1. 1 Dynamical Effects of Cosmological Constant Antigravity Μ. Αξενίδης, Λ. Περιβολαρόπουλος, Ε. Φλωράτος Ινστιτούτο 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. 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. 3 What is the Cosmological Constant The Cosmological Constant is a form of energy inherent in empty space remaining constant as the Universe expands. The only effects of this energy are on gravity. Einstein Equations:

4. 4 Effects on FRW Metric Friedman Equation: Redshifting of energy density: Acceleration:

5. 5 Bounds on Λ from Supernovae Total Luminocity (Light Curves) + Observed Flux Luminocity Distance Supernovae data: Other data hints: Age constraints: z 0.11

6. 6 Schwarzchild - de Sitter Metric Spherically Symmetric Vacuum with non-zero Λ: Newtonian Gravitational Interaction: Repulsive term dominates at: Q: What are effects of the additional repulsive term on the various astrophysical scales ? (solar system, galactic, cluster) r 1 : distance in pc, M 1 : Mass in Solar Masses

7. 7 Solar System Scales Additional Orbit Precession due to Λ: Mercury ( ): Predicted Precession: Observ. Resolution: Solar System Tests are not Sensitive to the presence of the Cosmological Constant

8. 8 Galactic Scales Stable Circular Star Orbit: The galactic dark halo mass M(Λ) is found from astrophysical data ( ). Calculated Mass Increase due to Λ:

9. 9 Cluster Scales (Local Group) Local Group approximation: Isolated Two Body System (MW, M31) MW M31 Conditions:

10. 10 Conclusions 1. Dynamical Effects of the Cosmological Constant Antigravity are not detectable with present technology on galactic scales and below. 2. On Cluster Scales (Local Group) and larger these dynamical effects can be significant enough to affect the dynamics at an observable level. 3. Non-dynamical measurements of galactic masses (eg gravitational lensing) can be combined with dynamical estimates on cluster scales and lead to a direct measurement of the Cosmological Constant