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)

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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

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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

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Mukhanov-Sasaki equation for the curvature perturbations

Mode function

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Solution to the mode functions

Adiabatic vacuum

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Minkowski limit in the short-wavelength limit

Picks out the solution

Scaling relation

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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

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Slow-roll

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Comoving Hubble radius

Kinetic—slow-roll

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Chen and YHL, PRD 93, 023503 (2016)

Kinetic—slow-roll

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Slow-roll—kinetic—slow-roll

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Chen and YHL, PRD 93, 023503 (2016)

Slow-roll—kinetic—slow-roll

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Superinflation—slow-roll

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Chen and YHL, PRD 93, 023503 (2016)

Two-field inflation

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Two-field system

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Perturbations

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Initial conditions

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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

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Chen and YHL, PRD 93, 023503 (2016)

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Chen and YHL, PRD 93, 023503 (2016)

CMB TT spectrum scan coupling constant

Messages

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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