Published work from collaborations with Sabino Matarrese and Antonio Riotto(Padova) [and occasionally Alessio Notari (McGill)] Published work from collaborations with Published work from collaborations with SabinoSabino MatarreseMatarrese and Antonio and Antonio RiottoRiotto((PadovaPadova) [and occasionally ) [and occasionally AlessioAlessio NotariNotari (McGill)] (McGill)]

Ongoing collaborations with Ongoing collaborations with ValentinValentin KostovKostov and and ValerioValerio MarraMarra (Chicago)(Chicago)

There Is No Dark Energy and theThere Is No Dark Energy and theUniverse Is Not AcceleratingUniverse Is Not Accelerating

Kolb, Kolb, MatarreseMatarrese, and , and RiottoRiotto, , New Journal of PhysicsNew Journal of Physics 88, 322 (2006), 322 (2006)

Origins of Dark Energy May 2007

Rocky Kolb University of Chicago

Origins of Dark Energy May 20Origins of Dark Energy May 200707

Rocky Kolb University of ChicagoRocky Kolb University of Chicago

PerhapsPerhaps

in the Usual Sensein the Usual Sense

DON’T KILL

ROCKY

No Dark Energy, No Acceleration!!!!!No Dark Energy, No Acceleration!!!!!No Dark Energy, No Acceleration!!!!!

ν

ν

ν

Cold Dark Matter: 25%

Dark Energy (Λ): 70%

Stars:0.5%

Free H & He:4%

Chemical Elements: (other than H & He) 0.025%

Neutrinos: 0.47%

ΛCDMΛΛCDMCDM

Radiation: 0.005%

The construction of a model … consists of snatching from the enormous and complex mass of facts called reality a few simple, easily managed key points which, when put together in some cunning way, becomes for certain purposes a substitute for reality itself.

Evsey DomarEssays on the Theory of Economic Growth

ΛCDM: Reality Or Substitute for It?

It hardly matters to me whether he [Copernicus] claims that Earth moves or that it is immobile, so long as we get an absolutely exact knowledge of the movements of the stars and the periods of theirmovements, so long as both are reduced to altogether exact calculation.

Gemma Frisius16th century Dutch astronomer

• Age of the universe ( ) ( ) ( )0 1

z dzt zz H z

′∝

′ ′+∫

Evolution of H(z) Is a Key QuantityEvolution of Evolution of H(z)H(z) Is a Key QuantityIs a Key Quantity

Many observables based on H(z) through coordinate distance r(z) ( )0

sin( ) 1

sinh

z dzr zH z

⎫⎛ ⎞′⎪= ⎜ ⎟⎬⎜ ⎟′⎝ ⎠⎪

⎭∫

( ) ( )( )1Ld z r z z∝ +• Luminosity distanceFlux = (Luminosity / 4π dL

2)

( ) ( )( )1A

r zd z

z∝

+• Angular diameter distance

α = Physical size / dA

• Volume (number counts) N ∝ V −1(z)

Robertson–Walker metric ( )2

2 2 2 2 221

drds dt a t r dkr

⎡ ⎤= − + Ω⎢ ⎥−⎣ ⎦

( )( )

2

21

r zdV drd

kr z= Ω

−

3) age of the universe4) structure formation

High-z SNe are fainter than expected in the Einstein-deSitter model

1) Hubble diagram (SNe)2) subtraction

Ast

iere

t al.

(200

6)SN

LSEinstein-de Sitter:

spatially flatm

atter-dominated m

odel(m

aximum

theoretical bliss)

ΛCDM

conf

usin

g as

tron

omic

al n

otat

ion

rela

ted

to s

uper

nova

brig

htne

ss

supernova redshift z

Evidence for Dark EnergyEvidence for Dark EnergyEvidence for Dark Energy

The case for Λ:5) baryon acoustic oscillations6) weak lensing7) galaxy clusters

cmb

dynamics x-ray gaslensing

Ωi ≡ ρi/ρC ρC ≡ 3H02/ 8πG

power spectrum

simulations

ΩTOTAL = 1 (CMB) ΩM = 0.3

SubtractionSubtractionSubtraction

1 − 0.3 = 0.7

ΩTOTAL − ΩM = ΩΛ

How Do We “Know” Dark Energy Exists?How Do We How Do We ““KnowKnow”” Dark Energy Exists?Dark Energy Exists?• Assume model cosmology:

– Friedmann-Lemaître-Robertson-Walker (FLRW) modelFriedmann equation: H2 = 8π Gρ / 3 − k/a2

– Energy (and pressure) content: ρ = ρM + ρR + ρΛ + …

– Input or integrate over cosmological parameters: H0, ΩM, etc.

• Calculate observables dL(z), dA(z), H(z), …

• Compare to observations

• Model cosmology fits with ρΛ, but not without ρΛ

• All evidence for dark energy is indirect : observed H(z) is notdescribed by H(z) calculated from the Einstein-de Sitter model[spatially flat (k = 0) from CMB ; matter dominated (ρ = ρM)]

Take Sides!Take Sides!Take Sides!• Can’t hide from the data – ΛCDM too good to ignore

– SNIa– Subtraction: 1.0 − 0.3 = 0.7– Age– Large-scale structure– …

H(z) not given byEinstein–de Sitter

G00 (FLRW) ≠ 8π GT00(matter)

• Modify left-hand side of Einstein equations (ΔG00)3. Beyond Einstein (non-GR: f (R), branes, etc.)4. (Just) Einstein (back reaction of inhomogeneities)

• Modify right-hand side of Einstein equations (ΔT00)1. Constant (“just” Λ) 2. Not constant (dynamics driven by scalar field: M ∼ 10−33 eV)

anthropic principle(the landscape)

scalar fields(quintessence)

Tools for the Right-Hand SideTools for the RightTools for the Right--Hand SideHand Side

Duct Tape

Modifying the left-hand sideModifying the leftModifying the left--hand sidehand side• Braneworld modifies Friedmann equation

• Gravitational force law modified at large distance

• Tired gravitons

• Gravity repulsive at distance R ≈ Gpc

• n = 1 KK graviton mode very light, m ≈ (Gpc)−1

• Einstein & Hilbert got it wrong f (R)

• Backreaction of inhomogeneities

Five-dimensional at cosmic distancesDeffayet, Dvali& Gabadadze

Gravitons metastable - leak into bulkGregory, Rubakov & Sibiryakov;

Dvali, Gabadadze & Porrati

Kogan, Mouslopoulos,Papazoglou, Ross & Santiago

Csaki, Erlich, Hollowood & Terning

Räsänen; Kolb, Matarrese, Notari & Riotto;Notari; Kolb, Matarrese & Riotto

Binetruy, Deffayet, Langlois

( ) ( )1 4 416S G d x g R Rπ μ−= − −∫Carroll, Duvvuri, Turner, Trodden

“Acceleration” from Inhomogeneities““AccelerationAcceleration”” from from InhomogeneitiesInhomogeneities

• Most conservative approach — nothing new– no new fields (like 10−33 eV mass scalars)– no extra long-range forces– no modification of general relativity– no modification of gravity at large distances– no Lorentz violation– no extra dimensions, bulks, branes, etc.– no anthropic/landscape or similar faith-based reasoning

• Magnitude?: calculable from observables related to δρ /ρ

• Why now?: acceleration triggered by era of non-linear structure

Acceleration from InhomogeneitiesAcceleration from Acceleration from InhomogeneitiesInhomogeneitiesHomogeneous model Inhomogeneous model

3h

h h

h h h

a VH a a

ρ

∝=

( )3

i

i i

i i i

x

a VH a a

ρ

∝

=

( )h i xρ ρ=We think not!

( ) ( )& ?h ih i L LH H d z d z⇒ = =

≠

Acceleration from InhomogeneitiesAcceleration from Acceleration from InhomogeneitiesInhomogeneities• View scale factor as zero-momentum mode of gravitational field

• In homogeneous/isotropic model it is the only degree of freedom

• Inhomogeneities: non-zero modes of gravitational field

• Non-zero modes interact with and modify zero-momentum mode

cosmology scalar-field theory

zero-mode a hφ i (vev of a scalar field)

non-zero modes inhomogeneities thermal/finite-density bkgd.

modify a(t) modify hφ(t)ie.g., acceleration e.g., phase transitions

Cosmology ↔ scalar field theory analogue

physical effect

Different ApproachesDifferent ApproachesDifferent Approaches

• Expansion rate of aninhomogeneous Universe ≠expansion rate of homogeneousUniverse with ρ = hρi

• Inhomogeneities modifyzero-mode [effective scalefactor is aD ≡ VD

1/3 ]

• Effective scale factor has a(global) effect on observables

• Potentially can account for acceleration without dark energy or modified GR

• Model an inhomogeneousUniverse as a homogeneousUniverse model with ρ = hρi

• Zero-mode [a(t) ∝ V1/3] iszero-mode of homogeneous model with ρ = hρi

• Inhomogeneities only have alocal effect on observables

• Cannot account for observedacceleration

Standard approach Our approach

Acceleration from InhomogeneitiesAcceleration from Acceleration from InhomogeneitiesInhomogeneities

• We do not use super-Hubble modes for acceleration.(If it works the first time, it’s over-designed.)

• We do not depend on large gravitational potentials such as black holes and neutron stars.

• We assert that the back reaction should be calculated in a frame comoving with the matter—other frames can give spurious results.

• We demonstrate large corrections in the gradient expansion, butthe gradient expansion technique can not be used for the finalanswer—so we have indications (not proof) of a large effect.

• The basic idea is that small-scale inhomogeneities “renormalize”the large-scale properties.

Inhomogeneities–CosmologyInhomogeneitiesInhomogeneities––CosmologyCosmology

• The expansion rate of an inhomogeneous universe of averagedensity ⟨ρ⟩ is NOT! the same as the expansion rate of a homogeneous universe of density ρ = ⟨ρ⟩!

• Difference is a new term that enters an effective Friedmannequation — the new term need not satisfy energy conditions!

• We deduce dark energy because we are comparing to the wrongmodel universe (i.e., a homogeneous/isotropic model)

Räsänen, Kolb, Matarrese, Notari, Riotto, Schwarz

Ellis, Barausse, Buchert

Inhomogeneities–ExampleInhomogeneitiesInhomogeneities––ExampleExample

( ) ( ) ( )

( ) ( ) ( )

FLRW

FLRW00 00 00

2

00

, ,

, 8 ,

8 33 8

G x t G t G x t

G t G x t GT x t

a G Ga G

μν μν μνδ

δ π

π ρ δπ

= +

+ =

⎛ ⎞ ⎡ ⎤= −⎜ ⎟ ⎢ ⎥⎝ ⎠ ⎣ ⎦

• (a/a)2 is not 8π G ⟨ρ⟩/3.

• Perturbed Friedmann–Lemaître–Robertson–Walker model:Kolb, Matarrese, Notari & Riotto

• (a/a is not even the expansion rate)

• Could ⟨δ G00⟩ be large, or is it 10−10?

• Could ⟨δ G00⟩ play the role of dark energy?

.

Inhomogeneities–CosmologyInhomogeneitiesInhomogeneities––CosmologyCosmology

• For a general fluid, four velocity uμ = (1,0)(local observer comoving with energy flow)

• For irrotational dust, work in synchronous and comoving gauge

• Velocity gradient tensor

• Θ is the volume-expansion factor and σ ij is the shear tensor(shear will have to be small)

• For flat FLRW, hij(t) = a2(t)δij

Θ = 3H and σ ij = 0

2 2 ( , ) i jijds dt h x t dx dx= − +

1; 2 ( is traceless)i i ik i i i

j j kj j j ju h h δ σ σΘ = = = Θ +

( ) ( )2

22

36 2 0q Gσ π ρ

Θ + Θ= − = + ≥

Θ

• No-go theorem: Local deceleration parameter positive:

• However must coarse-grain over some finite domain: 3

3D

D

D

h d x

h d x

ΘΘ = ∫

∫• Evolution and smoothing do not commute:

22D DD D D

• • •Θ = Θ + Θ − Θ ≥ Θ

What Accelerates?What Accelerates?What Accelerates?

Buchert & Ellis;Kolb, Matarrese & Riotto

•

Hirata & Seljak; Flanagan; Giovannini;Ishibashi & Wald

D D

• •Θ ≠ Θ Can have q 0 but ⟨q⟩D 0 (“no-go” goes)

D D

• •Θ ≠ Θ

( )1/3 30 D D D D

D

a V V V d x h≡ = ∫

• Define a coarse-grained scale factor:

• Coarse-grained Hubble rate:13

DD D

D

aHa

= = Θ

( )eff eff

2

eff

4 33

83

D

D

D

D

a G pa

a Ga

π ρ

π ρ

= − +

⎛ ⎞=⎜ ⎟

⎝ ⎠

• Effective evolution equations:

eff

eff

16 1633

16 16

D DD

D D

RQG GRQp

G G

ρ ρπ π

π π

= − −

= − +

notdescribedby a simplep = w ρ

Inhomogeneities and SmoothingInhomogeneities and SmoothingInhomogeneities and Smoothing

• Kinematical back reaction: ( )22 223 2D DD D

Q σ= Θ − Θ −

Kolb, Matarrese & Riottoastro-ph/0506534;Buchert & Ellis

eff eff3 04

DD

QpG

ρ ρπ

+ = − <

Inhomogeneities and SmoothingInhomogeneities and SmoothingInhomogeneities and Smoothing

• Kinematical back reaction: ( )22 223 2D DD D

Q σ= Θ − Θ −

• For acceleration:

• Integrability condition (GR): ( ) ( )6 4 2 3 0D D D D Da Q a a R

••+ =

• Acceleration is a pure GR effect:– curvature vanishes in Newtonian limit– QD will be exactly a pure boundary term, and small

• Particular solution: 3QD = − h3RiD = const. – i.e., Λeff = QD (so QD acts as a cosmological constant)

• 2nd-order perturbation theory in φ(x) (Newtonian potential):Kolb, Notari, Matarrese & Riotto

( )

2 42 2 2

2 4, 2 2 ,

, ,

20 239 54

130 4 27 27

i iji ij

HH

τ τφ φ φ

τ τφ φ φ φ φ φ

Θ −= − ∇ − ∇ ∇

+ + ∇ ∇ −

– Each derivative accompanied by conformal time τ = 2/aH– Each factor of τ accompanied by factor of c.– Highest derivative is highest power of τ ∝ c : “Newtonian”

– Lower derivative terms ∝ c−n : “Post-Newtonian”

– φ and its derivatives can be expressed in terms of δρ /ρ

Can We See It in Perturbation Theory?Can We See It in Perturbation Theory?Can We See It in Perturbation Theory?

mean of 2 0φ∇ =

Post-Newtonian Newtonian

•( ) ( )

( )

( )

1 2

1 2

3 332 1 2

1 23 32 2 ( )

2 2 52 2

00

4 ( ) 2 2

1 10H

i k k x

k kV R

k

d k d kd x k k ea H V R

aA dk k T ka H a

τ φ φ φ φπ π

+ ⋅

−

∇ ⋅∇ = − ⋅∫ ∫ ∫

∫ ∼

Some ExamplesSome ExamplesSome Examples

– Individual Newtonian terms large, i.e., h∇2φ∇2φi =O(1)

– But total Newtonian term vanishes h∇2φ∇2φi = hφ,,ijφ,ij i– Post-Newtonian: h∇φ ·∇φ i = O(10−5) huge! (large k2/a2H2)

•

Räsänen

( ) ( )( )

( )

1 2

1 2

3 334 2 2 2 21 2

1 23 34 4 ( )

22 3 2 0

4 400

1 ( ) 2 2

1 10H

i k k x

k kV R

k

d k d kd x k k ea H V R

aA dk k T ka H a

τ φ φ φ φπ π

+ ⋅∇ ∇ = −

⎛ ⎞⎜ ⎟⎝ ⎠

∫ ∫ ∫

∫ ∼

Sub-Hubble InstabilitiesSubSub--Hubble InstabilitiesHubble Instabilities

• Disconnected fourth-order moment of φ :

• Notice n = 3 contributes to QD and hRiD terms ∝ a0, i.e.,expansion as if driven by a cosmological constant !!!

• Lowest-order term to make big contribution is n = 3 (6 derivatives)

• Gradient expansion:

• But why stop at n = 3 ?????

( ) ( )2 22

4 20 0

H H

φ φ∇ ∇

• We have developed a RG-improved calculation (still inadequate)

( )

( )

23

1

23

2

2 derivatives

2 derivatives

nn m

n nDn m n

nn m

D n nn m n

R r a r n

Q q a q n

φ

φ

∞−

= =

∞−

= =

⎛ ⎞= =⎜ ⎟⎝ ⎠⎛ ⎞= =⎜ ⎟⎝ ⎠

∑ ∑

∑ ∑

Many issues:• non-perturbative nature• shell crossing• comparison to observed LSS• gauge/frame choices• physical meaning of coarse graining

Program:• can inhomogeneities change effective zero mode?• how does (does it?) affect observables?• can one design an inhomogeneous universe that accelerates?• could it lead to an apparent dark energy?• can it be reached via evolution from usual initial conditions?• does it at all resemble our universe?• large perturbative terms resum to something harmless?• is perturbation theory relevant?

InhomogeneitiesInhomogeneitiesInhomogeneities• Does this have anything to do with our universe?

• Have to go to non-perturbative limit!

• Shell crossing?

• How to relate observables (dL(z), dA(z), H(z), …) to QD & ⟨3R⟩D ?

• Can one have large effect and isotropic expansion/acceleration?(related to small shear?)

• What about gravitational instability?

• Scalar field correspondence (Buchert, Larena, Alimi)

• Toy model proof of principle: Lemaître-Tolman-Bondi dust model

CommentsCommentsComments• “Do you believe?” is not the relevant question• Acceleration of the Universe is important; this must be explored • How it could go badly wrong:

– Backreaction should not be calculated in frame comoving with matter flow

– Series re-sums to something harmless– No reason to stop at first large term– Synchronous gauge is tricky

Residual gauge artifactsSynchronous gauge develops coordinatesingularities at late time (shell crossings)

☺ Problem could be done in Poisson gauge

cmb

dynamics x-ray gaslensing

Ωi ≡ ρi/ρC ρC ≡ 3H02/ 8πG

power spectrum

simulations

ΩTOTAL = 1 (CMB) ΩM = 0.3

SubtractionSubtractionSubtraction

1 − 0.3 = 0.7

ΩTOTAL − ΩM = ΩΛ

SubtractionSubtractionSubtractionHow can 1.0 = 0.3?

For a spatially flat FLRW universe H 2 = 8π Gρ / 3

This is another way of stating Ω = 1.

This expression is not valid if FLRW is not valid

e.g., 200

8 33 8GH G

Gπ ρ δ

π⎡ ⎤= −⎢ ⎥⎣ ⎦

The Morphon FieldThe The MorphonMorphon FieldField

• Dynamics of the of inhomogeneities on the smoothed scale factor can be modeled by a scalar field, the morphon.

• Can lead to quintessence-like potentials, even phantom quintessence-like potentials. (k-essence?).

• Easier to study dynamics (phase diagrams, etc.).

• Suggests solutions not obtainable from perturbations of FLRW

Buchert, Larena, Alimi

Can be arbitrarily close to FLRW, but not obtainable from perturbation of FLRWNEW DYNAMICS!

Celerier 1999 astro-ph/9907206Iguchi, Nakamura, Nakao 2002 Prog. of Theo. Phys. 809 Moffat 2005 astro-ph/0505326 Nambu and Tanimoto 2005 gr-qc/0507057 Mansouri 2005 astro-ph/0512605 Chang, Gu, Hwang 2005 astro-ph/0512651Alnes, Amarzguioui, Grøn 2006 Phys. Rev. D73 083519 Mansouri 2006 astro-ph/0601699 Apostolopoulos, Brouzakis, Tetradis, Tzavara 2006 astro-ph/0603234 Garfinkle 2006 gr-qc/0605088Kai, Kozaki, Nakao, Nambu, Yoo 2006 gr-qc/0605120

Lemaître–Tolman–BondiLemLemaaîîtretre––TolmanTolman––BondiBondi

• We regard LTB models as toy models

Lemaître–Tolman–BondiLemLemaaîîtretre––TolmanTolman––BondiBondi( )

( ) ( )2

2 2 2 2 2,,

1R r t

ds dt dr R r t drβ

′= − + + Ω

+

2 2 2 2 rH R R H R R⊥ ′ ′= =

( ) ( )( ) ( )2

,8 ,

, ,r t

G r tR r t R r t

απ ρ

′=

′

Spherically symmetric metric

Spherically symmetric density

d dt d dr′≡ ≡

Expansion rates

( ) ( )( ) ( )

( )( )

2 20

2 30

,

,

k

M

R r t ra t

R r t a t

r H r

r H r

β

α

→

′ →

→ Ω

→ Ω

FRW

Lemaître–Tolman–BondiLemLemaaîîtretre––TolmanTolman––BondiBondi

Specify α (r) and β (r) : ( )

( )

3 00

2 0

1 tanh2 2

1 tanh2 2

r

r

r rr r

r rr r

α

α

α α

β

⎧ ⎫⎡ ⎤⎛ ⎞Δ −⎪ ⎪∝ − −⎨ ⎬⎢ ⎥⎜ ⎟Δ⎝ ⎠⎪ ⎪⎣ ⎦⎩ ⎭⎡ ⎤⎛ ⎞Δ −

∝ − −⎢ ⎥⎜ ⎟Δ⎝ ⎠⎣ ⎦

Δα = 0.90 r0 = 1.35 GpcΔr = 0.4 r0

Alnes, Amarzguioui, Grøn

, ,0.2 1.0 0.65 0.51M inner M outer in outh hΩ = Ω = = =

comoving radial coordinate comoving radial coordinate

• Spherical model• Asymptotically Einstein–de Sitter• Inner underdense Gpc region • Calculate dL(z)• Compare to SNIa data• Fit with Λ = 0!

(counterexample tono-go theorems)

Alnes, Amarzguioui, Grøn

Lemaître–Tolman–BondiLemLemaaîîtretre––TolmanTolman––BondiBondi

• regular everywhere• no shell crossing• It’s not a gauge artifact• Newtonian: φ < 1• Is there acceleration?

comoving radial coordinate

Lemaître–Tolman–BondiLemLemaaîîtretre––TolmanTolman––BondiBondi

Lemaître–Tolman–BondiLemLemaaîîtretre––TolmanTolman––BondiBondi

comoving radial coordinate

150M

pc=

dA δθ

150 Mpc =δ D(z)

Baryon Acoustic OscillationsBaryon Acoustic OscillationsBaryon Acoustic Oscillations• LTB models have different radial and transverse expansions

• Standard rulers will have different radial and transverse behavior

• BAO experiments are sensitive to both! (Kolb & Kostov)

Lemaître–Tolman–BondiLemLemaaîîtretre––TolmanTolman––BondiBondi• The large effect in dL(z) when observer near center

• What happens if observer and source outside hole?• Many smaller voids rather than one large one?

EdSEdS LTB

Lemaître–Tolman–BondiLemLemaaîîtretre––TolmanTolman––BondiBondi• Cosmology 101 derivation of dL(z)

( ) ( ) ( )22 2Area 1 Ld z S z= × +

not directly related to aDdirectly related to aD

Lemaître–Tolman–BondiLemLemaaîîtretre––TolmanTolman––BondiBondi• Einstein—Strauss: embed Schwarzschild in FRW

EdSEdS Void

• FRW observer evolves as in FRW universe

• QD = 0 for volume encompassing observer/source

• In spherically symmetric model

( )2Area S unaffected if source & observer in FRW region

( )1 z+ changes only if evolution in ρ (r) in interior region

The Swiss Cheese UniverseThe Swiss Cheese UniverseThe Swiss Cheese Universe

Apollonian Gasket

• start with Einstein—de Sitter model (the cheese)• carve out spherical underdense regions (the holes)• place extra matter density in shells (the crust)• evolution of cheese unaffected by holes (Birkhoff)• evolution of spherical hole/crust (LTB)

Khosravi, Kourkchi, Mansouri & Arkami; Biswas & Notari; Marra & Kolb

The Swiss Cheese UniverseThe Swiss Cheese UniverseThe Swiss Cheese Universe

• observer in void• observer in crust• observer in cheese

• one hole• three holes• five holes

• z (r)• dL(z)

Marra & Kolb

The Swiss Cheese UniverseThe Swiss Cheese UniverseThe Swiss Cheese Universe• Where to put the observer/source?• Is Swiss the best cheese?• Can we explore perturbations of sphericity?• Do results depend on particular LTB model?• See Notari’s talk on Saturday

Observer in aSwiss CheeseUniverse

ConclusionsConclusionsConclusions• Must properly smooth inhomogeneous Universe• In principle, acceleration possible even if “locally” ρ +3p > 0• Super-Hubble modes, of and by themselves, cannot accelerate• Sub-Hubble modes have large terms in gradient expansion

– Newtonian terms can be large but combine as surface terms– Post-Newtonian terms are not surface terms, but small– Mixed Newtonian × Post-Newtonian terms can be large– Effect from “mildly” non-linear scales

• The first large term yields effective cosmological constant• No reason to stop at first large term• Can have w < −1? • Advantages to scenario:

– No new physics– “Why now” due to onset of non-linear era

Published work from collaborations with Sabino Matarrese and Antonio Riotto(Padova) [and occasionally Alessio Notari (McGill)] Published work from collaborations with Published work from collaborations with SabinoSabino MatarreseMatarrese and Antonio and Antonio RiottoRiotto((PadovaPadova) [and occasionally ) [and occasionally AlessioAlessio NotariNotari (McGill)] (McGill)]

Ongoing collaborations with Ongoing collaborations with ValentinValentin KostovKostov and and ValerioValerio MarraMarra (Chicago)(Chicago)

There Is No Dark Energy and theThere Is No Dark Energy and theUniverse Is Not AcceleratingUniverse Is Not Accelerating

Kolb, Kolb, MatarreseMatarrese, and , and RiottoRiotto, , New Journal of PhysicsNew Journal of Physics 88, 322 (2006), 322 (2006)

Origins of Dark Energy May 2007

Rocky Kolb University of Chicago

Origins of Dark Energy May 20Origins of Dark Energy May 200707

Rocky Kolb University of ChicagoRocky Kolb University of Chicago

PerhapsPerhaps

in the Usual Sensein the Usual Sense