Lecture 11 Flashcards
Concordance model
the generally consistent and tight constraints on cosmological model parameters over a wide range of redshifts
observed thermal history of the universe
matches theory over a wide range of temperatures with the physical properties of the CMBR and the light element abundances being accurately predicted
Flatness problem
is about explaining how the initial value of |Ω (total) (t) -1|could have been so finely tuned to a value of zero
zero curvature -> dimensionless density parameter diverges rapidly from zero
|Ω (total) (t) -1|would have to be unfeasibly close to zero in the early universe
|Ω (total) (t) -1| =
|k|/a^2H^2
|Ω (total) (t) -1| is an
increasing function of time
The Horizon problem
The particle horizon of the universe was much smaller
the CMBR sky consists of thousands of casually disconnected regions.
and the CMBR is not exactly isotropic
isotropy implies
thermal equilibrium
thermal equilibrium implies
sufficient interactions have happened
The CMBR formed at the
epoch of decoupling
Cosmological Inflation : de sitter universes
scale factor grows exponentially
H^2 = Λ/3 =>
a(t) ∝ exp( √(Λ/3) t)
solving the flatness inflation
a(t) = a(t(begin)) exp [H(t-t(begin)]
then using|Ω (total) (t) -1| =|k|/a^2H^2 we find
|Ω (total) (t) -1|= |Ω (total) (t(begin)) -1| exp [ -2H(t-t(begin))]
whatever value |Ω (total) (t) -1|has when inflation begins is
very quickly driven to zero
how much inflation is needed
|Ω (total) (t) -1|= |Ω (total) (t0) -1| (t(eq)/t(0))^2/3 = 1.5x10^-51
|Ω (total) (t(end)) -1|/|Ω (total) (t(begin)) -1| =
(a(begin)/a(end))^2
the scale factor easily grows by enough to
solve the flatness problem
