1

Dynamical Effects of Cosmological Constant

Antigravity

Μ. Αξενίδης,

Λ. Περιβολαρόπουλος,

Ε. ΦλωράτοςΙνστιτούτο Πυρηνικής Φυσικής

Κέντρο Ερευνών ‘Δημόκριτος’

http://leandros.chem.demokritos.gr

WWW Site of Talk: http://leandros.chem.demokritos.gr/cosm-const/index.html

astro-ph/0004080

2

Contents

1. What is the Cosmological Constant? How is Gravity Modified?

2. Universe Dynamics, Bounds from Supernovae.

3. Effects on Other Metrics: Schwarzchild - de Sitter Metric

4. Newtonian Limit: Gravity vs Antigravity

5. Dynamical Effects on Astrophysical Scales(Solar System, Galaxy, Local Group)

6. Conclusion

3

What is the Cosmological Constant

The Cosmological Constant is a form of energyinherent in empty space remaining constant as

the Universe expands.

The only effects of this energy are on gravity.

Einstein Equations:

4

Effects on FRW Metric

Friedman Equation:

2

2.

2

3

8

a

kG

a

aH

ii

Redshifting of energy density:

0)(Λ 0

2

4

3

a

a

a

a

vac

curv

rad

m

ini a

Acceleration:

iiin

G

a

a )2(

3

4..

02

02

02

..

..

..

an

an

an

i

i

i

5

Bounds on Λ from Supernovae

Total Luminocity(Light Curves)

+Observed Flux

LuminocityDistance

1.07.0 Supernovae data:

Other data hints:Age constraints: 1

252107.0 m

z

0.1 1

),( , iiL nzD FDL L

24

6

Schwarzchild - de SitterMetric

Spherically Symmetric Vacuum with non-zero Λ:

3

21)(

) sin()(

)(

2

2

22222

222

r

rc

GMrA

ddrrA

drdtcrAds

Newtonian Gravitational Interaction:

ggrc

r

GMg

3

2

2

Repulsive term dominates at:3/1

2

3

c

GMrr c

Q: What are effects of the additional repulsiveterm on the various astrophysical scales ?

(solar system, galactic, cluster)

1

31525

32

105.03

r

GM

rc

g

gq

r1: distance in pc, M1: Mass in Solar Masses

7

Solar System Scales

2010

g

gqss

1

10

1

52

51

1

r

M

Additional Orbit Precession due to Λ:

rad/orbit 6 q

Mercury ( ):61 10r

orbitrad /10 22 Predicted Precession:

Observ. Resolution: orbitradres /10 9

Solar System Tests are not Sensitive to thepresence of the Cosmological Constant

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Galactic Scales

410

g

gqgal

1

10

10

52

41

101

r

M

Stable Circular Star Orbit:3

222 rc

r

GMvc

The galactic dark halo mass M(Λ) is found fromastrophysical data ( ). - rvc

42

100

210

5

52

5252 10103

)0(

)0()1(

v

r

M

MMp

Calculated Mass Increase due to Λ:

0 10 20 30 40 50 60 70 80

0.0

5.0x10-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

p =

M / M

r kpc

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Cluster Scales (Local Group)

)1(Og

gqss

1

10

10

52

71

141

r

M

Local Group approximation: Isolated Two Body System (MW, M31)

MW M31r

c

r

GM

dt

rd

3

)( 2

22

2

Conditions:

0.0 5.0x10-53

1.0x10-52

1.5x10-52

2.0x10-52

2.5x10-52

1.0

1.2

1.4

1.6

1.8

2.0

2.2

close

sup

M31 using Local Group Dynamics M33 using Rotation Velocity

M(

) / M

(=0

)

m-2

0)0(

sec/123)(

800)(

0

0

tdt

dr

kmttdt

dr

kpcttr

35.0p

10

Conclusions

1. Dynamical Effects of the Cosmological Constant Antigravity are not detectablewith present technology on galacticscales and below.

2. On Cluster Scales (Local Group) and largerthese dynamical effects can be significant enough to affect the dynamicsat an observable level.

3. Non-dynamical measurements of galactic masses (eg gravitational lensing) can becombined with dynamical estimates on cluster scales and lead to a direct measurement of the Cosmological Constant