Download - Cosmic Acceleration Then and Now
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Cosmic Acceleration Then and Now
Josh FriemanFermilab and the University of Chicago
Progress on Old and New Themes in CosmologyAvignon, April 18, 2014
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Last Supper(in earlier version of program)
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Cosmologists discuss BICEP2 results at PONT banquet
April, c. 33 AD
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Caveats and Thoughts• I am a recovering or lapsed theorist,
depending on your point of view.• Theoretical landscape that has developed in
recent years looks very rich, but a bit overwhelming
• BICEP2 results tremendously exciting, potentially transformative upon confirmation
• Theorists should be cautious about getting overly excited about 1-2 sigma discrepancies from standard model/expectations (only small fraction of `tensions’ will develop into significant inconsistencies).
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We have been very lucky so far
• Over the last 20+ years, at each new stage of experimental precision, a simple (few-parameter) cosmological paradigm has been confirmed: it didn’t have to turn out that way
• Observations consistent with Λ+Cold Dark Matter in a spatially flat, initially hot Universe, with adiabatic, nearly Gaussian, slightly non-scale-invariant scalar and (now likely) tensor perturbations, as expected from inflation
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Challinor
Simplicity staring us in the face
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Challinor
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Challinor
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Challinor
BICEP2
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Relax!
Baumann
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Baumanncontours without running shift slightly downward
Simple models written down 25-30 years ago are consistent with the data
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How important is it to test the consistency relation?
Dodelson
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What is the best way to tighten constraints on (ns,r)?
Dodelson
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Brief History of the Universe
Evidence for two epochs of accelerated expansionWhat are their physical origins?
Dark Energy Survey
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Mt. Ventoux
Elev. Gain 1640 m
Tues PM
Period of painful decelerationfollowed by rapid acceleration
Strong Mistral blowing
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Mt. Ventoux
Elev. Gain 1640 m
Tues PM Wed. AMI can confirm that my energy scale during the 2nd epoch was substantially lower
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Early Inflation• Early epoch of cosmic acceleration motivated
by flatness and horizon problems (Ne-folds>50-60)
• Theoretical context: GUTs and 1st order phase transitions
• Simplest model: weakly self-coupled scalar field that takes a cosmologically long time to reach its ground state
• Bonus: causal origin of density perturbations for structure formation and gravitational waves from quantum fluctuations.
• Growing observational evidence starting with COBE (April, 1992) through BICEP2 (March, 2014)
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Late Inflation• Current epoch of cosmic acceleration
motivated by missing energy and age problems (early/mid-1990s)– inflation predicted Ω0=1, clusters indicated
Ωm=0.25. Need a smooth component that only recently came to dominate
– H0t0~1 from Hubble parameter and globular cluster ages
– ΛCDM+inflation fit galaxy clustering measurements (APM)
• Simplest model: weakly self-coupled scalar field that takes a cosmologically long time to reach its ground state
• Growing observational evidence starting with supernovae (1998) through JLA (Dec. 2013)
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Late Inflation• Current epoch of cosmic acceleration
motivated by missing energy and age problems (early/mid-1990s)– inflation predicted Ω0=1, clusters indicated
Ωm=0.25. Need a smooth component that only recently came to dominate
– H0t0~1 from Hubble parameter and globular cluster ages
– ΛCDM+inflation fit galaxy clustering measurements (APM)
• Simplest model: cosmological constant
• Growing observational evidence starting with supernovae (1998) through JLA (Dec. 2013)
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Cosmological Constant and Late Inflation
• What is the justification for theoretical prejudice in favor of Λ as origin of current acceleration?
• Imagine theorists sitting around 10−35 sec after the Big Bang, when inflation had just started. – They would have said the Universe was
becoming Λ-dominated.– They would have been wrong.
• Being wrong once is not necessarily a strong argument in favor of it the 2nd time around.
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On the Other Hand
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Li
Modified Gravity Bestiary I
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Ferreira
Bestiary II
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Collective Schizophrenia?
• We appear to be both less (Λ prejudice) and more (Modified Gravity bestiary) agnostic about the physical origin of late acceleration relative to early acceleration. If so, why?
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Experiments can Probe the Physics of Cosmic
Acceleration
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Supernova Ia Hubble Diagram
33 SNeDis
tanc
e m
odul
us
(lo
g di
stan
ce)
SN figures by A. Conley
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52 SNe
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740 SNe
arXiv:1401.4064
JLA Collaboration
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vacu
um e
nerg
y de
nsity
matter density
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Supernovae
Cosmic Microwave Background (Planck, WMAP)
CMB+BAO
Here assuming w=−1
Progress over the last 16 years Betoule+ 2014
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Scalar Fields and Cosmic Acceleration
A homogeneous scalar field φ(t), slowly evolving in a potential, V(φ):
Density & pressure:
Slow roll:
V(j)
j
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Scalar Fields and Cosmic Acceleration
A homogeneous scalar field φ(t), slowly evolving in a potential, V(φ):
Density & pressure:
Slow roll:
V(j)
j
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Current Dark Energy Constraints from Supernovae, CMB, and Large-scale
Structure
Betoule etal 2014
Assuming constant w Assuming w=w0+wa(1-a)
Consistent with vacuum energy (Λ): w0=−1, wa=0
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• Probe dark energy through the history of the expansion rate:
• and the growth of large-scale structure:
• Weak Lensing cosmic shear Distances+growth
• Supernovae Distances• Baryon Acoustic Oscillations Distances and H(z)• Cluster counts Distances+growth• Redshift Distortions Growth
What can we probe?
Distance vs.redshift
Growth of DensityPerturbations
Require both to disentangle Dark Energy from Modified Gravity
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I. Clusters
Volume Growth
Number of clusters above mass threshold
Dark Energy equation of state
•Clusters are proxies for massive halos and can be identified to redshifts z>1• Galaxy colors provide photometric redshift estimates for each cluster, σ(z)~0.01•Challenge: determine mass-observable relation p(O|M,z) with sufficient precision• Multiple observable proxies O for cluster mass: optical richness (DES), SZ flux (SPT), weak lensing mass (DES), X-ray flux
Mohr
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Observer
Dark matter halos
Background sources
• Spatially coherent shear pattern, ~1% distortion• Radial distances depend on expansion history of
Universe• Foreground mass distribution depends on growth of
structure
II. Weak Lensing: Cosmic Shear
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Weak Lensing Mass and Shear
DES Simulation
Tick marks: shear
Colors: projected mass density
Becker, Kravtsov, etal
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III. Baryon Acoustic Oscillations
Fosalba & Gaztanaga
Galaxy angular power spectrumin photo-z bins (relative to model without BAO)
Photometric surveys provide this angular measure
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B. D
ilday
SDSS-II: 500 spectroscopically confirmed SNe Ia, >1000 with host redshifts from SDSS-III
IV. Supernovae
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Dark Energy Survey
Four Probes of Dark Energy
• Galaxy Clusters• Tens of thousands of clusters to
z~1• Synergy with SPT, VHS
• Weak Lensing• Shape and magnification
measurements of 200 million galaxies
• Baryon Acoustic Oscillations• 300 million galaxies to z = 1
and beyond• Supernovae
• 30 sq deg time-domain survey• 3500 well-sampled SNe Ia to z
~1
Forecast Constraints on DE Equation of State
DES forecastSee Gus Evrard’s talk
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Dark Energy Survey
Four Probes of Dark Energy
• Galaxy Clusters• Tens of thousands of clusters to
z~1• Synergy with SPT, VHS
• Weak Lensing• Shape and magnification
measurements of 200 million galaxies
• Baryon Acoustic Oscillations• 300 million galaxies to z = 1
and beyond• Supernovae
• 30 sq deg time-domain survey• 3500 well-sampled SNe Ia to z
~1
Forecast Constraints on DE Equation of State
DES forecast
current constraints: Betoule
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Inflation Models
Large-field
Small-field
Chaotic Natural
ΔΦ/MPl>3(r/0.1)1/2 BICEP r~0.2 favors large-field models
Baumann, McAllister
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Scalar Field Inflation(for large-field models favored by BICEP)
Equation of state: w > 1 and evolves in timeHierarchy: m/φ ~ 10−5 , H/M~10−2
Weak coupling: Quartic self-coupling ~ 1010
General features:
m ~ Hinf ~ 6x1014 GeV (slow roll) (BICEP)
V ~ M4~m2j2 ~ H2infM2
Pl ~ (2x1016 GeV)4
ji > MPl ~1019 GeV
V(j)
j1019 GeV
(1016 GeV)4
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Scalar Field Dark Energy
Equation of state: w > 1 and evolves in timeHierarchy: m/φ ~ 10−60 , H/M~10−30
Weak coupling: Quartic self-coupling < 10122
General features:
m < H0 ~ 10−33 eV (slow roll)
V ~ M4~m2j2 ~ H20M2
Pl ~ (10−3 eV)4
ji > MPl ~1019 GeV
V(j)
j1019 GeV
(10–3 eV)4
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The Coincidence Problem
Why do we live at the `special’ epoch when the dark energy density is comparable to the matter energy density?
matter ~ a-3
DE~ a-3(1+w)
a(t)
Today
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Scalar Field Models and Coincidence
VV
j
Runaway potentialsDE/matter ratio constant(Tracker Solution)
Pseudo-Nambu Goldstone BosonLow mass protected by symmetry(Cf. axion, natural inflation)M~10−3 eV JF, Hill, Stebbins, Waga
e.g., e–φ or φ–n
MPl
Ratra & Peebles; Caldwell, etal
`Dynamics’ models(Freezing models)
`Mass scale’ models(Thawing models)
j
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Caldwell & Linder
Dynamical Evolution of Freezing vs. Thawing Models
Measuring w and its evolution can potentially distinguish between physical models for acceleration
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Goal for Stage IV (LSST, Euclid, DESI, WFIRST)
Goal for Stage III DETF (e.g., DES)
Caution: ellipse sizes are impressionistic
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Effective Field Theory and Acceleration Models
• Technical naturalness: small dimensionless parameters in a theory (e.g., hierarchy of mass scales or coupling constants) should be protected by symmetries from large radiative corrections (t’Hooft)
• NOTE: small ≠ fine-tuned• Strong naturalness: small parameters or hierarchies
should emerge dynamically in fundamental theories without small parameters (e.g., QCD scale from logarithmic running of strong coupling)
• Inflation model-builders, coming out of hep-th, adopted EFT framework
• Dark Energy model-builders (astro-ph) not so much• In absence of such framework, not clear what
physics one learns from writing down arbitrary functions V(Φ)
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PNGB Models for Acceleration
Freese, JF, Olinto 1990
JF, Hill, Stebbins, Waga 1995
• Natural Inflation:
• Dark Energy:
• Spontaneous symmetry breaking at fundamental scale f
• Explicit breaking at lower scale M• Hierarchy protected by shift symmetry
(technically natural)• Lower scale M might be generated dynamically by
non- perturbative effects (strongly natural)
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Freese & Kinney
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Quintessential Inflation Tilted Mexican hat:
Rosenfeld, JF 2005, 2006
• Radial mode: inflaton• Angular mode: dark energy• Simplest model with 2 epochs of acceleration that
unifies the trans-Planckian scalar field amplitudes/excursions
f
M4
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Quintessential InflationRosenfeld, JF 2005, 2006
in Planck mass units
w0=−0.932, wa=−0.126 (fit to z<1) Testable
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Current Dark Energy Constraints from Supernovae, CMB, and Large-scale
Structure
Betoule etal 2014
Assuming constant w Assuming w=w0+wa(1-a)
Consistent with vacuum energy (Λ): w0=−1, wa=0
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Large-r Problem: Suppressing Higher order terms in EFT
This works
This doesn’t but is what you expect when φ is of order mPl
Shift symmetry, axion monodromy, natural inflation,…?
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Extranatural Inflation• Models with ΔΦ>MPl (BICEP2) and/or
f>MPl go beyond domain of validity of Effective Field Theory (Lyth)
• Expect global shift symmetry to be broken by Quantum Gravity corrections ~(Φ/MPl)n
• Inflaton as component of 5-d gauge field compactified on circle of radius R
• QG corrections under control if R>1/MPl
• Estimated ns=0.96, r=0.11 Arkani-Hamed, Cheng, Creminelli, Randall 2003
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Inflation and Equation of State
• Slow Roll parameters:• εV=(M2
P/2)(V’/V)2=r/16• ηV=M2
P(V”/V)• Scalar spectral index: ns-1=2ηV-6εV• Translation to Equation of State
parameter: 1+w=2εV/3=r/24• dln(1+w)/dlna=−2ηV+4εV=1-ns-r/8• Planck (ns=0.96)+BICEP (r=0.2): εV=0.0125, w=−0.992±0.003, ηV=0.0175, dln(1+w)/dlna=0.015±0.008 (50-60 e-folds before end of inflation)
Ilic, Kunz, Liddle, JF 2010
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What do we know?• First epoch of acceleration ended• It lasted at least N=50-60 e-folds• Observations probe ~10 e-folds range• Planck (ns=0.96)+BICEP (r=0.2): w=−0.992±0.003, dln(1+w)/dlna=0.015±0.008 (50-60 e-folds before end of inflation)• 2nd epoch has lasted N~0.4 e-folds so far• JLA: w0=−0.957±0.124, wa=−0.336±0.552• Stage IV DE uncertainties: w0~0.01,
wa~0.1
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Where do we go from here?• On-going and near-future CMB
experiments will test BICEP results• Probe physics of Inflation:
– nT=−r/5 consistency relation (challenging)– Primordial non-Gaussianity constraints– Higher-precision measurements of r, ns
• Probe physics of Late Acceleration:– Expansion history– Growth of structure– Surveys underway and planned
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PONT c’est merveilleux!(S’marvelous)
Merci beaucoup Chiara, Geraldine, Marco, Philippe!