonal-wave cosmology across 29 decades in frequency,” Lasky et al, PRX 2016
  28. 28. To detect ultra-long wavelength GWs from inflation: Use the CMB surface of last scattering as a test body!
  29. 29. Light passing through a gravitaBonal wave: Redshiled (loses energy) when stretched Blueshiled (gains energy) when squeezed d ln ⌫ d⌧ = 1 2 @ @⌧ hijni nj CMB PolarizaBon
  30. 30. Look outside at the blue sky for an example! Thomson scattering so-called “E mode” paSern CMB PolarizaBon
  31. 31. CMB PolarizaBon origin of the “B mode” paSern
  32. 32. Temperature B PolarizaBon Exactly what are we looking for? CMB PolarizaBon
  33. 33. T+ B+ TR BR
  34. 34. rms fluctuaBon vs. angular scale “B modes” compete with foreground contaminaBon and gravitaBonal lensing effects. Exactly what are we looking for? CMB PolarizaBon
  35. 35. Gravita-onal Wave Cosmology “GravitaBonal-wave cosmology across 29 decades in frequency,” Lasky et al, PRX 2016
  36. 36. Looking forward to a new era of GravitaBonal Wave Cosmology
  37. 37. PolarizaBon Haidinger’s Brush

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