Inflation and the origin of structure
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Inflation and the origin of structure
Inflation and the origin of structure
David WandsInstitute of Cosmology and
GravitationUniversity of Portsmouth
Niew Views of the Universe, KICP Symposium 10th December 2005
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Standard model of structure formationStandard model of structure formationprimordial perturbations
in cosmic microwave background
Inflation:Inflation: initial false vacuum state drives accelerated expansion zero-point fluctuations yield spectrum of perturbations
large-scale structure of our Universe
gravitational
instability
new observational data offers precision tests of
• cosmological parameters
• the nature of the primordial perturbations
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• period of accelerated expansion in the very early universe
• requires negative pressure
e.g. self-interacting scalar field
• speculative and uncertain physics
Cosmological inflation: Starobinsky (1980)
Guth (1981)
V()
• just the kind of peculiar cosmological behaviour we observe today
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coherent oscillations in photon-baryon plasma due to primordial density
perturbations on super-horizon scales
Wilkinson Microwave Anisotropy Probe February 2003
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vacuum fluctuationsswept up by accelerated expansion
V()
• small-scale/underdamped zero-point fluctuations
• large-scale/overdamped perturbations in growing mode
linear evolution Gaussian random field
ka
e ik
k2
2
3
23
2
2)2(
4
Hk k
aHk
fluctuations of any scalar light fields (m<3H/2) `frozen-in’ on large scales
Hawking ’82, Starobinsky ’82, Guth & Pi ‘82
linking the very small to the very large!
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inflation probes high energies
• cosmic expansion on large scales
• reconstruct inflaton potential• modified Friedmann equation
• quantum vacuum on small scales
• trans-Planckian effects (modified dispersion relation, Lorentz-violation...)
...)(8
22
VM
HPl
...2
22
a
k
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Field perturbations on a branecoupled to metric perturbations
recover 4D gravity at low energies
but probe 5D at high energies
• 5D backreaction at high energycan damp small scale oscillations
:backreaction from 5D
Koyama, Mizuno & Wands ‘05
advertisement: see talk by Andy Mennim on Monday!
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primordial perturbations from scalar fields
during inflation field perturbations (x,ti) on initial spatially-flat hypersurface
in radiation-dominated era curvature perturbation on uniform-density hypersurface
final
initialdtHN
II I
initial
NNN
on large scales, neglect spatial gradients, treat as “separate universes”
Sasaki & Stewart ’96
t
x
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density perturbations from inflaton field perturbations• quantum fluctuations on spatially flat (N=0)
hypersurfaces during inflation
• produce density perturbations in radiation-dominated era
aHk
H
d
dN
222
2
2
225
1
25
1
aHkSW
H
T
T
2
2
2
2
3,where
126ln
ln1:tilt
Hm
HH
kd
dn
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tensor metric perturbations
• transverse, traceless metric perturbations
• amplitude, h(t), obeys same wave equation for massless field
• remain decoupled from matter perturbations
)()(),( ),(3 xethkdxtg ijkij
2
22
2
64
aHkPl
H
MT
2
2
where2ln
ln:tilt
HH
kd
TdnT
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“smoking gun” for inflation...
• inflation predicts primordial gravitational wave background
• could be
• or could be
• only detectable if inflationary scale > 10 15 GeV
aHkPlM
VT
4
2
12
416
1010
PlM
GeV
64
4
101
PlM
TeV
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Seljak et al (2004)
162
2
T
r
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• coupled fields during slow-roll during inflation
Starobinski & Yokoyama; Sasaki & Stewart; Mukhanov & Steinhardt; Linde, Garcia-Bellido & Wands.... (1995)
•curvaton decay after inflation
weakly-coupled, late-decaying scalar field
Enqvist & Sloth; Lyth & Wands; Moroi & Takahashi (2001)
• inhomogeneous / modulated reheating or preheating
inflaton decay-rate modulated by another light field
Dvali, Gruzinov & Zaldariaga; Kofman (2003); Kolb, Riotto & Vallinotto (2004)
•inhomogeneous end of inflation
Lyth; Salem (2005)
but fluctuations in other fields can also perturb radiation density after inflation
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primordial perturbations from isocurvature fields during inflation• quantum fluctuations on spatially flat (N=0)
hypersurfaces during inflation
• produce density perturbations in radiation-dominated era
• amplitude depends upon physics• but spectral tilt set during inflation
d
dN
22
2
2
225
1
25
1
aHkSW
H
d
dN
T
T
2
2
2 3,where
221:tilt
Hm
HH
n
where N() dependent on physics
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chaotic inflation:chaotic inflation:
(I) inflaton perturbations
16.0
96.0261
r
n
01.0
2
1
2
1 22222
mmV
(II) isocurvature perturbations
16.0
1221
r
n
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Seljak et al (2004)
modulated preheating?Byrnes & Wands (astro-ph)
inflaton
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distinctive observational predictions inflaton perturbations
adiabatic no isocurvature perturbations Gaussian
isocurvature field perturbations non-adiabatic possible residual isocurvature modes... ... correlated with curvature perturbation possible non-Gaussianity
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Gaussian field perturbations to first order
give non-Gaussian metric perturbation to second order
linear evolution -> Gaussian perturbations stay Gaussian
non-linear evolution -> non-Gaussianity!single-field inflation Maldacena (2002);
Acquaviva, Bartolo, Matarrese & Riotto (2002+);
beyond slow roll Creminelli & Zaldarriaga (2003);
Lidsey & Seery (2004);
multi-field inflation Rigopoulos, Shellard & van Tent (2003+)
Lyth & Rodriguez (2004);
Allen, Gupta & Wands (2005)
11
N
212
2
22 2
1
NN
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“local” non-Gaussianity
constraints from WMAP: -58 < fNL < 134
simplest kind of non-Gaussianity:Komatsu & Spergel (2001)
Wang & Kamiokowski (2000)
211 5
3 NLf
gives bispectrum:
)()()()()()(),,( 133221321 kPkPkPkPkPkPfkkkB NL
more data to come...
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• perturbation due to inflaton field
• where can be calculated during inflation
• N, must be small during slow-roll inflation
• but perturbations from non-adiabatic perturbations dependent upon subsequent expansion history
Detectable non-Gaussianity can come from non-adiabatic perturbations in non-inflaton fields Lyth & Rodriguez (2005)
21,2,2
1,1
NN
N
)/()/(,/ 2,, HHHNHN
21,2,2
1,1
NN
N
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non-Gaussianity from curvaton decay
constraints on fNL from WMAP - fNL < 58
hence ,decay > 0.01 and 10 -5 < / < 10 -3
simplest kind of non-Gaussianity:Komatsu & Spergel (2001)
Wang & Kamiokowski (2000)
211 )5/3( NLf
2
decay,decay,
recall that for curvaton
Lyth, Ungarelli & Wands ‘02
decay,decay,1 6
5,
NLf
corresponds to
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Conclusions:Conclusions:
• Inflation links very small scale vacuum fluctuations to very large scale structure of our universe
• Precision cosmology (especially cosmic microwave background data) offer detailed measurements of primordial density perturbations
• Gravitational waves, primordial isocurvature perturbations and/or non-Gaussianity could provide valuable info about origin of perturbations
• Single-field slow-roll inflation predicts adiabatic density perturbations with negligible non-Gaussianity could give detectable gravitational waves
• Multi-field inflation allows non-adiabatic perturbations during inflation, which could give detectable primordial isocurvature perturbations and/or local non-Gaussianity