PHYS 182 Lecture Notes - Lecture 21: Antiparticle, Black Body, Thermal Equilibrium
PHYS182: Our Evolving Universe
2017-11-23 LEC 21
Summary of Last Time
a(t) is the radius of a chunk of the universe
Expansion rate: H(t) = ∆a(t)/∆t
- H is called the “hubble constant”, however it is not constant, it varies with time
H2 = 8πGϱ/3
- ϱ is the energy density, G is Newton’s gravitational constant (very small)
New: ∆rϱ/∆t = -4πG(ϱ+p)
- P is the pressure density
- Different types of matter have different pressure even if they have the same density, so you need both
the energy density and the pressure to know how the universe is expanding
Example: cold matter (galaxies + dark matter), p=0
- a(t) ~ t2/3
- H(t) = 2/3t
- ϱmatter(t) ~ a-3(t)
- This would give you the age of the universe if matter were cold (i.e. always cold)
- This is not a good approximation for the early universe because as you go back in time, temperature
gets increasingly hot
- This is a good approximation for fairly late times in the universe
o Dark energy dominates energy content of the universe today, but if you go back a few million
years it doesn’t, therefore it is not a good approximation today
Example: radiation p = 1/3ϱ
a(t) ~ t1/2
- This is a good approximation at early times
ϱradiation(t) ~ a-4(t)
Eradiation ~ a-1(t)
- Energy of mass is constant, but energy of radiation is decreasing
- The total energy in dark energy is increasing, therefore eventually
dark energy will dominate
- If the gravitational force holding together galaxy clusters is
overcome by the strength of expansion of the universe, galaxies
will be ripped apart
Why is energy not conserved?
- Energy is only conserved in certain conditions
- If you have a system invariant in time
Document Summary
Summary of last time a(t) is the radius of a chunk of the universe. H is called the hubble constant , however it is not constant, it varies with time. Is the energy density, g is newton"s gravitational constant (very small) Different types of matter have different pressure even if they have the same density, so you need both the energy density and the pressure to know how the universe is expanding. Example: cold matter (galaxies + dark matter), p=0 a(t) ~ t2/3. This would give you the age of the universe if matter were cold (i. e. always cold) This is not a good approximation for the early universe because as you go back in time, temperature. Example: radiation p = 1/3 a(t) ~ t1/2. This is a good approximation at early times. Energy of mass is constant, but energy of radiation is decreasing. The total energy in dark energy is increasing, therefore eventually dark energy will dominate.
