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Could Dark Energy be novel matter or modified gravity?
Rachel BeanCornell University
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Modern (20th century) Cosmology
Observations Theory
Hubble
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Einstein
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Philosophy
As we know,There are known knowns.There are things we know we know.We also knowThere are known unknowns.That is to sayWe know there are some thingsWe do not know.But there are also unknown unknowns,The ones we don't knowWe don't know.
—Feb. 12, 2002, Department of Defense news briefing
Modern (20th century) Cosmology
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Overview
The `known knowns’ – kinematical acceleration
The ‘known unknowns’– theoretical approaches to dark energy
Can we know the known unknowns?– Observational tests for dark energy
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Expansion today
• Observe a cosmological redshift <-> expansion rate and acceleration
• Luminosity distance F = L/4dL2
a(t)
ttodayHubble factor
Deceleration parameter
dL
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Hubble’s law: true to even larger distances
Riess 1996
Hubble 19293 million
Distance (lightyears)
0
500
1000
Velocity (km/sec)
0
06 million
Observations of distant Supernovae
Distance (millions of lightyears)300 600 900 1200 150000
Velocity (km/sec)
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Two alternative explanations for the expanding universe
• In this model, the universe will always look the same, and had no beginning
• The universe is expanding but new matter is being created all the time (from nothing!).
• Universe is expanding and is always changing, matter becomes less dense & cooler
• Universe had a hot and incredibly small beginning: “The Hot Big Bang”
Steady State Model vs. Big-Bang Model
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Which theory was correct?
Pigeons? Primordial radiation?
What was causing it?
Penzias & Wilson in NJ in 1964 observed electromagnetic radiation from all directions in the sky, all at the same temperature, 2.7 Kelvin.
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Evidence of deceleration followed by recent acceleration
z evolution of luminosity distance of Supernovae in HST/Goods survey
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z
Riess et al 2004
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Overview
The `known knowns’ – kinematical acceleration
The ‘known unknowns’– theoretical approaches to dark energy
Can we know the known unknowns?– Observational tests for dark energy
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Observations have driven key theoretical developments
But also create many unanswered questions in themselves!
What happened right at the beginning?
What is dark matter?
Can we detect the dark matter in ground based experiments?
What is dark energy?
An expanding universe Cosmic microwave background
Galaxy outer rotation velocities
An accelerating universe
General relativityApplied to the cosmos
Hot Big Bang Dark matter Dark energy
Hubble 19291 Distance (Mpc)
0
500
1000
Velocity (km/sec)
0
0 2
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Einstein’s description of the cosmos
• On the largest scales the universe is controlled by gravity.
• Our best description of gravity is GR, as formulated by Einstein: G = 8G T
c4
Einstein’s Tensor: Evolution of space and time
Stress-Energy Tensor: Evolution of matter density and pressure
Matter tells space how to bend/expandSpace tells matter how to move
Matter makes the universe expand
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Friedmann-Lemaitre-Robertson-Walker Universe
• The CMB shows that the universe is homogeneous and isotropic
• FLRW applies Einstein’s equations to this simplified case– Described by single number, the size of the universe,
a(t)
• Acceleration possible only if dominant matter has negative pressure, w<-1/3
Friedmann
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Evidence of deceleration followed by recent acceleration
z evolution of luminosity distance of Supernovae in HST/Goods survey
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Riess et al 2004
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Einstein’s `Biggest Blunder’?
• Prior to Hubble’s observations, scientists believed the universe was static
• Einstein added in a fudge factor to his equations, called the “cosmological constant” to enable a static universe.
• Later when Hubble’s discovery of expansion was made, Einstein is said to have called the cosmological constant “my biggest blunder”.
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Current conclusions
• Observations from supernovae, cosmic microwave background and large scale structure all give a remarkably consistent picture
• However, this picture is dumbfounding since we do not understand 96% of it!
w=-1 w~0
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The key dark energy questions
• How do we modify Einstein’s Field Equations to explain acceleration?
- Non-minimal couplings to gravity? –Higher dimensional gravity?–Effects of anisotropy and inhomogeneity
Adjustment to gravity?
-An ‘exotic’, dynamical matter component “Quintessence”? – ‘Unified Dark Matter’?
Adjustment to matter?Cosmological constant “”?
-“Vacuum energy” left over from early phase transitions?-Holographic?-Anthropic?
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Why so small?
UV divergences are the source of a dark energy fine-tuning problem
• The cut off scale would have to be way below the scales currently in agreement with QFT (Casimir effect, Lamb shift)
- The problems with it
= ?
a) QFT = ∞?b) regularized at the Planck scale = 1076 GeV4?c) regularized at the QCD scale = 10-3 GeV4 ?d) 0 until SUSY breaking then = 1 GeV4?e) all of the above = 10 -47 GeV4?f) none of the above = 10 -47 GeV4?g) none of the above = 0 ?
Why now?
• Coincidence problem– Any later still negligible, we
would infer a pure matter universe– Any earlier chronically affects
structure formation; we wouldn’t be here
• Inevitably led to anthropic arguments– At most basic predict / m<125
Transition to dark energy domination
e+
e-
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• Scalar x,t - spin 0 particle (e.g Higgs)
• Accelerative expansion when potential dominates
• Scaling potentials– Evolve as dominant background matter
– Need corrections to create eternal or transient acceleration
• Tracker potentials–Insensitive to initial conditions
Wetterich 1988, Ferreira & Joyce 1998
Kinetic
Potential V(
Tackling the fine-tuning problem
Ratra & Peebles 1988
Wang, Steinhardt, Zlatev 1999
Scaling potentials
Tracker potentials
.
.
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w(z) evolution with an oscillatory potential
W tot
Dodelson , Kaplinghat, Stewart 2000
Tackling the coincidence problem: are we special?
• We’re not special: universe sees periodic epochs of acceleration
• We are special: the key is our proximity to the matter/ radiation equality
–Non-minimal coupling to matter (Amendola 2000, Bean & Magueijo 2001)
–k-essence : A dynamical push after zeq with non-trivial kinetic Lagrangian term (Armendariz-Picon, et al 2000)
–the coincidence is a result of a coupling to the neutrino (Fardon et al 2003), ghostlike behavior (de la Macorra et al 2006)
V~M4e- (1+Asin )
Dodelson , Kaplinghat, Stewart 2000
w(z) evolution with a non-minimal coupling to dark matter
log(a)
log(a)
w tot
Bean & Magueijo 2001
21/46 STSci Mar 7th 2007Bean, Hansen, Melchiorri 2001
Early constraints on dark energy density
Dark energy vs baryon density BBN constraints
Tackling the problems: implications for BBN
• Scaling potentials can predict significant dark energy at earlier times – treating Q as Nrel Ferreira & Joyce
1998, Bean, Hansen, Melchiorri 2001
• Bounds on Helium mass fraction, YHe
– YHe=0.24815 ± 0.00033 ±0.0006 (sys) Stegiman 2005
• Relative Deuterium abundance D/H– D/H=(2/58+0.14-0.13).10-5
Steigman(2005)– But collated more recent value D/H =
2.6 ±0.4).10-5 Kirkman et al (2003)
• Abundance limits conservatively correspond to Nrel<0.2 – This translates into Q (MeV)<0.05
(2)
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• ‘Unified’ dark matter/ dark energy– Clustering at early times like CDM, w~0, cs
2~0 – Accelerating expansion at late times like , w <0
• Phenomenology: Chaplygin gases–an adiabatic fluid, parameters w0,
• Strings interpretation? Born-Infeld action is of this form with e.g. Gibbons astro-ph/0204008 )
w
lg(a)
Tackling the dark matter and dark energy problems as one
Bean and Dore PRD 68 2003
Evolution of equation of state for Chaplygin Gas
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• Quintessential inflation (e.g. Copeland et al 2000, Binetruy, Deffayet,Langlois 2001)
– Brane world scenario – 2 term increases the damping of as rolls down potential at early (inflationary) times
–inflation possible with V () usually too steep to produce slow-roll
• Curvature on the brane (Dvali ,Gabadadze Porrati 2001)
–Gravity 5D (Minkowski) on large scales l>lc~H0
-1 i.e. only visible at late times–Although 4D on small scales not Einstein gravity
–Potential implications for solar system tests as well as horizon scales
• Large scale modifications to GR–Modify action so triggered at large scales R~H0
2 –Potential implications for solar system tests as well as horizon scales
Modifications to gravity rather than matter
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Overview
The `known knowns’ – kinematical acceleration
The ‘known unknowns’– theoretical approaches to dark energy
Can we know the known unknowns?– Observational tests for dark energy
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Dark energy perturbations: an important discriminator?• Natural extension to looking for w≠-1 ,dw/dz≠0 from (a)
– Include constraints on (a) sensitive to cs2 = dP/d
• To distinguish between theories …– only effecting the background , alterations to FRW cosmology)– with negligible clustering cs
2 = 1 (minimally coupled quintessence)
– that could contribute to structure formation (non-minimally coupled DE, k-essence)
• To test if dark matter and dark energy are intertwined?– unified dark matter?
• From a theorist’s perspective, to decipher the dark energy action– probing the dark energy external and self-interactions (or lack of) bound up in an effective potential
• From an observational perspective, to check that a prior assuming no perturbations is fair– Does it effect the combination of perturbation independent (SN) and potentially dependent (CMB/LSS/WL) observations?
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Linking theory and observations
SN 1a HST Legacy, Essence,DES, SNAP
Baryon Oscillations SDSS Alcock-Paczynski test
CMB WMAP
CMB/ Globular cluster
Tests probing background
evolution only
• Late time probes of w(z)– Luminosity distance vs. z– Angular diameter distance vs. z
• Probes of weff
– Angular diameter distance to last scattering
– Age of the universe
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Linking theory and observations
Galaxy /cluster surveys, SZ and X-rays from ICMSDSS, ACT, APEX, DES, SPT
CMB and cross correlationWMAP, PLANCK, with SNAP, LSST, SDSS
Tests probing perturbations and background
Weak lensing CFHTLS, SNAP, DES, LSST
• Late time probes of w(z)– Luminosity distance vs. z– Angular diameter distance vs. z
• Probes of weff
– Angular diameter distance to last scattering
– Age of the universe
• Late time probes of w(z) and cs
2(z)
– Comoving volume * no. density vs. z
– Shear convergence– Late time ISW
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• Early time probes of Q(z)– Early expansion history
sensitivity to relativistic species
BBN/ CMB WMAP
Tests probing early behavior of dark energy
Linking theory and observations
• Late time probes of w(z)– Luminosity distance vs. z– Angular diameter distance vs. z
• Probes of weff
– Angular diameter distance to last scattering
– Age of the universe
• Late time probes of w(z) and cs
2(z)
– Comoving volume * no. density vs. z
– Shear convergence– Late time ISW
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Linking theory and observations
• Late time probes of w(z)– Luminosity distance vs. z– Angular diameter distance vs. z
• Probes of weff
– Angular diameter distance to last scattering
– Age of the universe
• Late time probes of w(z) and cs
2(z)
– Comoving volume * no. density vs. z
– Shear convergence– Late time ISW
• Early time probes of Q(z)– Early expansion history
sensitivity to relativistic species
• Alternate probes of non-minimal couplings between dark energy and R/ matter or deviations from Einstein gravity– Equivalence principle
tests– Deviation of solar
system orbits– Varying alpha testsTests probing
general deviations in GR or 4D existence
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Evolution of H(z) is the primary observable• In a flat universe, many
measures based on the comoving distance
• Luminosity distance
• Angular diameter distance
• Comoving volume element
• Age of universe
r(z) = ∫0z dz’ / H(z’)
dL(z) = r(z) (1+z)
dA(z) = r(z) / (1+z)
dV/dzdΩ(z) = r2(z) / H(z)
t(z) = ∫ z∞ dz/[(1+z)H(z)]
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Acoustic baryon oscillations
• Compares tranverse + radial scale
• Observe the ‘sound wave’ generated at last scattering surface– 500 million light years across– Expect correlations in the
large scale structure on this scale
• Systematics do not mimic features in correlation (Seo and Eisenstein 2003)– Dust extinction, – galaxy bias, – redshift distortion – non-linear corrections
wmh2mh2
Distance to z=0.35 (Mpc)
Eisenstein et al 2004
SDSS ~48000 galaxies with z~0.35
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Kinematical constraints on constant w and w(a)
Davis et al 2007
w0wa
w0
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Davis et al 2007
Kinematical constraints on DGP background
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Kinematical constraints on Chaplygin gas as dark energy
Davis et al 2007
w0
w0
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f(R) gravity has difficulties fitting observations
Bean et al 2006
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• Ansatz for H(z), dl(z) or w(z)
• w(z) applies well to scalar fields as well as many extensions to gravity Linder 2003
–Taylor expansions robust for low-z
• Do parameterizations relate to microphysical properties (w=p/andcs
2 = p/) or just an effective description?–Need to have multi pronged observational approach
Reconstructing dark energy : a cautionary note
• But, parameterizations can mislead
• Need to consider additional parameter dependencies (Curvature, neutrino mass)
Maor et al 2002
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Reconstructing dynamic evolution
w=-0.7+0.8z with constant w
Constant w fit
w>-1 fit
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Beyond CDM: Dark Energy Robust
mv (eV)
k
w
CMB + SN + LSS
w + massive neutrinosw
CMB + SN + LSS
w + curvature
Spergel et al 2006
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Should also leverage evolution on different spatial scales
From Max Tegmark for SDSS
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• Dark energy domination suppresses growth in gravitational potential wells ,
Ga2
• Late time Integrated Sach’s Wolfe effect (ISW) in CMB photons results- Net blue shifting of photons as they traverse gravitational potential well of baryonic and dark matter on way.
• ISW important at large scales
• Dark energy clustering counters suppression due to accelerative expansion–Decreases ISW signature
x
x(t)
CDM dominatedor clustering DE
dominated orNon clustering DE
CMB spectra for DE models incl/excl perturbations
w<-1 w>-1
without
with
without
with
Hu 1998, Bean & Dore PRD 69 2003Lewis & Weller 2003
ISW: Dark energy signature in CMB photons
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Beyond CDM: Dark Energy
Sensitive to assumptions about clustering properties of Dark Energy
Clustering dark energy cs2=1 w≠-1If fluctuations in DE negligible
WMAPWMAP+SDSS
WMAPWMAP+2dF
WMAPWMAP+SN (HST/GOODS)
WMAPWMAP+SN (SNLS)
WMAPWMAP+SDSS
WMAPWMAP+2dF
WMAPWMAP+SN (HST/GOODS)
WMAPWMAP+SN (SNLS)
m m m m
ww w
w ww w
w
m m m m
Spergel et al 2006
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• Degeneracies & cosmic variance prevent constraints on clustering itself–Large scale anisotropies also altered by spectral tilt, running in the tilt and tensor modes
• Dark energy clustering will be factor in combining future high precision CMB with supernova data.
• Avoid degeneracies by cross correlating ISW with other observables ….– galaxy number counts– Radio source counts– Weak lensing of galaxies or CMB ….
ISW: Perturbations and CMB & LSS inferences
Bean & Dore 2003, Lewis & Weller 2003
‘Constraints’ on w and cs2 from WMAP
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• ISW intimately related to matter distribution
• Cross-correlation of CMB ISW with LSS.e.g. NVSS radio source survey (Boughn & Crittenden 2003 Nolta et al 2003, Scranton et al 2003)
• WMAP+SDSS LRG +SDSS QSO +NVSS 6 sigma detection (Scranton et al in progress)
• Current observations cannot distinguish dark energy features (Bean and Dore PRD 69 2003)
• Future large scale surveys which are deep, ~z=2, such as LSST might well be able to (if w≠ -1) (Hu and Scranton 2004)
(deg)
CNT (cnts k)
contours
Nolta et al. 2003
Cross correlation of radio source number counts and WMAP
ISW
0 5 10 15 200
20
10
30
50
40
Likelihoo
d
0 1 12
18
0
1
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ISW: CMB cross correlation with LSS
Nolta et al 2003
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Weak lensing: recent constraints from CFHT
Hoekstra et al 2005, Semboloni et al 2005
-1.5
-1.0
-0.5
0.
w
-1.5
-1.0
-0.5
0.
w
m
0.40.2 0.6 0.8m
0.40.2 0.6 0.8
CFHT Legacy Survey Wide Field Survey (22sq deg)
CFHT Legacy Survey Wide Field +Deep Surveys (2x 1 deg)
Constraints on CDM density and dark energy equation of state from Weak lensing
-2.0-2.0
Spergel et al 2006m
8
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Weak lensing tomography :prospects
• SNAP and LSST offer exciting prospects for WL– e.g. SNAP measuring 100 million galaxies
over 300 sqdeg
• Tomography => bias independent z evolution of DE– Ratios of growth factor (perturbation)
dependent observables at different z give growth factor (perturbation) independent measurement of w, w’
• Possibly apply technique to probe dark energy clustering ?
• Understanding theoretical and observational systematics key– effect of non-linearities in power spectrum – Accurately reconstructing anisotropic point
spread function– z-distribution of background sources and
foreground halo– inherent ellipticities …– Use of higher order moments to reduce these
…
SNAP collaborationAldering et al 2004
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Deep survey
Wide survey
SNAPSN1a
w
0.0
-0.5
-1.0
-1.5
-2.00.0 0.2 0.4 0.6 0.8
Wide survey+ non-Gaussian info
M
Prospective constraints on w from the SNAP SN1a + WL
measurements
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Acoustic baryon oscillations: prospects
• 30,000 sq degree survey with ~54 galaxies per arcminute2
• Redshift slices between z=0.2 and 3
• Competitive predictions with WL tomography and future large supernovae surveys
• Cross correlation of weak lensingand BAO ?
2000 SN1a
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Linking Dark Energy Observations and Theory
Einstein on Theory:“If an idea does not appear absurd at first then there is
no hope for it”
Einstein on Observation:"Joy in looking and
comprehending is nature's most beautiful gift.”
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