Primordial gravitational waves from inflation could be detected using the cosmic microwave background. Gravitational waves passing through the last scattering surface would induce B-mode polarization patterns in the CMB. Future experiments aim to detect these B-modes as a signature of primordial gravitational waves, which would provide insights into inflation and the very early universe.

1. Primordial Gravita-onal Waves
Robert Caldwell / Dartmouth College

2. Nobel Prize 2017?
Kip Thorne (Caltech) and Rai Weiss (MIT), and ?
For the direct detec+on of gravita+onal waves by LIGO.

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. 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. 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. PolarizaBon
h+ hL

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

10. What LIGO/VIRGO Saw
arXiv:1709.09660 (LIGO/VIRGO)

12. Cosmic Origins

13. Cosmic Origins
Phase transiBons:
Bubble Collisions,
Topological Defects
Both scenarios would produce
a broad spectrum of
gravitaBonal radiaBon

14. Cosmic InflaBon A speculaBve early epoch in the history of the Universe,
during which the scale of the cosmos grows exponenBally.

15. 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

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

17. Gravita-onal Wave Cosmology
“GravitaBonal-wave cosmology across 29 decades in frequency,”
Lasky et al, PRX 2016

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

22. LISA:
Laser Interferometer Space Antenna
See sci.esa.int/lisa

23. LISA:
Laser Interferometer Space Antenna
See sci.esa.int/lisa
L=16.7cs

24. 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.

25. Platonic Solids as GravitaBonal Wave Detectors
Tristan Smith & RC 2017

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

27. Angular SensiBvity
ABC-ABC (I) ABC-DEF (I) ABC-FEB (V)
A mulBfaceted detector has greater
angular resoluBon than a single pane

28. Gravita-onal Wave Cosmology
“GravitaBonal-wave cosmology across 29 decades in frequency,”
Lasky et al, PRX 2016

29. To detect ultra-long wavelength
GWs from inflation:
Use the CMB surface of last
scattering as a test body!

30. 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

31. Look outside at the blue sky
for an example!
Thomson scattering
so-called “E mode” paSern
CMB PolarizaBon

32. CMB PolarizaBon
origin of the “B mode” paSern

33. Temperature B PolarizaBon
Exactly what are we looking for?
CMB PolarizaBon

34. T+ B+
TR BR

36. rms fluctuaBon
vs.
angular scale
“B modes” compete with foreground contaminaBon and gravitaBonal lensing effects.
Exactly what are we looking for?
CMB PolarizaBon

37. Gravita-onal Wave Cosmology
“GravitaBonal-wave cosmology across 29 decades in frequency,”
Lasky et al, PRX 2016

38. Looking forward to a new era of
GravitaBonal Wave Cosmology

39. PolarizaBon
Haidinger’s Brush