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Cosmology
Table of Contents
Unit 5 Overview: The Cosmic Microwave Background Radiation
5.1 Discovery and properties of the CMB
5.2 Temperature anisotropies and their significance
5.3 Polarization of the CMB
5.4 Implications for cosmological parameters and models

🌌cosmology review

5.2 Temperature anisotropies and their significance

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The cosmic microwave background (CMB) holds clues to our universe's earliest moments. Its tiny temperature variations, just 1 part in 100,000, reveal quantum fluctuations from the inflationary period that seeded cosmic structure.

The CMB power spectrum maps these fluctuations across angular scales. Its peaks and troughs encode crucial information about the universe's composition, geometry, and evolution, allowing scientists to test cosmological models and measure fundamental parameters.

Cosmic Microwave Background (CMB) Temperature Anisotropies

Temperature anisotropies in CMB radiation

  • Minuscule variations in the temperature of the CMB radiation observed across the celestial sphere
    • Magnitude of these fluctuations is approximately 1 part in 100,000 compared to the mean CMB temperature of 2.725 K
  • Temperature anisotropies span a wide range of angular scales from large to small
    • Large angular scales represent fluctuations over immense distances in the primordial universe
      • Earth's motion relative to the CMB rest frame induces a dipole anisotropy with a 180-degree angular scale
    • Small angular scales correspond to fluctuations over more compact regions in the early universe
      • Peaks in the CMB power spectrum at angular scales of around 1 degree and smaller arise from acoustic oscillations in the primordial plasma

Evidence for quantum fluctuations

  • Prevailing theory attributes the origin of CMB temperature anisotropies to quantum fluctuations in the early universe during the inflationary period
    • Inflation posits a fleeting phase of exponential expansion that magnified these quantum fluctuations to macroscopic scales
  • Quantum fluctuations in the inflaton field, the driving force behind inflation, generated inhomogeneities in the density and temperature of the primordial plasma
    • Gravitational collapse of overdense regions ultimately formed the galaxies, clusters, and other large-scale structures we observe today
  • The statistical characteristics of the CMB temperature anisotropies align with the predictions of inflationary models
    • The amplitude and angular power spectrum of the anisotropies provide compelling evidence for the quantum origin of cosmic structure

Significance of CMB power spectrum

  • Graphical representation of the variance (power) of the temperature fluctuations as a function of angular scale (multipole moment $\ell$)
    • Contains information about the physical processes that influenced the CMB anisotropies and the fundamental properties of the universe
  • The position, amplitude, and width of peaks in the power spectrum exhibit sensitivity to various cosmological parameters
    • Parameters include $\Omega_m$ (matter density), $\Omega_b$ (baryon density), $\Omega_\Lambda$ (dark energy density), and $H_0$ (Hubble constant)
  • Comparing the measured CMB power spectrum with theoretical predictions from different cosmological models enables researchers to:
    • Place constraints on the values of these parameters
    • Evaluate theories of the early universe
  • The location of the first peak at $\ell \approx 200$ favors a spatially flat universe
  • The relative amplitudes of odd and even peaks indicate the presence of dark matter

Effects shaping CMB anisotropies

  • The Sachs-Wolfe effect contributes to CMB anisotropies on large angular scales ($\ell \lesssim 100$)
    • Results from gravitational redshifts and time dilation experienced by photons as they escape potential wells in the early universe
  • The Doppler effect contributes to CMB anisotropies on intermediate angular scales ($100 \lesssim \ell \lesssim 1000$)
    • Caused by the motion of the primordial plasma relative to the CMB rest frame
    • Imprints a distinctive acoustic peak structure on the power spectrum
  • Silk damping suppresses CMB anisotropies on small angular scales ($\ell \gtrsim 1000$)
    • Occurs due to photon diffusion in the primordial plasma, erasing temperature fluctuations on scales smaller than the photon mean free path
    • The damping tail of the CMB power spectrum provides insights into the thickness of the last scattering surface and the primordial helium abundance

Implications of CMB observations

  • The observed CMB temperature anisotropies have profound implications for the geometry and structure of the universe on the grandest scales
  • The remarkable uniformity of the CMB temperature across the sky, with anisotropies at the level of merely 1 part in 100,000
    • Offers robust evidence for the homogeneity and isotropy of the universe
    • Supports the cosmological principle, which states that the universe appears the same from every location and in every direction on sufficiently large scales
  • The position of the first acoustic peak in the CMB power spectrum at $\ell \approx 200$ is consistent with a spatially flat universe
    • In a curved universe, the peak would be shifted to larger or smaller angular scales
  • The flatness of the universe, with $\Omega_\text{total} = \Omega_m + \Omega_\Lambda + \Omega_r \approx 1$, suggests that inflation drove the universe extremely close to spatial flatness in the early stages of its evolution