13.3 Cosmic Microwave Background Radiation

The cosmic microwave background radiation is a relic of the early universe, offering a snapshot of the cosmos when it was just 380,000 years old. This ancient light, discovered in 1964, provides crucial evidence for the Big Bang theory and holds clues about the universe's composition and structure.

Scientists study tiny temperature fluctuations in the CMB to understand the early universe's conditions. These fluctuations, mapped by satellite missions like COBE, WMAP, and Planck, reveal information about cosmic inflation, dark matter, and the formation of galaxies and large-scale structures we see today.

Cosmic Microwave Background (CMB)

Discovery and Characteristics of CMB

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• CMB represents the oldest light in the universe dating back to approximately 380,000 years after the Big Bang
• Discovered accidentally by Arno Penzias and Robert Wilson in 1964 while working on a radio antenna at Bell Labs
• Exhibits characteristics of blackbody radiation with a temperature of about 2.7 K
• Blackbody radiation follows Planck's law describes the electromagnetic radiation emitted by an ideal absorber at thermal equilibrium
• CMB spectrum peaks in the microwave region of the electromagnetic spectrum (~160 GHz)

Temperature Anisotropies and Their Significance

• Temperature anisotropies refer to tiny fluctuations in the CMB temperature across different directions in the sky
• These fluctuations are typically on the order of 1 part in 100,000 (about 30 μK)
• Anisotropies provide crucial information about the early universe's structure and composition
• Originated from quantum fluctuations in the very early universe amplified by cosmic inflation
• Serve as seeds for the formation of large-scale structures in the universe (galaxies, galaxy clusters)

Satellite Missions and CMB Observations

• COBE (Cosmic Background Explorer) launched in 1989 confirmed the blackbody nature of CMB and detected anisotropies
• WMAP (Wilkinson Microwave Anisotropy Probe) operated from 2001 to 2010 provided more detailed maps of CMB anisotropies
• Planck satellite mission (2009-2013) offered the highest resolution and sensitivity in CMB measurements to date
• Each successive mission improved angular resolution and sensitivity allowing for more precise measurements of cosmological parameters
• These missions have been instrumental in establishing the current standard model of cosmology (Lambda-CDM model)

CMB Power Spectrum

Understanding the Angular Power Spectrum

• Angular power spectrum quantifies the strength of CMB temperature fluctuations at different angular scales
• Calculated by decomposing the CMB temperature map into spherical harmonics
• Expressed mathematically as $C_l = \frac{1}{2l+1} \sum_{m=-l}^l |a_{lm}|^2$
• $l$ represents the multipole moment inversely related to the angular scale on the sky
• Lower $l$ values correspond to larger angular scales higher $l$ values to smaller scales

Acoustic Peaks and Their Implications

• Acoustic peaks in the CMB power spectrum result from acoustic oscillations in the primordial plasma before recombination
• First acoustic peak (at $l \approx 200$) provides information about the curvature of the universe
• Height ratio of odd to even peaks constrains the baryon density of the universe
• Position and amplitude of peaks help determine other cosmological parameters (Hubble constant, dark matter density)
• Typically observe 5-7 distinct peaks in current CMB power spectrum measurements

The Sachs-Wolfe Effect and Large-Scale Structure

• Sachs-Wolfe effect describes the gravitational redshift of CMB photons due to large-scale structure
• Contributes to CMB anisotropies on large angular scales (low $l$ values)
• Consists of two components: ordinary Sachs-Wolfe effect (gravitational redshift at the surface of last scattering) and integrated Sachs-Wolfe effect (time-varying gravitational potentials along the photon path)
• Provides information about the distribution of matter in the early universe
• Helps constrain models of cosmic inflation and the growth of structure in the universe

CMB Polarization

Types and Origins of CMB Polarization

• CMB polarization results from Thomson scattering of photons off electrons during the epoch of recombination
• Two types of polarization patterns observed: E-modes and B-modes
• E-modes (curl-free) primarily generated by scalar perturbations in the early universe
• B-modes (divergence-free) can be produced by tensor perturbations (gravitational waves) or by gravitational lensing of E-modes
• Polarization patterns provide complementary information to temperature anisotropies enhancing our understanding of the early universe

Observational Techniques and Challenges

• Polarization signals are much weaker than temperature anisotropies typically about 10% of the temperature signal for E-modes
• Requires highly sensitive instruments and careful control of systematic errors
• Ground-based experiments (BICEP, POLARBEAR) and balloon-borne instruments (SPIDER) complement satellite missions in measuring CMB polarization
• Detecting primordial B-modes remains a major goal in cosmology could provide evidence for cosmic inflation
• Foreground contamination (galactic dust, synchrotron radiation) poses significant challenges in isolating the primordial polarization signal

Implications for Cosmology and Fundamental Physics

• E-mode polarization measurements have confirmed and refined our understanding of the standard cosmological model
• B-mode detection could provide indirect evidence for gravitational waves in the early universe
• Constrains the energy scale of inflation and helps discriminate between different inflationary models
• Polarization data improves constraints on cosmological parameters when combined with temperature data
• Offers a unique probe of physics at extremely high energies inaccessible to particle accelerators