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STANDARD COSMOLOGY; PROBLEMS AND THEIR SOLUTIONS

KUMAR ATMJEET (UNIV. OF DELHI) SUPERVISOR: T. SOURADEEP IUCAA, PUNE (May-July, 2006). STANDARD COSMOLOGY; PROBLEMS AND THEIR SOLUTIONS. CONTENTS. STANDARD MODEL Assumptions Geometrical Description Successes

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STANDARD COSMOLOGY; PROBLEMS AND THEIR SOLUTIONS

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

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

  11. lnflationary model

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

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

  14. Rolling Slowly • Chaotic model of inflation 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)

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

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

  19. References:

  20. THANKS! 07-09-06 THURSDAY

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