4. CONTENT
An introduction to the expanding universe and
Hubble’s Law
Causes of the expansion?
Structure of the universe
Standard candle: type I a supernovae
Theoretical and observational analysis
6. • Matter tells space time how to curve and curved space
time tells matter how to move
• More curved the universe the more the current
expansion will halt
• Lesser the curvature the more the expansion will
continue
• A universe composed only of normal matter cannot expand
• It will collapse back on itself as a big crunch due to gravity
• Einstein introduced cosmological constant in order to
maintain a stable static universe
7.
8. Galaxies are receding away from us with a velocity that is
proportional to their distance from us
HUBBLE’
S LAW
V = H0 × d
10. HUBBLE PARAMETER (H0 )
• The fractional rate of change of scale factor with time
• It is roughly the reciprocal of the age of the universe and the
age increases with time
• H0 of present universe is about 72 km/sec/parsec
11. RELATION BETWEEN REDSHIFT
AND BETA (V/C)
No galaxy can recede with a velocity greater than the velocity
of light since v/c=1 is the upper limit
13. • Observations of the explosions of the type 1a supernovae
• Dark energy responsible for driving an acceleration in the
expansion of the universe
• What is dark energy?
15. FRIEDMANN EQUATION
𝒂
𝒂
𝟐
=
𝟖𝝅𝑮
𝟑
𝝆 −
𝒌𝒄 𝟐
𝒂 𝟐
Important in understanding the expansion and different models of the
universe
a -scale factor which measures the universal expansion rate
𝒂 -change of scale factor
ρ -cosmic density
k -curvature constant which tell us about the geometry of the universe
16. EVOLUTION OF S CALE FACTOR FOR VARIOUS VALUES OF k
When k = -1
𝒂
𝒂
𝟐
~
𝒄 𝟐
𝑹 𝟐
universe is described as an open universe
When k = 0 𝒂
𝒂
𝟐
=
𝟖𝝅𝑮
𝟑
𝝆
universe is described as flat universe
When k = 1 a=
universe is described as closed universe
17. Critical density (𝛒 𝐜)
Fate of the universe is governed by density (ρ)
𝛒 𝐜 is the critical density which is the average density of material in the
universe for it to be flat
𝝆 𝒄 =
𝟑𝑯 𝟐
𝟖𝝅𝑮
:Open universe
:Flat universe
:Closed universe
18. Density Parameters
Baryonic matter density parameter
𝝆 𝒄 − baryonic matter density
Radiation density parameter
𝝆 𝜸 − radiation density
Dark matter density parameter
𝝆 𝑫𝑴 − dark matter density
Dark energy density parameter
𝛒 𝚲 - dark energy density
21. • Source that has a known luminosity
• Type 1a supernovae
STANDARD
CANDLE
A white dwarf star in a binary pair with a red dwarf accretes
mass from the red dwarf until it reaches Chandrasekhar limit
of 1.4 solar mass
Core collapses due to gravitational pressure
A violent explosion called type 1a supernovae occurs
Same luminosity of explosion
22. RELATION BETWEEN DISTANCE MODULUS
AND LUMINOSITY DISTANCE
m - apparent magnitude which measures the observed brightness
of an object from any point.
M - absolute magnitude which gives the brightness of an object as
seen from 10 parsecs away.
27. The minimum value of χ2 equal to 228.8539 is got for
𝜴 𝒎 = 𝟎. 𝟐𝟕 and 𝜴 𝜦 = 𝟎. 𝟕𝟑
Best fit model of our universe containing 27% of matter (both
baryonic and dark matter) and 73% of dark energy
28. When the density parameters are added (Ωm + ΩΛ), it turns out
to be 1!
The condition for our universe to be Flat