Geometry of Universe Flashcards
What is the geometry of the universe?
CP shows that there are spatial sections that look the same in all places and directions at all times so geometry can’t change
It is isotropic - spherical co-ordinates are used
What is a cartesian spacial coordinate system?
A special relativistic metric
ds is a path through space time
What is the photons path through space time (ds)?
zero
If K > 0 what is the geometry of the object?
spherical (positive curvature)
over dense and recollapses
Space is finite and there is a r maximum and all angles are big so add up to more than 180 degrees
Ω_o > 1
If K < 0 what is the geometry of the object?
Horse sadle (hyperbolic space)
under dense and expands forever
Angles add up to less than 180 degrees and space is infinite (r is unbounded)
Ω_o < 1
If K = 0 what is the geometry of the object?
flat (Euclidean space)
critical and expands forever
All angles add up to 180 degrees and space is infinite (r is unbounded)
Ω_o = 1
Why is the universe not K > 0?
It is not dense enough
What does the Robertson Walker metric define?
Separation of space and time
What does Hubble’s law change with?
Time
What is the difference between H and H_o?
H is a parameter and is not constant
H_o is a constant and is value of density at present day
What is assumed about a critical density?
K = 0
Where does Hubble’s law apply?
It is normalised rate of expansion and applies everywhere not just locally
What is the value of critical density
1.88h^2 x 10^-26 kg/m^3
What is the equation of the density parameter?
Ω = ρ/ρ_crit
What is the density parameter of M/L of clusters of galaxies?
Ω ~ 0.3
