The Cosmic Microwave Background Radiation (CMBR), which is a
direct relic of the early Universe, currently provides the
deepest probe of cosmological structures and imposes severe
constraints on the various proposed matter evolution scenarios
and cosmological parameters. Although the CMBR is a unique and
deep probe of both the thermal history of the early Universe and
the primordial perturbations in the matter distribution, the
associated anisotropies are not exclusively primordial in nature.
Important modifications to the CMBR spectrum can arise from large
scale coherent structures due to the gravitational redshifting of
the photons through the SachsWolfe effect, even well after the
photons decouple from the matter at redshift
. Also, if the intergalactic medium reionizes sometime after the
decoupling, say from an early generation of stars, the increased
rate of Thomson scattering off the free electrons will erase
subhorizon scale temperature anisotropies, while creating
secondary Doppler shift anisotropies. To make meaningful
comparisons between numerical models and observed data, all of
these effects (and others, see for example §
3.3.3) must be incorporated selfconsistently into the numerical
models and to high accuracy in order to resolve the weak signals.
Many computational analyses based on linear perturbation theory
have been carried out to estimate the temperature anisotropies in
the sky (for example see [46] and the references cited in [37]). Although such linearized approaches yield reasonable results,
they are not wellsuited to discussing the expected imaging of
the developing nonlinear structures in the microwave background.
An alternative raytracing approach has been developed by Anninos
et al. [6] to introduce and propagate individual photons through the
evolving nonlinear matter structures. They solve the geodesic
equations of motion and subject the photons to Thomson scattering
in a probabilistic way and at a rate determined by the local
density of free electrons in the model. Since the temperature
fluctuations remain small, the equations of motion for the
photons are treated as in the linearized limit, and the
anisotropies are computed according to
, where
, and the photon wave vector
and matter rest frame fourvelocity
are evaluated at the emission (e) and reception (r) points.
Applying their procedure to a Hot Dark Matter (HDM) model of
structure formation, Anninos et al. [6] find the parameters for this model are severely constrained by
the COBE data such that
, where
and
h
are the density and Hubble parameters.
In models where the InterGalactic Medium (IGM) does not reionize,
the probability of scattering after the photonmatter decoupling
epoch is low, and the SachsWolfe effect dominates the
anisotropies at angular scales larger than a few degrees. However
if reionization occurs, the scattering probability increases
substantially and the matter structures, which develop large bulk
motions relative to the comoving background, induce Doppler
shifts on the scattered CMBR photons and leave an imprint of the
surface of last scattering. The induced fluctuations on
subhorizon scales in reionization scenarios can be a significant
fraction of the primordial anisotropies, as observed by Tuluie et
al. [61]. They considered two possible scenarios of reionization: A
model that suffers early and gradual (EG) reionization of the IGM
as caused by the photoionizing UV radiation emitted by the
decaying HDM, and the late and sudden (LS) scenario as might be
applicable to the case of an early generation of star formation
activity at high redshifts. Considering the HDM model with
and
h
=0.55, which produces CMBR anisotropies above current COBE limits
when no reionization is included, they find that the EG scenario
effectively reduces the anisotropies to the levels observed by
COBE and generates smaller Doppler shift anisotropies than the LS
model. The LS scenario of reionization is not able to reduce the
anisotropy levels below the COBE limits, and can even give rise
to greater Doppler shifts than expected at decoupling.
Additional sources of CMBR anisotropy can arise from the
interactions of photons with dynamically evolving matter
structures and nonstatic gravitational potentials. Tuluie et al.
[60] considered the impact of nonlinear matter condensations on the
CMBR in
Cold Dark Matter (CDM) models, focusing on the relative
importance of secondary temperature anisotropies due to three
separate effects: 1) timedependent variations in the
gravitational potential of nonlinear structures as a result of
collapse or expansion; 2) proper motion of nonlinear structures
such as clusters and superclusters across the sky; and 3) the
decaying gravitational potential effect from the evolution of
perturbations in open models. They applied the raytracing
procedure of [6] to explore the relative importance of these secondary
anisotropies as a function of the density parameter
and the scale of matter distributions. They find that the
secondary temperature anisotropies are dominated by the decaying
potential effect at large scales, but that all three sources of
anisotropy can produce signatures of order
and are therefore important contributors to the composite images
(see figure
3
for a visual example of secondary anisotropy effects).
In addition to the effects discussed in the previous
paragraphs, many other sources of secondary anisotropies (such as
gravitational lensing, the Vishniac effect and the
SunyaevZel'dovich effect) can also be significant. See reference
[37] for a more complete list and thorough discussion of the
different sources of CMBR anisotropies.
Figure 3:
Temperature map from a
Mpc simulation of the large scale structure in a critically
closed universe using
photons in a
window. The signal is displayed at a redshift
z
=0.425 with
, and shows the secondary anisotropy from the intrinsic
ReesSciama effect and the proper motion of a cluster of galaxies
moving across the sky. The minimum (maximum) values in the image
are
(). The proper motion effect leaves a clear signature in the
center of the image, forming a dipolar pattern with the clusters
at the center.

Physical and Relativistic Numerical Cosmology
Peter Anninos
http://www.livingreviews.org/lrr19982
© MaxPlanckGesellschaft. ISSN 14338351
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