Lecture 3: Redshift & Density Parameters Flashcards
if we differentiate D (relation between proper distance, co-moving separation and scale factor), we can extract
velocity, multipling RHS by a0/a0 gives Hubble-Lemaitre law
how to relate the scale factor a(t) to what we can measure, ie z
looking at radial distance travelled by light in the RW metric: ds^2=0
(d theta and d phi terms now also 0 since only looking radially)
present day value of H0
100 h kms^-1 Mpc^-1 where h is approx 0.7
hubble tension is the disagreement between
measurements of the Hubble constant made with nerby/late or inferred from far away/ early measurements
examples of nearby/late measurements
blue
cepheids/supernovae
low redshifts
examples of far away/ early measurements
red
CMBR/WMAP
higher redshifts
critical density universe is where density is such that
k=0 in FE
represents ‘knife-edge’ between open k<0 and closed k>0 universes
for a critical density universe, assuming cos const=0, to find pc
set k=0 in FE
currently measure pc to be
1.88 h x 10 ^-26 kgm^-3
2.78 h^-1 x 10^11 solar masses / (h^-1Mpc)^3
dimensionless density parameters
Ωm, Ωk, ΩΛ
Ωm+Ωk+ΩΛ=
1
current observations of the universe indicate
matter density around 30% of critical density
luminous matter <1% of pc
dark matter is mostly non-baryonic and cold (non-relativistic)
universe has a flat geometry, k=0
Ωk0=
0
Ωm0=
0.3
ΩΛ0=
0.7
why is it referred to as the
Concordance Cosmological Model.
This description of our universe is supported by a wide range of different
cosmological data and simulations
Officially, this model is known as the ΛCDM (Lambda-Cold-Dark-Matter)
model, because it
requires that the universe contains cold dark matter, as well as a cosmological constant, Λ
take first RHS term of FE, assuming mass conservation and (p/p0)=(1+z)^3 then
can relate matter density to redshift
and similarly for curvature and cos const.
we can rewrite FE purely in terms of
z
why some forms of FE include radiaiton term
in very early universe, when radiation dominated it is important to include this term
in matter dominated universe, not so much
time evolution of the omegas
Ωr begins dominating and decreases over time
Ωm begins at 0 and increases over time to dominate at present
Ω dark energy (ΩΛ and Ωr) horizontal line until present day where rapidly increasing
Following the discovery of expansion
by Hubble, cosmologists expected that
universe was decelerating
if we Taylor expand the scale factor a(t) we can extract a
deceleration parameter from the second term in the expansion, q0
If we assume a matter-dominated universe with a cosmological constant we find that
q0=-0.55
hence negative deceleration parameter so universe accelerating
