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
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