kumar atmjeet univ of delhi supervisor t souradeep iucaa pune may july 2006 n.
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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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kumar atmjeet univ of delhi supervisor t souradeep iucaa pune may july 2006
KUMAR ATMJEET

(UNIV. OF DELHI)

SUPERVISOR: T. SOURADEEP

IUCAA, PUNE

(May-July, 2006)

STANDARD COSMOLOGY; PROBLEMS AND THEIR SOLUTIONS
contents
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
slide3

STANDARD MODEL

  • INTRODUCTION
  • Assumptions :
  • homogeneous
  • isotropic
  • perfect fluid
  • hot dense fireball
slide6

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
slide7

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?

slide8

INFLATIONARY UNIVERSE

  • Definition:

7

8

9

10

slide9

Horizon problem:

Flatness problem

slide10

to

lp(t)

t(rec)

t(R)

xp

lp(t)

ti

slide12

Solution to the cosmological problems

to

lp(t)

t(rec)

t(R)

xp

lp(t)

a(t)=exp(Ht)

ti

slide13

log()

start of inflation

end of inflation

present day

future

slide14

Rolling Slowly

  • Chaotic model of inflation

Vacuum Energy

slide15

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
slide18

field dynamics continued....

14

15

16

17 (a), (b,c), (d)

slide19

“Slow roll aprrox.(SRA)” condition for inflation

parameters:

SR Aprroximation

18(a)]

18(b)

19(a)

19(b)

slow roll condition

20

slide21

THANKS!

07-09-06

THURSDAY