standard cosmology; problems and their solutions kumar atmjeet (univ. of delhi) supervisor: t....

STANDARD COSMOLOGY; PROBLEMS AND THEIR

SOLUTIONS

KUMAR ATMJEET(UNIV. OF DELHI)

SUPERVISOR: T. SOURADEEP IUCAA, PUNE (May-July, 2006)

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

STANDARD MODEL

INTRODUCTION Assumptions : – homogeneous

– isotropic – perfect fluid

– hot dense fireball

Geometrical Description(FRW*- model)

1

Friedmann's equations:

2

3

4

5

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

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?

INFLATIONARY UNIVERSE

•Definition:

7

8

9

10

Horizon problem:

Flatness problem

lp(t)

t(rec)

t(R)

to

lp(t)xp

ti

lnflationary model

Solution to the cosmological problems

lp(t)

t(rec)

t(R)

to

lp(t)xp

a(t)=exp(Ht)

ti

start of inflation end of inflation future present day

log(

Chaotic model of inflation

Rolling Slowly

Vacuum Energy

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

Lagrangian for a scalar field:

11

12

13(a)

13(b)

field dynamics continued....

14

15

16

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

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

parameters: SR Aprroximation

slow roll condition

18(a)]

18(b)

19(a)

19(b)

20

References:

THANKS!

07-09-06 THURSDAY

0.01 0.05 0.1 0.5 1 5 10

1

0.001 0.005 0.01 0.05 0.1 0.5 1

1

0.001 0.005 0.01 0.05 0.1 0.5 1

1

1 2 5 10 20 50

1