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A	Unique	and	Observable	Imprint	of	Infla8on	
Robert	Caldwell	/	Dartmouth	College
Dartmouth	College	
Hanover,	New	Hampshire
Cosmic	Microwave	Background	/	Temperature	Anisotropy	/	Planck	2015	
SMICA	map:	combined	input,	painted	mask
Cosmic	Microwave	Background	/	Temperature	Anisotropy	/	Planck	2015	
353	GHz	map:	polarized	emission	from	dust	grains	trace...
What	are	we	looking	for?	
Swirls	in	the	paIern	of	polarizaGon	of	
the	cosmic	microwave	background	
	
Coherent	on	~degree	s...
cosmic	whirls	
Right ascension [deg.]
Declination[deg.]
BICEP2: B signal
0.3μK
−50050
−65
−60
−55
−50
−0.3
0
0.3
μK
BICEP2...
What	Is	Infla%on?	
A	burst	of	expansion	in	which	the	early	Universe	grows	exponenGally	in	Gme	
It	puts	the		BANG		in	the		B...
Space-Gme	distorGon	hij	as	a	quantum	field	
Classical	Pendulum:	very	boring.	
Quantum	Pendulum:	very	exciGng!	
initial fina...
What	Is	Infla%on?	
A	burst	of	expansion	in	which	the	early	Universe	grows	exponenGally	in	Gme	
It	puts	the		BANG		in	the		B...
What	Is	Infla%on?	
A	burst	of	expansion	in	which	the	early	Universe	grows	exponenGally	in	Gme	
It	puts	the		BANG		in	the		B...
What	Is	Infla%on?	
A	(Nearly)	Scale	Invariant	Spectrum	of	Density	PerturbaGons	and	GravitaGonal	Waves	
“Let’s	go	to	the	boa...
Picture	of	the	CMB	
A	snapshot	of	the	early	universe	
“Let’s	go	to	the	board”
cosmic	whirls	
?	
These	are	a	unique,	and	possibly	observable	imprint	of	inflaGon.	
Kamionkowski,	Kosowsky,	Stebbins;	Selja...
What	Is	Infla%on?	
A	burst	of	expansion	in	which	the	early	Universe	grows	exponenGally	in	Gme	
It	puts	the		BANG		in	the		B...
Novel	GravitaGonal	Behavior	
L = 1
2 M2
P R 1
4
~Fµ⌫ · ~Fµ⌫
~Fµ⌫ = @µ
~A⌫ @⌫
~Aµ g ~Aµ ⇥ ~A⌫ SU(2)
Aa
i = (⌧) a
i flavor sp...
inspiraGon:	Tadashi	Tokieda	
camera:	Ralph	Gibson
Models	of	InflaGon	
Adshead	&	Wyman	2012;		
Maleknejad	&	Sheikh-Jabbari	2011;	
Dimastrogiovanni	&	Peloso	2013	
Chromo-Natur...
Models	of	InflaGon	
ns = 0.9667 ± 0.0040 (1 )
r < 0.07 (95% C.L.)
Planck	2016	
BKP	2016	
CMB-S3
New:	Toy	Model	of	InflaGon	
Devulder	&	RC	2017		
L = 1
2 M2
P R 1
2 (@ )2
V ( ) 1
4 Fa
µ⌫Fµ⌫
a + M Fa
µ⌫
eFµ⌫
a
V = 1
n m4
...
New:	Toy	Model	of	InflaGon	
V	is	too	steep	to	inflate:	
	
But,	for	a	wide	range	of	iniGal	condiGons	the	
coupling	flaIens	the...
New:	Toy	Model	of	InflaGon	
Scalar	FluctuaGons:	δχ, δΑ
three	dynamical	modes,	three	constraints	
	
Tensor	modes:	h,	δΑ
	fou...
New:	Toy	Model	of	InflaGon	
CMB-S3
Chiral	GravitaGonal	Waves	
TB	
BB	
EB	
' 0.9
Gluscevic	&	Kamionkowski	2010	
This	model	predicts		
An	addi8onal,	unique	obs...
Look	for	curl	paIern	in	the	polarizaGon.	
	
If	you	see	it	on	large	angular	scales,		
then	you	have	spoIed	gravitaGonal	wav...
Leptogenesis	
NR NL = 1
24(16⇡2)
R
d4
x
p
gR eR
Eguchi,	Gilkey,	Hanson	(1980)	
leptons	created,		
with	asymmetry
Leptogenesis	
Sakharov	CondiGons	
•  ViolaGon	of	baryon	number	
•  CP	violaGon	
•  Out	of	equilibrium	
…	saGsfied	
•  Lepto...
Leptogenesis	
⌘ ⌘ nB
n
' 1
7 ⇥ 28
79 ⇥ hn`i
s
⌘ ' 6.1(±0.04) ⇥ 10 10
Planck	2016	
Convert	to	baryon	asymmetry	
by	SM	elect...
Axion	Gauge-Field	Infla8on	
Viable	scalar	spectrum,	Observable	tensor	spectrum	
Unique	imprint:	chiral	asymmetric	SGWB	
Lep...
Caldwell seminar
Caldwell seminar
Caldwell seminar
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Caldwell seminar

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Caldwell seminar

  1. 1. A Unique and Observable Imprint of Infla8on Robert Caldwell / Dartmouth College
  2. 2. Dartmouth College Hanover, New Hampshire
  3. 3. Cosmic Microwave Background / Temperature Anisotropy / Planck 2015 SMICA map: combined input, painted mask
  4. 4. Cosmic Microwave Background / Temperature Anisotropy / Planck 2015 353 GHz map: polarized emission from dust grains traces galacGc magneGc field
  5. 5. What are we looking for? Swirls in the paIern of polarizaGon of the cosmic microwave background Coherent on ~degree scales, with sub-micro Kelvin magnitude A preferred handedness? (already spoIed)
  6. 6. cosmic whirls Right ascension [deg.] Declination[deg.] BICEP2: B signal 0.3μK −50050 −65 −60 −55 −50 −0.3 0 0.3 μK BICEP2 2014 BICEP2 / KECK x Planck 2015 Infla%onary gravita%onal waves? Not so fast! The search conGnues…
  7. 7. What Is Infla%on? A burst of expansion in which the early Universe grows exponenGally in Gme It puts the BANG in the BIG BANG InflaGon is the physics of a cosmic scalar field V φ Slow roll: @V/@ ⌧ 3H ˙ H ⌘ d ln a dt ' constant ! a / eHt The scale of the Universe grows exponenGally H ' 1014 GeV ! t ' 10 36 sec, ln a/ai ' 60 Solves the horizon problem! A clean slate for the observable Universe! ✏ ⌘ ˙H/H2 ⌧ 1 ¨ + 3H ˙ + V, = 0
  8. 8. Space-Gme distorGon hij as a quantum field Classical Pendulum: very boring. Quantum Pendulum: very exciGng! initial final Ei = 1 2 ~!i Ef = 1 4 ~!i !i = p g/Li !f = p g/Lf ni = 0 nf = !i/4!f initial final Ei = 1 2 ~!i Ef = 1 2 ~!f !i = p g/Li !f = p g/Lf ni = 0 nf = 0 Let the rope out quickly Let the rope out slowly For inflaGon, nf > 1027 ! Consider the QM of h as a pendulum whose length is controlled by the cosmic expansion ti, Li tf , Lf Quantum Mechanics of Space-Time
  9. 9. What Is Infla%on? A burst of expansion in which the early Universe grows exponenGally in Gme It puts the BANG in the BIG BANG InflaGon is the physics of a cosmic scalar field V δφ Quantum fluctuaGons: Explains the origin of large scale structure, as observed in the cosmic microwave background anisotropy paIerns and in the distribuGon of galaxies! h 2 ik = (H/2⇡) 2 Density spectrum: GW spectrum: φ hh2 i+,⇥,k = 2 (2/MP )2 h 2 ik h⇣2 ik = (H/ ˙)2 h 2 ik Review: Baumann 2012
  10. 10. What Is Infla%on? A burst of expansion in which the early Universe grows exponenGally in Gme It puts the BANG in the BIG BANG InflaGon is the physics of a cosmic scalar field V δφ Tilt: H slowly decays during inflaGon The PRIZE of cosmology: detect the long wavelength GWs, a unique feature of inflaGon φ RaGo: Amplitude of GW to density spectra V ' (r/0.01) ⇥ (1016 GeV)4 h⇣2 ik = 1 8⇡2✏ ✓ H 2⇡ ◆2 ! P⇣ / kns 1 r ⌘ hh2 i+⇥/h⇣2 i = 16✏
  11. 11. What Is Infla%on? A (Nearly) Scale Invariant Spectrum of Density PerturbaGons and GravitaGonal Waves “Let’s go to the board” cosmic %ny SIZE early late TIME H 1 Only inflaGon stretches density, GWs to lengths “outside” the Hubble radius (Nearly) Scale Invariant pick a radius: h i = 0 h 2 i = constant
  12. 12. Picture of the CMB A snapshot of the early universe “Let’s go to the board”
  13. 13. cosmic whirls ? These are a unique, and possibly observable imprint of inflaGon. Kamionkowski, Kosowsky, Stebbins; Seljak & Zaldariagga 1997
  14. 14. What Is Infla%on? A burst of expansion in which the early Universe grows exponenGally in Gme It puts the BANG in the BIG BANG Slow roll for a scalar field: V = 1 2 m2 2 if then m MP ✏ = 1 2 M2 P (V 0 /V )2 ⌧ 1 Detectable GW spectrum implies large field excursion MP = O(1) p r/0.01
  15. 15. Novel GravitaGonal Behavior L = 1 2 M2 P R 1 4 ~Fµ⌫ · ~Fµ⌫ ~Fµ⌫ = @µ ~A⌫ @⌫ ~Aµ g ~Aµ ⇥ ~A⌫ SU(2) Aa i = (⌧) a i flavor space locked ~Aµ · ~e⌫ = a(⌧)yµ⌫ gµ⌫ = a2 (⌧)hµ⌫ Devulder, Maksimova, RC 2016, 2017 Bielefeld, RC 2015, 2016
  16. 16. inspiraGon: Tadashi Tokieda camera: Ralph Gibson
  17. 17. Models of InflaGon Adshead & Wyman 2012; Maleknejad & Sheikh-Jabbari 2011; Dimastrogiovanni & Peloso 2013 Chromo-Natural InflaGon, Gauge-FlaGon L = 1 2 M2 P R 1 2 (@ )2 V ( ) 1 4 Fa µ⌫Fµ⌫ a + M Fa µ⌫ eFµ⌫ a L = 1 2 M2 P R 1 4 Fa µ⌫Fµ⌫ a + (Fa µ⌫ eFµ⌫ a )2 V = µ4 (1 cos /f) ! 1 2 m2 2
  18. 18. Models of InflaGon ns = 0.9667 ± 0.0040 (1 ) r < 0.07 (95% C.L.) Planck 2016 BKP 2016 CMB-S3
  19. 19. New: Toy Model of InflaGon Devulder & RC 2017 L = 1 2 M2 P R 1 2 (@ )2 V ( ) 1 4 Fa µ⌫Fµ⌫ a + M Fa µ⌫ eFµ⌫ a V = 1 n m4 ( /m)n
  20. 20. New: Toy Model of InflaGon V is too steep to inflate: But, for a wide range of iniGal condiGons the coupling flaIens the effecGve potenGal InflaGon! @ @ ⇣ V M F eF ⌘ ! 0 ✏V 1
  21. 21. New: Toy Model of InflaGon Scalar FluctuaGons: δχ, δΑ three dynamical modes, three constraints Tensor modes: h, δΑ four dynamical modes GeneralizaGon: SU(2) to SU(N)
  22. 22. New: Toy Model of InflaGon CMB-S3
  23. 23. Chiral GravitaGonal Waves TB BB EB ' 0.9 Gluscevic & Kamionkowski 2010 This model predicts An addi8onal, unique observable!
  24. 24. Look for curl paIern in the polarizaGon. If you see it on large angular scales, then you have spoIed gravitaGonal waves. Is the curl paIern correlated with hot or cold spots? Or with the gradient paIern in the polarizaGon? If no, then the gravitaGonal waves have no preferred handedness. If yes, then the gravitaGonal waves do have a preferred handedness.
  25. 25. Leptogenesis NR NL = 1 24(16⇡2) R d4 x p gR eR Eguchi, Gilkey, Hanson (1980) leptons created, with asymmetry
  26. 26. Leptogenesis Sakharov CondiGons •  ViolaGon of baryon number •  CP violaGon •  Out of equilibrium … saGsfied •  Lepton number violated •  Inflaton/gauge field are parity-odd •  InflaGon is far out of equilibrium
  27. 27. Leptogenesis ⌘ ⌘ nB n ' 1 7 ⇥ 28 79 ⇥ hn`i s ⌘ ' 6.1(±0.04) ⇥ 10 10 Planck 2016 Convert to baryon asymmetry by SM electroweak processes CMB-S3 (3σ) An observable within reach!
  28. 28. Axion Gauge-Field Infla8on Viable scalar spectrum, Observable tensor spectrum Unique imprint: chiral asymmetric SGWB Leptogenesis implies a lower bound for B modes

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