could dark energy be novel matter or modified gravity?

1/46 STSci Mar 7th 2007

Could Dark Energy be novel matter or modified gravity?

Rachel BeanCornell University


Modern (20th century) Cosmology

Observations Theory

Hubble

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are needed to see this picture.

Einstein


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


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


Expansion today

• Observe a cosmological redshift <-> expansion rate and acceleration

• Luminosity distance F = L/4dL2

a(t)

ttoday

Hubble factor

Deceleration parameter

dL


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)


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


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.


Evidence of deceleration followed by recent acceleration

z evolution of luminosity distance of Supernovae in HST/Goods survey



z

Riess et al 2004


Overview





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


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






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


Evidence of deceleration followed by recent acceleration

z evolution of luminosity distance of Supernovae in HST/Goods survey



z QuickTime™ and aTIFF (Uncompressed) decompressor




Riess et al 2004


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”.




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


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?


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-


• 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

.

.


w(z) evolution with an oscillatory potential

Wtot

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)

wtot

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)


• ‘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


• 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


Overview





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 cs2 = 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?


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


to last scattering

– Age of the universe



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




vs. z

• Probes of weff


to last scattering


• Late time probes of w(z) and

cs2(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

BBN/ CMB WMAP

Tests probing early behavior of dark energy





vs. z

• Probes of weff


to last scattering



cs2(z)


density vs. z


– Late time ISW






vs. z

• Probes of weff


to last scattering



cs2(z)


density vs. z


– 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


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)]


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


Kinematical constraints on constant w and w(a)

Davis et al 2007

w0wa

w0


Davis et al 2007

Kinematical constraints on DGP background


Kinematical constraints on Chaplygin gas as dark energy

Davis et al 2007

w0

w0


f(R) gravity has difficulties fitting observations

Bean et al 2006


• 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



Reconstructing dynamic evolution

w=-0.7+0.8z with constant w

Constant w fit

w>-1 fit


Beyond CDM: Dark Energy Robust

mv (eV)

k

w

CMB + SN + LSS

w + massive neutrinosw

CMB + SN + LSS

w + curvature

Spergel et al 2006


Should also leverage evolution on different spatial scales

From Max Tegmark for SDSS


• 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


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


• 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


• 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


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 2006

m

8


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



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


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


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.”

could dark energy be novel matter or modified gravity?

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