4.1
Cosmic microwave background
The Cosmic Microwave Background Radiation (CMBR) is a direct
relic of the early Universe, and currently provides the deepest
probe of evolving cosmological structures. Although the CMBR is
primarily a uniform black body spectrum throughout all space,
fluctuations or anisotropies in the spectrum can be observed at
very small levels to correlate with the matter density
distribution. Comparisons between observations and simulations
generally support the mostly isotropic, standard Big Bang model,
and can be used to constrain the various proposed matter
evolution scenarios and cosmological parameters. For example, sky
survey satellite observations
[34, 149]
suggest a flat
-dominated Universe with scale-invariant Gaussian fluctuations
that is consistent with numerical simulations of large sale
structure formation (e.g., galaxy clusters, Ly
forest).
As shown in the timeline of Figure
8, CMBR signatures can be generally classified into two main
components: primary and secondary anisotropies, separated by a
Surface of Last Scattering (SoLS). Both of these components
include contributions from two distinctive phases: a surface
marking the threshold of decoupling of ions and electrons from
hydrogen atoms in primary signals, and a surface of reionization
marking the start of multiphase secondary contributions through
nonlinear structure evolution, star formation, and radiative
feedback from the small scales to the large.
4.1.1
Primordial black body effects
Update
The black body spectrum of the isotropic background is
essentially due to thermal equilibrium prior to the decoupling of
ions and electrons, and few photon-matter interactions after
that. At sufficiently high temperatures, prior to the decoupling
epoch, matter was completely ionized into free protons, neutrons,
and electrons. The CMB photons easily scatter off electrons, and
frequent scattering produces a blackbody spectrum of photons
through three main processes that occur faster than the Universe
expands:
-
Compton scattering
in which photons transfer their momentum and energy to
electrons if they have significant energy in the electron’s
rest frame. This is approximated by Thomson scattering if the
photon’s energy is much less than the rest mass. Inverse
Compton scattering is also possible in which sufficiently
energetic (relativistic) electrons can blueshift photons.
-
Double Compton scattering
can both produce and absorb photons, and thus is able to
thermalize photons to a Planck spectrum (unlike Compton
scattering which conserves photon number, and, although it
preserves a Planck spectrum, relaxes to a Bose-Einstein
distribution).
-
Bremsstrahlung
emission of electromagnetic radiation due to the acceleration
of electrons in the vicinity of ions. This also occurs in
reverse (free-free absorption) since charged particles can
absorb photons. In contrast to Coulomb scattering, which
maintains thermal equilibrium among baryons without affecting
photons, Bremsstrahlung tends to relax photons to a Planck
distribution.
Although the CMBR is a unique and deep probe of
both the thermal history of the early Universe and primordial
perturbations in the matter distribution, the associated
anisotropies are not exclusively primordial in nature. Important
modifications to the CMBR spectrum, from both primary and
secondary components, can arise from large scale coherent
structures, even well after the photons decouple from the matter
at redshift
, due to gravitational redshifting, lensing, and scattering
effects.
4.1.2
Primary anisotropies
Update
The most important contributions to primary anisotropies between
the start of decoupling and the surface of last scattering
include the following effects:
-
Sachs-Wolfe (SW) effect:
Gravitational redshift of photons between potentials at the
SoLS and the present. It is the dominant effect at large
angular scales comparable to the horizon size at decoupling (
).
-
Doppler effect:
Dipolar patterns are imprinted in the energy distribution from
the peculiar velocities of the matter structures acting as the
last scatterers of the photons.
-
Acoustic peaks:
Anisotropies at intermediate angular scales (
) are atttributed to small scale processes occurring until
decoupling, including acoustic oscillations of the
baryon-photon fluid from primordial density inhomogeneities.
This gives rise to acoustic peaks in the thermal spectrum
representing the sound horizon scale at decoupling.
-
SoLS damping:
The electron capture rate is only slightly faster than
photodissociation at the start of decoupling, causing the SoLS
to have a finite thickness (
). Scattering over this interval damps fluctuations on scales
smaller than the SoLS depth (
).
-
Silk damping:
Photons can diffuse out of overdense regions, dragging baryons
with them over small angular scales. This tends to suppress
both density and radiation fluctuations.
All of these mechanisms perturb the black
body background radiation since thermalization processes are not
efficient at redshifts smaller than
.
4.1.3
Secondary anisotropies
Secondary anisotropies consist of two
principal effects, gravitational and scattering. Some of the more
important gravitational contributions to the CMB include:
-
Early ISW effect:
Photon contributions to the energy density of the Universe may
be non-negligible compared to ordinary matter (dark or
baryonic) at the last scattering. The decreasing contribution
of photons in time results in a decay of the potential,
producing the early Integrated Sachs-Wolfe (ISW) effect.
-
Late ISW effect:
In open cosmological models or models with a cosmological
constant, the gravitational potential decays at late times due
to a greater rate of expansion compared to flat spacetimes,
producing the late ISW effect on large angular scales.
-
Rees-Sciama effect:
Evolving nonlinear strucutures (e.g., galaxies and clusters)
generate time-varying potentials which can seed asymmetric
energy shifts in photons crossing potential wells from the SoLS
to the present.
-
Lensing:
In contrast to ISW effects which change the energy but not
directions of the photons, gravitational lensing deflects the
paths without changing the energy. This effectively smears out
the imaging of the SoLS.
-
Proper motion:
Compact objects such as galaxy clusters can imprint a dipolar
pattern in the CMB as they move across the sky.
-
Gravitational waves:
Perturbations in the spacetime fabric affect photon paths,
energies, and polarizations, predominantly at scales larger
than the horizon at decoupling.
Secondary scattering effects are associated
with reionization and their significance depends on when and over
what scales it takes place. Early reionization leads to large
optical depths and greater damping due to secondary scattering.
Over large scales, reionization has little effect since these
scales are not in causal contact. At small scales, primordial
anisotropies can be wiped out entirely and replaced by secondary
ones. Some of the more important secondary scattering effects
include:
-
Thomson scattering:
Photons are scattered by free electrons at sufficiently large
optical depths achieved when the Universe undergoes a global
reionization at late times. This damps out fluctuations since
energies are averaged over different directions in space.
-
Vishniac effect:
In a reionized Universe, high order coupling between the bulk
flow of electrons and their density fluctuations generates new
anisotropies at small angles.
-
Thermal Sunyaev-Zel’dovich effect:
Inverse Compton scattering of the CMB by hot electrons in the
intracluster gas of a cluster of galaxies distorts the black
body spectrum of the CMB. Low frequency photons will be shifted
to high frequencies.
-
Kinetic Sunyaev-Zel’dovich effect:
The peculiar velocities of clusters produces anisotropies via
a Doppler effect to shift the temperature without distorting
the spectral form. Its effect is proportional to the product of
velocity and optical depth.
-
Polarization:
Scattering of anisotropic radiation affects polarization due
to the angular dependence of scattering. Polarization in turn
affects anisotropies through a similar dependency and tends to
damp anisotropies.
To make meaningful comparisons between
numerical models and observed data, all of these (low and high
order) effects from both the primary and secondary contributions
(see for example Section
4.1.4
and
[94
, 101]) must be incorporated self-consistently into any numerical
model, and to high accuracy in order to resolve and distinguish
amongst the various weak signals. The following sections describe
some work focused on incorporating many of these effects into a
variety of large-scale numerical cosmological models.
4.1.4
Computing CMBR anisotropies with ray-tracing methods
Many efforts based on linear perturbation
theory have been carried out to estimate temperature anisotropies
in our Universe (for example see
[114]
and references cited in
[131, 94
]). Although such linearized approaches yield reasonable results,
they are not well-suited to discussing the expected imaging of
the developing nonlinear structures in the microwave background.
Also, because photons are intrinsically coupled to the baryon and
dark matter thermal and gravitational states at all spatial
scales, a fully self-consistent treatment is needed to accurately
resolve the more subtle features of the CMBR. This can be
achieved with a ray-tracing approach based on Monte-Carlo methods
to track individual photons and their interactions through the
evolving matter distributions. A fairly complete simulation
involves solving the geodesic equations of motion for the
collisionless dark matter which dominate potential interactions,
the hydrodynamic equations for baryonic matter with high Mach
number shock capturing capability, the transport equations for
photon trajectories, a reionization model to reheat the Universe
at late times, the chemical kinetics equations for the ion and
electron concentrations of the dominant hydrogen and helium
gases, and the photon-matter interaction terms describing
scattering, redshifting, depletion, lensing, and Doppler
effects.
Such an approach has been developed by Anninos
et al.
[15
], and applied to a Hot Dark Matter (HDM) model of structure
formation. In order to match both the observed galaxy-galaxy
correlation function and COBE measurements of the CMBR, they
find, for that model and neglecting reionization, the
cosmological parameters are severely constrained to
, where
and
are the density and Hubble parameters respectively.
In models where the IGM does not reionize, the
probability of scattering after the photon-matter decoupling
epoch is low, and the Sachs-Wolfe 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.
[157]
also using ray-tracing methods. 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 decaying neutrinos, 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
, which produces CMBR anisotropies above current COBE limits when
no reionization is included (see Section
4.1.4), 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, as demonstrated in
Figure
9
. 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.
[156]
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
different effects: (i) time-dependent variations in the
gravitational potential of nonlinear structures as a result of
collapse or expansion (the Rees-Sciama effect), (ii) proper
motion of nonlinear structures such as clusters and superclusters
across the sky, and (iii) the decaying gravitational potential
effect from the evolution of perturbations in open models. They
applied the ray-tracing procedure of
[15]
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 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
as shown in Figure
10
.
In addition to the effects discussed in this section, many other
sources of secondary anisotropies (as mentioned in Section
4.1, including gravitational lensing, the Vishniac effect accounting
for matter velocities and flows into local potential wells, and
the Sunyaev-Zel’dovich (SZ) (Section
4.5.4) distortions from the Compton scattering of CMB photons by
electrons in the hot cluster medium) can also be fairly
significant. See
[94, 152, 28, 80, 93]
for more thorough discussions of the different sources of CMBR
anisotropies.