W. Kinney - Scale-Invariant Perturbations: is Inflation the only Way?
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Transcript of W. Kinney - Scale-Invariant Perturbations: is Inflation the only Way?
Inflation … Or What?Will Kinney
SeenetMTP WorkshopBalkan Summer Institute, Donji Milanovac31 August 2011
CMB: Basic PropertiesCMB: Basic Properties
Adiabatic density perturbations
Superhorizon correlations
Gaussian statistics
Q: What does this really tell us?
Near scaleinvariance over a factor of1000 in wavelength
Generation of PerturbationsGeneration of Perturbations
Horizon
Mode freezing
Generation of PerturbationsGeneration of Perturbations
Comoving horizon:
Key ingredient for generation of perturbations: shrinking horizon
Decelerating Expansion:Accelerating Expansion:
The Comoving Horizon in InflationThe Comoving Horizon in Inflation
Decelerating
Accelerating
The Comoving Horizon in InflationThe Comoving Horizon in Inflation
Mode Exit and ReentryMode Exit and Reentry
exit
reentry
quantum
classical
Larger Scales Exit EarlierLarger Scales Exit Earlier
Superhorizon PerturbationsSuperhorizon Perturbations
The Horizon Is Not The HorizonThe Horizon Is Not The Horizon
The Hubble length is notthe causal horizon in inflation.
Mode freezing has absolutelynothing to do with causality.
The Horizon Is Not The HorizonThe Horizon Is Not The Horizon
In general, the Hubble length is not even the freezeout horizon:
Scale invariance and freezeout:
Is Inflation the Only Way?Is Inflation the Only Way?
Comoving Horizon (constant equation of state):
Duality:
Decelerating Expansion:Accelerating Expansion:
(Boyle, et al., hepth/0403026)
The Comoving Hubble Horizon in InflationThe Comoving Hubble Horizon in Inflation
Decelerating
Accelerating
The Comoving Hubble Horizon in Bouncing CosmologyThe Comoving Hubble Horizon in Bouncing Cosmology
Bounce
Contraction
Expansion
Slow RollSlow Roll
The Cyclic Dual to Slow RollThe Cyclic Dual to Slow Roll
Slow RollSlow Roll
The Cyclic Dual to Slow RollThe Cyclic Dual to Slow Roll
Slow RollSlow Roll
DualSlow RollDualSlow Roll
The Cyclic Dual to Slow RollThe Cyclic Dual to Slow Roll
Quasistatic contraction
Slow RollSlow Roll DualSlow RollDualSlow Roll
(WHK, Moradinezhad Dizgah, arXiv:1007.0753)
PerturbationsPerturbations
EkpyrosisEkpyrosis: Problems: Problems
Shrinking proper Hubble length: blue spectraInstabilities: growing mode
Singular bounce
Negative potential
Name sounds like a skin disease
Buchbinder, Khoury & Ovru, PRD 76, 123503 (2007)Khoury & Steinhardt, arXiv:0910.2230Linde, Mukhanov & Vikman, arXiv:0912.0944
Generating Superhorizon PerturbationsGenerating Superhorizon Perturbations
(1) Accelerated Expansion
(2) Superluminal Sound Speed
(3) SuperPlanckian Energy Density
New result:
In an expanding universe, to generate perturbations consistent with observation, youmust have one of:
(Geshnizjani, WHK, Moradinezhad Dizgah, arXiv:1107.1241)
NonCanonical Lagrangians as Bimetric TheoriesNonCanonical Lagrangians as Bimetric Theories
Lagrangian with arbitrary kinetic term:
Acoustic metric
Light cone:
Acoustic cone: Two horizons!
x
y
Light Cones in DBI InflationLight Cones in DBI Inflation
Acoustic Cone:Light cone:
Mode Freezing and HorizonsMode Freezing and Horizons
Tensor modes freeze out at theHubble Horizon
Scalar modes freeze out at theAcoustic Horizon
Curvature perturbations generatedby shrinking acoustic horizon!
(Garriga & Mukhanov, arXiv:hepth/9904176)
Horizons in DBI InflationHorizons in DBI Inflation
Hubble Horizon
Acoustic Horizon
Beyond InflationBeyond Inflation
For we still need inflation to generate superhorizonperturbations.
: generate superhorizon perturbations in a radiation or matterdominated universe
Tachyacoustic Cosmology
Causally selfconsistent cosmology: no timelike loops.Babichev, Mukhanov & Vikman, arXiv:0708.0561
Bessada, WHK, Stojkovic, Wang, arXiv:0908.3898
ArmendarizPicon, arXiv:astroph/0606168 Piao, arXiv:grqc/0609071
Magueijo, arXiv:08030859
x
y
Light Cones in Tachyacoustic CosmologyLight Cones in Tachyacoustic Cosmology
Light cone:
Acoustic Cone:
The Tachyacoustic SolutionThe Tachyacoustic Solution
Decelerating Expansion:
Decaying Sound Speed:
Horizons in Tachyacoustic CosmologyHorizons in Tachyacoustic Cosmology
Hubble Horizon:
Acoustic Horizon:
Hubble Horizon grows (no tensor modes!)
Acoustic Horizon shrinks
Horizons in Tachyacoustic CosmologyHorizons in Tachyacoustic Cosmology
Hubble Horizon
Acoustic Horizon
Perturbations in Tachyacoustic CosmologyPerturbations in Tachyacoustic Cosmology
Hubble Horizon:
Acoustic Horizon:
(Magueijo, arXiv:0803.0859)
(Bessada, WHK, Stojkovic, Wang, arXiv:0908.3898)
Tachyacoustic Cosmology: ProblemsTachyacoustic Cosmology: Problems
String embedding problematic
Does not solve flatness problem
Is it a dynamical attractor? (Preliminary: yes)
Initial singularity
SummarySummary
The Hubble length is not the horizon.
Expanding universe: only three ways to get scaleinvariance for a sufficient range of superHubble perturbations:
Accelerated expansionSuperluminal sound speedTransplanckian energy density
Nothing works nearly as well as inflation.