L. Perivolaropoulos Department of Physics University of Ioannina

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L. Perivolaropouloshttp://leandros.physics.uoi.gr

Department of PhysicsUniversity of Ioannina

Open page

http://leandros.physics.uoi.gr/uoi06.htm

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• Accellerating Expansion of the Universe from SNe Ia (and other) datasets

• Accelerating Expansion: Dark Energy or Modified Gravity

• The Gravitational Properties of Dark Energy are getting severely constrained by Cosmological Observations

• Extended Gravity Theories can be observationally distinguished from Dark Energy

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FRW Metric

Two Parameters: Geometry ( Curvature k=-1,0,+1),

Scale (Scale Factor a(t))

1k

1k

0k

22222

2

2222 sin

1,, drdr

krdrtacdtdsdddr

22222

2

2222 sin

1,, drdr

krdrtacdtdsdddr

22 2 2 2 2 2 2 2, , sin dr d d ds cdt a t dr r d r d

Closed

Flat

Open

1a t

2 2 1 a t t t

Universe Expands

329 /10 cmgrcrittot

29 310 /tot crit gr cm

29 310 /tot crit gr cm

4

aaGaH m 3

8

DirectlyObservable

DirectlyObservable

Dark Energy(Inferred)

NoYes

2

2 83 m

a GH a aa

Flat

Friedmann Equation 3~ taVm

m

5

1r cz

H z

Accelerating Universe: (rate of expansion) was smaller in the past. Thus H-1(t) was larger in the past.

1a t

pastt

0 01t a t

zt a t

aH ta

7

24 L

Lld

LdSnIa Obs

0( ) 1

22 20

( ) ( )(1 )4 ( ) ( ) 1

a tL

Ll d z x z za t x z z

8

0( ) 1

22 20

( ) ( )(1 )4 ( ) ( ) 1

a tL

Ll d z x z za t x z z

( ) ( )cdt a z dx z 2

1 2

1( )1

1Ld za dz H z

a c dz z

Know LMeasure l(z)

( ) ( )( )

ddz

Ldz

L d z H zl z

Distance Modulus: 102.5log Lm Ml

2Ld

1

Flat

02 ds

9

0 0.25 0.5 0.75 1 1.25 1.5 1.75

34

36

38

40

42

44

46

z

( ) 5log / 25Lm z M d z Mpc

Gold Dataset (157 SNeIa):Riess et. al. 2004

DeceleratingAccelerating

ta~

~ pastt

?

10

emptyL

L

ddlog5

emptyL

L

ddlog5

z~0.5: Acceleration starts

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Expected: Decelerated Expansion due to Gravity

Observed: Accelerated Expansion

Q: What causes the Acceleration?

ta

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1. Observed: Accelerated ExpansionExpected: Deceleration due to GravityQ: What causes acceleration?

2. Observed (CMB): Flat Geometry (ρtot=ρcrit) (LSS) : ρ0m=0.3ρcrit

Expected: ρ0m=ρcrit Q: Where (and what) is the missing mass?

3. Observed: Globular Cluster Age=13GyrsExpected (ρ0m=ρcrit): Age < (2/3)H0

-1=10GyrsQ: Why is the universe so old (t0>13Gyrs)?

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•Induces Repulsive Gravity (Accelerates)

•Has positive energy density (missing mass)

•Can increase the age of the Universe

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4 43 33 3i i m X

i

a G Gp pa

Equation of State: 4 1 3

3X

mp a Gw w

a

Necessary condition for acceleration:

1 Negative Pressure3

w

4 433 3i i m

i

a G Gpa

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a(t)

tt0

PRESENT

tH

02tH/3

t0

tH=H0-1

empty u

niv

accelerating universe k =No

D.E.

decelerating universe

k =+D.E.

k = 1, No D.E.

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3 3

3 1~X w

X

d a p d aa

p w

322 0

02

320 0

8( )3

1

m

m X

aa GH z aa a

H z z

~ =?a

00 0.3m

mcrit

(from large scale structure observations)

crit

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• Einstein (1915) G.R.:

• Einstein (1917) G.R. + Static Universe + Matter only:

G = T

G - g = T

The biggest blunder of my life

2

6GM rV r

r

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Since I introduced this term, I had always a bad conscience....

I am unable to believe that such an ugly thing is actually realized in nature

A. Einstein 1947 letter to Lemaitre

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Beauty: Flat Matter Dominated Ugly: Cosmological Constant

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Positive pressure pushes against the piston Negative pressure pulls in the piston (spring force)

Constant energy per unit volume V > 0 U=ρΛ ΔV> 0 Energy conservation: U= –pΛV

(V > 0, U > 0) (pΛ < 0)

constant energy conservation negative p

FΔV

21

32

32 200 0 02

8( ) 13 3m m

aa GH z H zaa

10 10( )2.5log ( ) 25 5log

( )L obs

L d zm z M Mpcl z

0 0

( ) 1;

z

L thm

dzd z c zH z

2020 2

1

( ) ( ; )minL i obs L i m th

mi

N

i

d z d z

0 1 m

Flat

22

SNLS

TruncatedGold

FullGold

S. Nesseris, L.P. astro-ph/0511040Phys.Rev.D72:123519,2005

Gold Dataset (157 SNeIa):Riess et. al. 2004

SNLS (115 SNeIa):Astier et. al. 2005

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0

02 2

min

2 2min

1 2

: 1 2

1 2

: 1 21 2

1 22min

; , ,...,

; , ,...,

; , ,...,; , ,...,

, ,...,; , ,...,

z

z

obsL i

obsL i

dz

n

dzData d zth

L n

n

Data d z L nn

n

Physical Model H z a a a ansatz

d z a a a

H z a a ad z a a a

a a aw z a a a

1 2, ,..., na a a

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2

300

2 ln1 1 ( )3( )

1 1

X

Xm

d Hz p zdzw zzH z

H

25

24.00 m

S. Nesseris, L.P. astro-ph/0511040Phys.Rev.D72:123519,2005

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VL 2

21 +: Quintessence

-: Phantom

2

0

2

12 112

VpwV

To cross the w=-1 line the kinetic energy term must change sign

(impossible for single phantom or quintessence field)

Phant < 1

Quint 1

Generalization for k-essence:

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Non-minimal Coupling

1

, U ΦF

1F

18 effG

28

p,

212

H p F HFF

FHU

FH 3

21

31 22

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Minimum: Generic feature

F(Φ)

ΦΦ

U(Φ)

L.P. astro-ph/0504582, JCAP 0510:001,2005, S. Nesseris, L.P. astro-ph/0502053, 2006 (accepted in Phys. Rev. D)

JCAP 0511:010,2005

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• The Expansion of the Universe is currently accelerating.

• This acceleration can be modeled either by a Dark Energy or by Extended Gravity Theories.

• All recent SnIa data indicate that w(z) is close to -1. Thus w(z) may be crossing the w=-1 line.

• Minimally Coupled Scalar predicts no crossing of w=-1 line

• Scalar Tensor Theories are consistent with crossing of w=-1

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Radial Geodesics:

4 1 33

Xm

p a Gw wa

3 1~ wa

S. Nesseris, L. P., Phys.Rev.D70:123529,2004

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33


340 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

Gold+CMB+BAO

Gold+CMB+BAO+Clusters+SNLS

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

Gold

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

0 0.25 0.5 0.75 1 1.25 1.5 1.75

1.5

1

0.5

0

0.5

1

1.5

Gold+CMB+BAO+Clusters

Crossing of w=-1consistent with

all datasets!

0 0.3m

S. Nesseris, L.P. in preparation

s zdA

10 0

' 1 '' 1 '

z z

As dz dzd z a t

H z z H z

12

0

'12 '

z

LL dzd z z

l H z

LdObs

Luminosity Distance

Ang. Diameter Distance

Standard Ruler:Sound Horizon (z=zrec,z=0.35)

dA(z) from Clusters

3/ 2 gas bi A i

tot mi

MB d z const

M

w

z

36

rF

FG

rG 0

0

37

ESSENCECFHT Legacy Survey

Higher-z SN Search(GOODS)

SN FactoryCarnegie SN Project

SNAP

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1. Measurements of the Cosmological Parameters Omega and Lambda from the First 7 Supernovae at z >= 0.35S. Perlmutter et al., Astrophys.J. 483 (1997) 565

10

0.7for Flat Universe

2. Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological ConstantS. Perlmutter et al., Nature 391 (1998) 51

3. Discovery of Supernova Explosion at Half the Age of the Universe A.G. Riess et al., Astron.J. 116 (1998) 1009-1038

0.65z0.35 SnIa 7

0.4for Flat Universe 8 SnIa 0.35 z 0.83

16 SnIa 0.16 z 0.62 ΜΩ 1, 0ruled out at 95%

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4. Cosmological results from high-z supernovaeTonry et al. The Astrophysical Journal, 594:1-24, 2003 September 1


5. New Constraints on ΩM, ΩΛ, and w from an Independent Set of 11 High-Redshift Supernovae Observed with the Hubble Space Telescope

R.A. Knop et al., The Astrophysical Journal, Volume 598, Issue 1, pp. 102-137

193 SnIa 0.3 z 1.2

Decelerating Expansion starts at z=0.46


11 new SnIa observed from HST

6. Type Ia Supernova Discoveries at z > 1 From the Hubble SpaceTelescope: Evidence for Past Deceleration and Constraints on Dark

Energy EvolutionA. Riess et al. The Astrophysical 607:665-687,2004

0.71for Flat Universe 157 SnIa 0.3 z 1.7 (Gold Sample)

16 new SnIa observed from HST7 of them with z>1.25

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•2m Telescope •~1 billion pixels, 144 CCDs•350-1700 nm wavelength coverage•Finds and follows 2500 SnIa each year, out to z = 1.7•Place good limits on both w and its time evolution

L. Perivolaropoulos Department of Physics University of Ioannina

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