3.4 Gravitational Lensing3 Physical Cosmology3.2 Newtonian Order Perturbations

3.3 Microwave Background 

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 Sachs-Wolfe effect, even well after the photons decouple from the matter at redshift tex2html_wrap_inline936 . 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 sub-horizon 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 self-consistently into the numerical models and to high accuracy in order to resolve the weak signals.

3.3.1 Ray-Tracing Methodology 

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 [37Jump To The Next Citation Point In The Article]). 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. An alternative ray-tracing approach has been developed by Anninos et al. [6Jump To The Next Citation Point In The Article] 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 tex2html_wrap_inline938, where tex2html_wrap_inline940, and the photon wave vector tex2html_wrap_inline942 and matter rest frame four-velocity tex2html_wrap_inline944 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. [6Jump To The Next Citation Point In The Article] find the parameters for this model are severely constrained by the COBE data such that tex2html_wrap_inline946, where tex2html_wrap_inline948 and h are the density and Hubble parameters.

3.3.2 Effects of Reionization 

In models where the InterGalactic Medium (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. [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 tex2html_wrap_inline952 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.

3.3.3 Secondary Anisotropies 

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 tex2html_wrap_inline956 Cold Dark Matter (CDM) models, focusing on the relative importance of secondary temperature anisotropies due to three separate effects: 1) time-dependent 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 ray-tracing procedure of [6] to explore the relative importance of these secondary anisotropies as a function of the density parameter tex2html_wrap_inline948 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 tex2html_wrap_inline960 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 Sunyaev-Zel'dovich effect) can also be significant. See reference [37] for a more complete list and thorough discussion of the different sources of CMBR anisotropies.


Click on thumbnail to view image

Figure 3: Temperature map from a tex2html_wrap_inline796 Mpc simulation of the large scale structure in a critically closed universe using tex2html_wrap_inline786 photons in a tex2html_wrap_inline800 window. The signal is displayed at a redshift z =0.425 with tex2html_wrap_inline804, and shows the secondary anisotropy from the intrinsic Rees-Sciama effect and the proper motion of a cluster of galaxies moving across the sky. The minimum (maximum) values in the image are tex2html_wrap_inline806 (tex2html_wrap_inline808). The proper motion effect leaves a clear signature in the center of the image, forming a dipolar pattern with the clusters at the center.

3.4 Gravitational Lensing3 Physical Cosmology3.2 Newtonian Order Perturbations

image Physical and Relativistic Numerical Cosmology
Peter Anninos
© Max-Planck-Gesellschaft. ISSN 1433-8351
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