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Could Dark Energy be novel matter or modified gravity?

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Modern (20th century) Cosmology

Philosophy

As we know,

There are known knowns.

There are things we know we know.

We also know

There are known unknowns.

That is to say

We know there are some things

We do not know.

But there are also unknown unknowns,

The ones we don\'t know

We don\'t know.

—Feb. 12, 2002, Department of Defense news briefing

3/46

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

4/46

Expansion today

- Observe a cosmological redshift <-> expansion rate and acceleration
- Luminosity distance F = L/4dL2

a(t)

today

t

Hubble factor

Deceleration parameter

dL

5/46

Hubble’s law: true to even larger distances

Observations of distant Supernovae

1000

Velocity (km/sec)

500

Hubble 1929

0

0

6 million

3 million

0

Distance (lightyears)

Velocity (km/sec)

Riess 1996

0

0

300

1200

1500

900

600

Distance (millions of lightyears)

6/46

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”

Two alternative explanations for the expanding universevs.

Big-Bang Model

Steady State Model

7/46

Which theory was correct?

Penzias & Wilson in NJ in 1964 observed electromagnetic radiation from all directions in the sky, all at the same temperature, 2.7 Kelvin.

What was causing it?

Pigeons?

Primordial radiation?

8/46

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

z

Evidence of deceleration followed by recent accelerationRiess et al 2004

9/46

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

10/46

Observations have driven key theoretical developments

1000

Velocity (km/sec)

500

0

0

Hubble 1929

2

0

1

Distance (Mpc)

Cosmic microwave background

Galaxy outer rotation velocities

An accelerating universe

An expanding universe

Hot Big Bang

Dark matter

General relativity

Applied to the cosmos

Dark energy

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?

11/46

c4

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:

Stress-Energy Tensor:

Evolution of matter density and pressure

Einstein’s Tensor:

Evolution of space and time

Matter tells space how to bend/expand

Space tells matter how to move

Matter makes the universe expand

12/46

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

13/46

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

z

Riess et al 2004

Evidence of deceleration followed by recent acceleration14/46

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”.

15/46

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

16/46

The key dark energy questions

- How do we modify Einstein’s Field Equations to explain acceleration?

Adjustment to gravity?

Adjustment to matter?

Cosmological constant “”?

- - Non-minimal couplings to gravity?
- Higher dimensional gravity?
- Effects of anisotropy and inhomogeneity

- “Vacuum energy” left over from early phase transitions?
- Holographic?
- Anthropic?

- -An ‘exotic’, dynamical matter component “Quintessence”?
- ‘Unified Dark Matter’?

17/46

Why so small?

UV divergences are the source of a dark energyfine-tuningproblem

The cut off scale would have to be way below the scales currently in agreement with QFT (Casimir effect, Lamb shift)

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

e+

e-

- 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 ?

Transition to dark energy domination

18/46

Scalar fx,t - spin 0 particle (e.g Higgs)

Accelerative expansion when potentialdominates

Scalingpotentials

Evolve as dominant background matter

Need corrections to create eternal or transient acceleration

Tracker potentials

Insensitive to initial conditions

Tackling the fine-tuning problem.

Scaling potentials

Wetterich 1988,

Ferreira & Joyce 1998

Tracker potentials

Ratra & Peebles 1988

Potential V(f)

Wang, Steinhardt,

Zlatev 1999

.

Kinetic f2/2

19/46

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)

Tackling the coincidence problem: are we special?w(z) evolution with an oscillatory potential

Dodelson , Kaplinghat, Stewart 2000

V~M4e-(1+Asin )

Wtot

log(a)

Dodelson , Kaplinghat, Stewart 2000

w(z) evolution with a non-minimal coupling to dark matter

wtot

log(a)

Bean & Magueijo 2001

20/46

Tackling the L problems: implications for BBN

Dark energy vs baryon density BBN constraints

- Scaling potentials can predict significant dark energy at earlier times
- treating Q as NrelFerreira & 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).10-5Steigman(2005)
- But collated more recent value D/H = 2.6±0.4).10-5Kirkman et al (2003)
- Abundance limits conservatively correspond to Nrel<0.2
- This translates into Q (MeV)<0.05 (2s)

Early constraints on dark energy density

Bean, Hansen, Melchiorri 2001

21/46

Tackling the dark matter and dark energy problems as one

- ‘Unified’ dark matter/ dark energy
- Clustering at early times like CDM, w~0, cs2~0
- Accelerating expansion at late times like L, w <0
- Phenomenology: Chaplygin gases
- an adiabatic fluid, parameters w0, a
- Strings interpretation? Born-Infeld action is of this form with a =1(e.g. Gibbons astro-ph/0204008 )

Evolution of equation of state for Chaplygin Gas

w

lg(a)

Bean and Dore PRD 68 2003

22/46

Quintessential inflation (e.g. Copeland et al 2000, Binetruy, Deffayet,Langlois 2001)

Brane world scenario

r2 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~H02

Potential implications for solar system tests as well as horizon scales

Modifications to gravity rather than matter23/46

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

24/46

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 (L, 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?

25/46

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

Linking theory and observationsSN 1a HST Legacy, Essence,

DES, SNAP

Baryon Oscillations SDSS

Alcock-Paczynski test

CMB WMAP

CMB/ Globular cluster

Tests probing background evolution only

26/46

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 cs2(z)

Comoving volume * no. density vs. z

Shear convergence

Late time ISW

Linking theory and observationsTests probing perturbations and background

Galaxy /cluster surveys, SZ and X-rays from ICM

SDSS, ACT, APEX, DES, SPT

Weak lensing CFHTLS, SNAP, DES, LSST

CMB and cross correlation

WMAP, PLANCK, with SNAP, LSST, SDSS

27/46

Early time probes of Q(z)

Early expansion history sensitivity to relativistic species

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 cs2(z)

Comoving volume * no. density vs. z

Shear convergence

Late time ISW

Linking theory and observationsBBN/ CMB WMAP

Tests probing early behavior of dark energy

28/46

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 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

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 tests

Linking theory and observationsTests probing general deviations in GR or 4D existence

29/46

In a flat universe, many measures based on the comoving distance

Luminosity distance

Angular diameter distance

Comoving volume element

Age of universe

Evolution of H(z) is the primary observabler(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)]

30/46

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

SDSS ~48000 galaxies

with z~0.35

w

Distance to z=0.35 (Mpc)

Wmh2

Wmh2

Eisenstein et al 2004

31/46

Reconstructing dynamic evolution

w=-0.7+0.8z with constant w

w>-1 fit

Constant

w fit

Reconstructing dark energy : a cautionary note- 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/r, andcs2 =dp/dr) or just an effective description?
- Need to have multi pronged observational approach

- But, parameterizations can mislead
- Need to consider additional parameter dependencies (Curvature, neutrino mass)

Maor et al 2002

36/46

Beyond CDM: Dark Energy Robust

w + curvature

CMB + SN + LSS

w + massive neutrinos

w

CMB + SN + LSS

w

k

mv (eV)

Spergel et al 2006

37/46

Dark energy domination suppresses growth in gravitational potential wells , Y

2F = 4p Ga2 rd

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

CDM dominated

or clustering DE

Y(x)

dominated or

Non clustering DE

x(t)

ISW: Dark energy signature in CMB photonsCMB spectra for DE models incl/excl perturbations

w>-1

w<-1

without

without

with

with

Hu 1998, Bean & Dore PRD 69 2003

Lewis & Weller 2003

39/46

Beyond CDM: Dark Energy

Clustering dark energy cs2=1 w≠-1

If fluctuations in DE negligible

w

w

w

w

WMAP

WMAP+SDSS

WMAP

WMAP+2dF

WMAP

WMAP+SDSS

WMAP

WMAP+2dF

m

m

m

m

w

w

w

w

WMAP

WMAP+SN

(HST/GOODS)

WMAP

WMAP+SN

(HST/GOODS)

WMAP

WMAP+SN

(SNLS)

WMAP

WMAP+SN

(SNLS)

m

m

m

m

Spergel et al 2006

Sensitive to assumptions about clustering properties of Dark Energy

40/46

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 ….

‘Constraints’ on w and cs2 from WMAP

ISW: Perturbations and CMB & LSS inferencesBean & Dore 2003, Lewis & Weller 2003

41/46

ISW: CMB cross correlation with LSS

Cross correlation of radio source number counts and WMAP ISW

- 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)

50

WLcontours

40

30

CNT (cntsmk)

20

10

0

0

20

10

5

15

q(deg)

Nolta et al. 2003

18

1

Likelihood

c2

0

12

0

1

Nolta et al 2003

WL

42/46

Weak lensing: recent constraints from CFHT

Constraints on CDM density and dark energy equation of state from Weak lensing

0.

0.

-0.5

-0.5

8

w

w

-1.0

-1.0

-1.5

-1.5

-2.0

-2.0

0.4

0.6

0.8

0.2

0.4

0.6

0.8

0.2

m

m

CFHT Legacy Survey Wide Field +Deep Surveys (2x 1 deg)

CFHT Legacy Survey Wide Field Survey (22sq deg)

m

Spergel et al 2006

Hoekstra et al 2005, Semboloni et al 2005

43/46

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 …

Prospective constraints on w from the SNAP SN1a + WL measurements

0.0

SNAP

SN1a

Deep

survey

-0.5

w

Wide survey

-1.0

-1.5

Wide survey+ non-Gaussian info

-2.0

0.0

0.2

0.4

0.6

0.8

WM

SNAP collaboration

Aldering et al 2004

44/46

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 lensing

and BAO ?

2000 SN1a

45/46

Linking Dark Energy Observations and Theory

Einstein on Observation:

"Joy in looking and comprehending is nature\'s most beautiful gift.”

Einstein on Theory:

“If an idea does not appear absurd at first then there is no hope for it”

46/46

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