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Initial conditions of inflation and the power suppression
of the CMB spectrum
Yu-Hsiang Lin National Taiwan University
LeCosPA
Mon, Dec 5, 2016 at “New perspectives of Cosmology and Quantum Gravity” mini workshop, NTU
1
Chen and YHL 2016 (1505.05980)
Messages
2
Long-wavelength spectrum at the end of inflation reflects the super-horizon spectrum of the initial state
CMB large-scale suppression hints at a pre-inflation super-inflationary (w < -1) era
Introduction
3
Inflation solves the horizon problem
COBE DMR (http://lambda.gsfc.nasa.gov/product/cobe/dmr_image.cfm)
Planck Collaboration, A&A 571, A6 (2014)
Recombination
Matterdominated
Present
Hubble radius
Wavelengths
Scalescausallyconnected
N
logH physical length L
4
Inflation solves the horizon problem
Slow-roll
Recombination
Matterdominated
Present
Hubble radius
Wavelengths
Scalescausallyconnected
N
logH physical length L
5
COBE DMR (http://lambda.gsfc.nasa.gov/product/cobe/dmr_image.cfm)
Planck Collaboration, A&A 571, A6 (2014)
Low-ℓ/High-ℓ Tension
ΛCDM parameters are mostly constrained by high-
Power at < 50 is lower than the prediction of best-fit model Hinshaw et al. (WMAP 9 year), ApJS 208, 19H (2013)
6
Tension Persists
Planck Collaboration, A&A 571, A15 (2014)7
Tension Persists
Planck Collaboration, A&A 594, A11 (2016)8
Suppression at pre-inflation kinetic era
9
Linde, arXiv:1402.0526; Mukhanov 2005; Contaldi et al., JCAP 07, 002 (2003)
Overlooked initial vacuum state
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Different dynamics gives different background geometry
Different background geometry gives different initial vacuum state
This non-perturbative effect has been overlooked in model building
Initial state
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Scalar field—gravity system
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Parametrize the universe by its fluid-like character
Provide useful categorization
Perturbations
13
Mukhanov-Sasaki equation for the curvature perturbations
Mode function
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Solution to the mode functions
Adiabatic vacuum
15
Minkowski limit in the short-wavelength limit
Picks out the solution
Scaling relation
16
Power spectrum
At super-horizon scales, the power spectrum has the scaling relation
Scaling relation
17Chen and YHL, PRD 93, 023503 (2016)
Scaling relation
18Chen and YHL, PRD 93, 023503 (2016)
Spectrum evolution
19
Slow-roll
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Comoving Hubble radius
Kinetic—slow-roll
21
Chen and YHL, PRD 93, 023503 (2016)
Kinetic—slow-roll
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Slow-roll—kinetic—slow-roll
23
Chen and YHL, PRD 93, 023503 (2016)
Slow-roll—kinetic—slow-roll
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Superinflation—slow-roll
25
Chen and YHL, PRD 93, 023503 (2016)
Two-field inflation
26
Two-field system
27
Perturbations
28
Initial conditions
29
Curvature perturbation spectrum
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Chen and YHL, PRD 93, 023503 (2016)
CMB TT spectrum
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Chen and YHL, PRD 93, 023503 (2016)
CMB TT spectrum scan initial heavy field
32
Chen and YHL, PRD 93, 023503 (2016)
33
Chen and YHL, PRD 93, 023503 (2016)
CMB TT spectrum scan coupling constant
Messages
34
Long-wavelength spectrum at the end of inflation reflects the super-horizon spectrum of the initial state
CMB large-scale suppression hints at a pre-inflation super-inflationary (w < -1) era