1. STANDARD COSMOLOGY; PROBLEMS AND THEIR SOLUTIONS KUMAR ATMJEET (UNIV. OF DELHI) SUPERVISOR: T. SOURADEEP IUCAA, PUNE (May-July, 2006)

2. CONTENTS ● STANDARD MODEL ● Assumptions ● Geometrical Description ● Successes ● PROBLEMS WITH THE STANDARD MODEL. Horizon problem ● Flatness problem ● Inhomogeneity problem ● Monopole problem ● INFLATIONARY UNIVERSE ● Inflation ● Chaotic model of inflation ● As a solution to cosmological problems ● INTRODUCTION TO CMBR ● MY WORK

3. STANDARD MODEL INTRODUCTION Assumptions : – homogeneous – isotropic – perfect fluid – hot dense fireball

4. Geometrical Description(FRW*- model) 1

5. Friedmann's equations: 2 3 4 5 6

6. Successes of Standard model ● Observed universe is homogenious and isotropic ● Expansion follows a linear V-r law (Hubble's Law) ● Explains the origin of light elements ● Prediction of CMB ● Planckian nature of spectrum ● Cmb isotropy ● Oldest steller system are no older than the inferred age of universe

7. PROBLEMS WITH THE STANDARD MODEL – Horizon problem – Flatness problem (fine tunning problem) – Inhomogeneity problem ( large scale structures formation) – Monopole problem Is there any solution to these problems?

8. INFLATIONARY UNIVERSE Definition: 7 8 9 10

9. Horizon problem: Flatness problem

10. lp(t) t(rec) t(R) to lp(t) xp ti

11. lnflationary model

12. Solution to the cosmological problems lp(t) t(rec) t(R) to lp(t) xp a(t)=exp(Ht) ti

13. start of inflation end of inflation future present day log(  )

14. Chaotic model of inflation Rolling Slowly Vacuum Energy

15. Inflation field dynamics ● single scalar field (Φ) ● consists of a self interacting potential V(Φ) ● field is initially in a false vacuum state ● initial chaos causes the field to roll down towards true vacuum state

16. Lagrangian for a scalar field: 11 12 13(a) 13(b)

18. field dynamics continued.... 14 15 16 17 (a), (b,c), (d)

19. “Slow roll aprrox.(SRA)” condition for inflation parameters: SR Aprroximation slow roll condition 18(a)] 18(b) 19(a) 19(b) 20

20. References:

21. THANKS! 07-09-06 THURSDAY