Lecture 8: CMBR as a Cosmological Probe Flashcards
(29 cards)
with sufficiently accurate measurements we have found that the temperature of the CMBR is
anisotropic
with variations observe at a tiny fraction of a kelvin
the pattern on CMBR temp variations can be used to
place extremely tight constraints on the values of the parameters that describe our cosmological models
COBE measured delta T to be
3.35 x 10^-3K
This dipole anisotropy is not believed to be intrinsic to the CMBR, but instead due to
our peculiar motion which causes a Doppler shift of the radiation of an amount which varies with direction according to the dipole formula
delta T / T_mean=
v_pec/c
all sky maps of CMBR
first looks completely constant
second shows dipole
third shows even more variation
setting T_mean to 3K suggests that v_pec is
330 kms^-1 which agrees well with estimates of our peculiar velocity derived by other methods
top pannel of all sky CMBR map
The top panel shows
the maps obtained with a coarse temperature scale, indicating an essentially isotropic black body temperature.
middle pannel of all sky CMBR map
The middle panel shows finer-scale temperature variations at the level of about 10−3 K which are dominated by a dipole pattern that is believed to be largely due to our peculiar velocity with respect to a reference frame in which the CMBR is approximately isotropic.
bottom pannel of all sky CMBR map
The bottom panel shows even finer-scale variations at the level
of about 10−6 K, after the dipole signal has been removed. The dominant residual signal is now ‘foreground’ radio emission (principally synchrotron and thermally-emitting dust) from the plane of the Milky Way galaxy
After also removing the Galactic foreground (which can be modelled using similar all-sky maps made at different radio and microwave frequencies), the COBE map revealed
intrinsic temperature fluctuations that are also of order 10−5 K
the comparison of the CMBR temperature maps with theoretical
predictions is also done statistically, comparing those predictions with the
angular power spectrum of the CMBR, given by Cl≡<|alm^2|>
From the properties of spherical harmonics, a good rule-of-thumb is that each multipole is sensitive
to temperature fluctuations on the scale of roughly
θ ≈ 180/l degrees,
the value of Cl indicates the
mean square amplitude of those fluctuations
the planck angular power spectrum has severl striking oscillator features, known as
acoustic peaks
prioir to decoupling, the universe consists of a
baryon-photon fluid
fluctuations in the CMBR imply that there were
tiny differences in gravitationla potential at the epoch of recombination
gravity tries to collapse the fluid and radiation pressure tries to expand it
the fluid ‘sloshes around’ in the potential wells and sets up
acoustic oscillations in the fluid
acoustic oscillation implies a
pressure or sound wave
when decoupling occurs, oscillations cease and their pattern is
frozen in to the CMBR pattern we observe today
a series of acoustic peaks are generated corresponding to
oscillations that were just at the right size to be at maximum compression or maximum rarefacion when the photons decouple
the physical scale of the oscillations is determined by
how far sound waves could have travelled before decoupling: the sound horizon
the particle horizon is
the limit of the region with which an observer can be in casual contact
its the proper size of the observable universe
the first acoustic peak corresponds to the
sound horizon at decoupling
it is a standard ruler
