# Inflationary Models in Cosmology

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```					Inflationary Models in
Cosmology

Supervisor: Dr Babar Qureshi
Student: Farooq Hassan
Hot Big Bang Model
Experimental Evidence
• Expanding Universe
• Relative abundance of light elements

Explanatory Potential
• Age of the Universe
• Origin and Fate of the Universe
Assumptions
Homogeneity and Isotropy
• Robertson Walker metric

• Friedmann Equation
Open, Closed and Flat Universe
Rearrange Friedmann Equation,

where
and

We get
Cosmological Parameter
• Energy Conservation Equation

• Define Equation of State parameter (w)

We get,
Evolution of the Universe
• Solution to Friedmann Equation

• Matter: w = 0
• Radiation: w = 1/ 3
• Dark Energy: w = -1
Problems with Big Bang Theory
• Horizon Problem
Why is the universe so homogeneous and
isotropic?
• Flatness Problem
Why is the universe so flat ?

• Unwanted Relics
Where are the monopoles?
Inflation
The universe undergoes a period of
accelerated expansion.
• The universe is homogeneous / isotropic
because distant points in the observable
universe are causally connected.
• The universe is flat because inflation
diminishes the curvature term.
• Inflation decreases the abundance of
monopoles tremendously
Meet the Inflaton
• Scalar fields with special potentials can
cause Inflation
• Recall, Dark Energy causes inflation
• If under certain conditions, the equation of
state parameter w ~ - 1, inflation occurs.
• Example:

• If         w ~ -1.
The Early Universe
• Scalar fields must have existed with high
energy densities in Primordial Universe .
• Inflaton need not be the only scalar field
present in the beginning.
• If high energy Inflaton is present in a
region of space-time no matter how small,
it will start expanding exponentially soon
overtaking the other regions of space-time
expanding via some power law.
Inflationary Cosmology Models
•   Chaotic inflation model
•   Hybrid Inflation Model
•   Inflation with Novel Kinetic terms
•   The curvaton Model
•   Low scale Models
•   Brane Inflation
•   Modulated Coupling Constants
Inflationary Cosmology Models
• Each model uses different kinds of scalar
fields.
• Models differ in how fast the expansion
rate is, how long inflation lasts, how many
regions of space-time undergo inflation at
a time and whether inflation can reoccur at
a later time such as the one observed
today.
Problems with Inflation
• Reheating and Preheating
Once the initial wave of inflation ends,
universe contains nothing but inflationary
scalar field condensate. How does this
lead to the matter we see today?
• What if high energy particles such as
monopoles arise after inflation stops
during reheating?
Problems with Inflation
• Can the present inflation last forever?
• Further understanding of the initial
conditions in Early universe when inflation
began require an understanding of
quantum theory of gravity. String theory
can be a useful reference for this.

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