Since the discovery of the CMB in 1964 [25] (predicted by Alpher & Herman in 1948 [26], extending the work of Gamow [27] and recognised by Dicke [28]), different observational experiments have mapped and analysed it. Observations show the CMB spectrum is an almost perfect blackbody with a temperature of 2.73K. The wavelengths of the CMB photons have been redshifted since they were emitted, shifting the peak of the blackbody, and the CMB was released in the early Universe, when temperatures were much hotter than they are today, meaning the photon temperature has been cooling ever since.
The CMB is found to be almost perfectly isotropic, but on angular scales smaller than approximately one degree, anisotropies are present. These anisotropies are an encoding of the density perturbations in the early Universe that go on to form all of the structure in the Universe today and their discovery won John Mather and George Smoot the Nobel Prize in 2006.
Spatial variations in the baryonic density mean photons originating from dif- ferent regions have slightly different temperatures. The motion of the photons through space is affected by growing inhomogeneities in the gravitational field which also affects their energies. As such, it is possible to correlate temperature fluctuations in the CMB to cosmological perturbations. The intricacies of the CMB are many and varied. We direct the reader to Ref. [29] for the subtleties and only give a brief overview of the relevant aspects here.
Cold dark matter particles do not interact with photons and so in the early Universe they are free to gravitationally cluster and grow. Baryons and pho- tons then fall into these density wells. However, before decoupling, baryons and photons are tightly coupled via the Thomson scattering of electrons. When the baryons fall into a density well and encounter a large number of photons, there is a restorative pressure due to the Thomson scattering of the photons which pushes the baryonic matter back out of the density well. There is a tug of war between the gravitational attraction of the CDM and the photon pressure which means the baryons oscillate in and out of the density well. These oscillations (known as baryonic acoustic oscillations (BAO)) manifest themselves in the CMB and
there is a finite distance the soundwave could have travelled before recombina- tion, which is known as the sound horizon,rs.
The soundwave can be decomposed into its Fourier components and different wavelengths will have had time to oscillate a different number of times. The frequency of an oscillation is ωs = kcs where k is a wavenumber in the Fourier
expansion and cs is the sound speed which quantifies the relationship between
pressure fluctuations and density fluctuations. Larger scales complete fewer os- cillations than smaller scales. Scales which are at the extremum of a compression or rarefaction when the CMB is released appear in the power spectrum of tem- perature fluctuations as peaks, often referred to as acoustic peaks.
Modelling the evolution of the density perturbations of the early Universe for- wards in time allows the power spectrum of temperature fluctuations in the CMB to be recreated. The subtleties of the locations, widths and heights of the peaks depend on the specifics of the Universe model being used. As such, the CMB, as an imprint of the evolution of Large Scale Structure (LSS) in the Universe, is a powerful test of both structure formation and the component densities of the Universe including its curvature. To reproduce the CMB primordial anisotropy, even though a detailed knowledge of the evolution of perturbations is needed, only five cosmological parameters are required. However, the parameters in ques- tion are degenerate, meaning the CMB cannot be used to constrain individual cosmological parameters, only combinations of them.
Observations of the CMB provide valuable evidence to support a recent devel- opment in the history of the Universe, that of a late-time accelerated expansion. Two separate groups in the 1990s discovered that the Universe expansion is cur- rently accelerating. They were studying distant supernovae and comparing their redshifts at different distances. Their results unequivocally point to a current period of accelerating expansion of the Universe, for which Adam Riess, Brian Schmidt and Saul Perlmutter won the Nobel prize in 2011 [30, 31].
Subsequent detailed analysis of the CMB has allowed the energy content of the Universe to be tightly constrained, and remarkably these observations leave approximately 70% of the energy content of the Universe unaccounted for. It is now generally accepted that the ‘missing’ energy component is responsible for the late-time accelerated expansion of the Universe. Primarily because it must be a
non-luminous substance (to account for the fact we have not observed it) and as a nod to its elusive nature it has been named ‘Dark Energy’, and has recently (relatively speaking) come to dominate the energy content of the Universe and drive the accelerated expansion. Just what this dark energy might be is a hotly debated topic and motivates a large portion of the original research in this thesis in Chapters 7 and 8, it is discussed further in Section 2.8.
First and foremost, analysis of the CMB allows a ‘concordance model of cos- mology’ to be formulated; ΛCDM. The acronym combines the cosmological con- stant, Λ, with Cold Dark Matter, CDM, both of which attempt to shed light on the ‘dark’ aspects of our Universe; dark energy and dark matter respectively. Nei- ther constituent interacts with electromagnetic radiation but it is fair to say their nomenclature arises equally from the fact that little is understood about them. That being said, the ΛCDM concordance model provides a very good description of the Universe we observe around us.
The CMB provides a host of information about the perturbed Universe but also encodes important information on the non-perturbed Universe and its pri- mordial origins. The observational constraints are detailed in Section 2.4.5 and we make use of them continually in the original research presented in this thesis, to analyse and constrain models of the Universe. This thesis is predominantly focused on the non-perturbed regime and the Universe as a whole. It is concerned with the parts of the evolution history which are less well understood than the epoch after the EW symmetry breaking; the time before the HBB, the transition between inflation and radiation domination, and the modern day when the expan- sion of the Universe again begins to accelerate. To be able to discuss these epochs of the Universe we need a formalism to describe the dynamics of the Universe.