9.5 Cosmological constraints from CMB

The cosmic microwave background (CMB) provides crucial insights into the early universe and its evolution. By studying its temperature fluctuations and polarization, scientists can uncover key information about the universe's composition, structure, and fundamental properties.

CMB observations have led to precise measurements of cosmological parameters, supporting the standard Lambda-CDM model. These findings have revolutionized our understanding of the universe's age, geometry, and content, while also providing evidence for cosmic inflation and constraining the properties of dark matter and dark energy.

Cosmic microwave background (CMB) overview

• The CMB is the oldest light in the universe, a remnant of the Big Bang that fills all of space with a faint glow of microwave radiation
• Studying the CMB provides crucial insights into the early universe, the formation of structure, and the fundamental properties of the cosmos
• The CMB is nearly uniform in all directions, with a temperature of about 2.7 Kelvin, but small fluctuations in its temperature and polarization hold key information about the universe's history and composition

Discovery of the CMB

Top images from around the web for Discovery of the CMB

• 

  The Cosmic Microwave Background | Astronomy View original

  Is this image relevant?

• 

  The Big Bang Archives - Universe Today View original

  Is this image relevant?

• 

  cosmic micorwave background radiation Archives - Universe Today View original

  Is this image relevant?

• 

  The Cosmic Microwave Background | Astronomy View original

  Is this image relevant?

• 

  The Big Bang Archives - Universe Today View original

  Is this image relevant?

1 of 3

Top images from around the web for Discovery of the CMB

• 

  The Cosmic Microwave Background | Astronomy View original

  Is this image relevant?

• 

  The Big Bang Archives - Universe Today View original

  Is this image relevant?

• 

  cosmic micorwave background radiation Archives - Universe Today View original

  Is this image relevant?

• 

  The Cosmic Microwave Background | Astronomy View original

  Is this image relevant?

• 

  The Big Bang Archives - Universe Today View original

  Is this image relevant?

1 of 3

• In 1965, Arno Penzias and Robert Wilson accidentally discovered the CMB while working on a radio antenna at Bell Labs
• They detected a persistent background noise that seemed to come from all directions in the sky, which they initially attributed to interference or equipment malfunction
• Further analysis revealed that this noise was actually the long-predicted afterglow of the Big Bang, providing crucial evidence for the hot Big Bang model of the universe's origin

Properties of the CMB

• The CMB has a nearly perfect blackbody spectrum, with a peak wavelength in the microwave range (around 1-2 mm)
• Its temperature is remarkably uniform across the sky, with an average value of 2.72548 ± 0.00057 Kelvin
• The CMB is unpolarized to a high degree, with only small polarization signals arising from specific physical processes in the early universe

CMB temperature and fluctuations

• Although the CMB is highly uniform, it exhibits tiny temperature fluctuations on the order of one part in 100,000 (around 30 microKelvin)
• These fluctuations arise from quantum fluctuations in the early universe that were stretched to cosmic scales during the period of inflation
• The pattern of temperature fluctuations encodes information about the universe's geometry, composition, and the seeds of cosmic structure formation

CMB anisotropies

• CMB anisotropies refer to the small variations in the temperature and polarization of the CMB across the sky
• These anisotropies arise from various physical processes in the early universe and provide a wealth of information about cosmology and fundamental physics
• Studying the statistical properties and angular power spectrum of the CMB anisotropies allows cosmologists to constrain key parameters of the universe and test theories of its origin and evolution

Primary vs secondary anisotropies

• Primary anisotropies are those that were imprinted on the CMB at the time of decoupling (around 380,000 years after the Big Bang) and reflect the conditions in the early universe
• Secondary anisotropies arise from physical processes that affect the CMB photons as they travel from the last scattering surface to Earth, such as gravitational lensing, the Sunyaev-Zel'dovich effect, and the integrated Sachs-Wolfe effect
• Distinguishing between primary and secondary anisotropies is crucial for accurately interpreting the CMB and extracting cosmological information

Sachs-Wolfe effect

• The Sachs-Wolfe effect is a primary anisotropy that arises from gravitational redshift and time dilation experienced by CMB photons as they climb out of gravitational potential wells in the early universe
• Regions of higher density (potential wells) at the time of decoupling appear slightly colder in the CMB, while regions of lower density (potential hills) appear slightly hotter
• The Sachs-Wolfe effect is most pronounced on large angular scales and provides information about the universe's geometry and the matter-energy content at the time of decoupling

Acoustic oscillations in the early universe

• Before decoupling, the universe consisted of a tightly coupled plasma of photons, electrons, and baryons that underwent acoustic oscillations driven by the competing forces of gravity and radiation pressure
• These oscillations created characteristic peaks and troughs in the power spectrum of the CMB anisotropies, known as acoustic peaks
• The positions and amplitudes of the acoustic peaks provide information about the baryon density, matter density, and geometry of the universe

Silk damping

• Silk damping is a physical process that suppresses CMB anisotropies on small angular scales (high multipole moments)
• It arises from the diffusion of photons in the early universe, which erases temperature fluctuations on scales smaller than the photon mean free path at the time of decoupling
• The angular scale at which Silk damping becomes significant depends on the baryon and matter densities, providing another probe of these cosmological parameters

CMB power spectrum

• The CMB power spectrum is a plot of the variance (power) of the CMB temperature fluctuations as a function of angular scale or multipole moment
• It encodes a wealth of information about the properties and evolution of the universe, and is a key tool for constraining cosmological models and parameters
• The power spectrum exhibits a series of peaks and troughs that arise from acoustic oscillations in the early universe, as well as a damping tail at high multipoles due to Silk damping

Angular power spectrum

• The angular power spectrum $C_\ell$ is defined as the variance of the CMB temperature fluctuations for a given multipole moment $\ell$
• It is computed by decomposing the CMB temperature map into spherical harmonics $Y_{\ell m}(\theta, \phi)$ and calculating the average power for each $\ell$ value
• The angular power spectrum is often plotted as $\ell(\ell+1)C_\ell/2\pi$ versus $\ell$, which gives a roughly flat spectrum for a scale-invariant distribution of fluctuations

Multipole moments

• Multipole moments $\ell$ are a measure of the angular scale of the CMB fluctuations, with low $\ell$ corresponding to large angular scales and high $\ell$ corresponding to small angular scales
• The monopole ($\ell=0$) represents the average temperature of the CMB, while the dipole ($\ell=1$) is dominated by the Doppler shift due to the Earth's motion relative to the CMB rest frame
• Higher multipoles ($\ell \geq 2$) encode the primordial fluctuations and the effects of various physical processes in the early universe

Peaks in the power spectrum

• The CMB power spectrum exhibits a series of peaks and troughs that arise from acoustic oscillations in the primordial plasma
• The first peak corresponds to the angular scale of the sound horizon at decoupling and is sensitive to the curvature of the universe
• The ratios of the peak heights provide information about the baryon density, matter density, and dark energy density

Cosmological parameters from power spectrum

• By fitting theoretical power spectra to the observed CMB data, cosmologists can constrain a wide range of cosmological parameters, such as the Hubble constant, the age of the universe, and the densities of various components (baryons, dark matter, dark energy)
• The shape and amplitude of the power spectrum also provide tests of inflationary models and the spectrum of primordial fluctuations
• Combining CMB data with other cosmological probes (such as galaxy surveys and supernovae) helps break degeneracies between parameters and provides tighter constraints on the properties of the universe

Cosmological constraints from CMB

• The CMB is one of the most powerful probes of cosmology, providing precise measurements of key cosmological parameters and testing fundamental theories of the universe's origin and evolution
• By combining CMB data with other cosmological observations (such as galaxy surveys, supernovae, and gravitational lensing), cosmologists can break degeneracies between parameters and obtain tight constraints on the properties of the universe
• The CMB supports the standard $\Lambda$CDM model of cosmology, which describes a flat universe dominated by cold dark matter and dark energy, with a nearly scale-invariant spectrum of primordial fluctuations

Age of the universe

• The CMB provides a measurement of the age of the universe, which is the time elapsed since the Big Bang
• This is determined by the distance to the last scattering surface and the expansion rate of the universe (Hubble constant)
• Current CMB data, combined with other cosmological probes, give an age of 13.8 billion years

Curvature of space

• The CMB is sensitive to the geometry of the universe, which can be flat (Euclidean), positively curved (spherical), or negatively curved (hyperbolic)
• The angular scale of the first acoustic peak in the CMB power spectrum depends on the curvature of space
• CMB observations are consistent with a flat universe, with a curvature parameter $|\Omega_k| < 0.005$

Dark matter and dark energy densities

• The heights and positions of the acoustic peaks in the CMB power spectrum provide constraints on the densities of dark matter and dark energy
• Dark matter affects the growth of structure and the depth of gravitational potential wells, influencing the Sachs-Wolfe effect and the heights of the odd-numbered acoustic peaks
• Dark energy affects the expansion rate of the universe and the angular diameter distance to the last scattering surface, shifting the positions of the acoustic peaks

Hubble constant

• The Hubble constant $H_0$ describes the current expansion rate of the universe and is a key parameter in cosmology
• The CMB provides an indirect measurement of $H_0$ through its effect on the angular scale of the acoustic peaks
• There is currently a tension between CMB-derived values of $H_0$ and those obtained from local distance ladder measurements (e.g., using Cepheid variables and supernovae)

Inflation models

• The CMB provides tests of inflationary models, which propose a period of exponential expansion in the early universe
• Inflation predicts a nearly scale-invariant spectrum of primordial fluctuations, which is consistent with the observed CMB power spectrum
• The CMB also constrains the spectral index $n_s$ of the primordial fluctuations and the tensor-to-scalar ratio $r$, which are key predictions of inflationary models

CMB polarization

• In addition to temperature fluctuations, the CMB also exhibits small polarization signals that arise from Thomson scattering of photons by electrons in the early universe
• CMB polarization provides complementary information to the temperature anisotropies and can be used to break degeneracies between cosmological parameters
• Measuring CMB polarization is technically challenging due to its small amplitude (about 10% of the temperature fluctuations) and the presence of foreground contamination

E-modes and B-modes

• CMB polarization can be decomposed into two types of patterns: E-modes (gradient-like) and B-modes (curl-like)
• E-modes arise from scalar (density) perturbations in the early universe and are generated by the same processes that create the temperature anisotropies
• B-modes can arise from tensor perturbations (gravitational waves) in the early universe or from gravitational lensing of E-modes by large-scale structure

Gravitational waves from inflation

• Inflationary models predict the existence of a background of primordial gravitational waves, which would leave a unique imprint on the CMB polarization in the form of B-modes
• The amplitude of these B-modes is characterized by the tensor-to-scalar ratio $r$, which depends on the energy scale of inflation
• Detecting primordial B-modes would provide strong evidence for inflation and help constrain the physics of the early universe

Reionization epoch

• The CMB polarization is also sensitive to the reionization of the universe, which occurred when the first stars and galaxies formed and ionized the neutral hydrogen in the intergalactic medium
• Reionization generates a large-scale polarization signal at low multipoles ($\ell < 20$) known as the reionization bump
• The amplitude and shape of the reionization bump provide constraints on the timing and duration of reionization

Polarization power spectra

• Similar to the temperature anisotropies, the CMB polarization can be characterized by angular power spectra: $C_\ell^{EE}$, $C_\ell^{BB}$, and the cross-spectrum $C_\ell^{TE}$
• The E-mode power spectrum $C_\ell^{EE}$ exhibits acoustic peaks similar to the temperature power spectrum, providing additional constraints on cosmological parameters
• The B-mode power spectrum $C_\ell^{BB}$ is a key target for current and future CMB experiments, as it could provide evidence for primordial gravitational waves and constrain inflationary models

CMB experiments and missions

• Measuring the CMB temperature and polarization anisotropies requires highly sensitive and precise instruments, often operating at cryogenic temperatures to minimize noise
• CMB experiments have evolved from ground-based and balloon-borne telescopes to dedicated satellite missions, providing ever-increasing sensitivity and angular resolution
• Current and future CMB experiments aim to measure the polarization signals with unprecedented accuracy, search for primordial B-modes, and constrain cosmological parameters to sub-percent levels

COBE satellite

• The Cosmic Background Explorer (COBE) was the first satellite dedicated to studying the CMB, launched in 1989
• COBE made three key discoveries: the precise blackbody spectrum of the CMB, the dipole anisotropy due to the Earth's motion, and the first detection of temperature fluctuations at the level of one part in 100,000
• These results provided strong evidence for the Big Bang model and laid the foundation for future CMB experiments

WMAP satellite

• The Wilkinson Microwave Anisotropy Probe (WMAP) was a NASA satellite that operated from 2001 to 2010
• WMAP provided the first detailed all-sky map of the CMB temperature anisotropies, with an angular resolution of about 0.3 degrees
• WMAP data confirmed the flat geometry of the universe, measured the baryon and dark matter densities, and provided evidence for cosmic inflation

Planck satellite

• The Planck satellite was a European Space Agency mission that operated from 2009 to 2013
• Planck provided the most precise measurements of the CMB temperature and polarization anisotropies to date, with an angular resolution of about 5 arcminutes
• Planck data refined the measurements of cosmological parameters, tested inflationary models, and provided new insights into the physics of the early universe

Ground-based CMB experiments

• Several ground-based CMB experiments have been developed to complement satellite missions, often focusing on measuring the CMB polarization at high angular resolution
• Examples include the South Pole Telescope (SPT), the Atacama Cosmology Telescope (ACT), and the BICEP/Keck Array
• Ground-based experiments benefit from larger telescope apertures and the ability to deploy the latest detector technology, but must contend with atmospheric noise and limited sky coverage

Future CMB observations

• Future CMB experiments aim to measure the polarization signals with unprecedented sensitivity and angular resolution, search for primordial B-modes, and constrain cosmological parameters to sub-percent levels
• These experiments will test the predictions of inflationary models, probe the physics of the early universe, and shed light on the nature of dark matter and dark energy
• Challenges for future CMB observations include controlling systematic errors, mitigating foreground contamination, and developing new detector technologies and analysis techniques

CMB-S4 experiment

• The next-generation ground-based CMB experiment, known as CMB-S4 (Stage 4), is a proposed collaboration between several institutions in the United States and worldwide
• CMB-S4 aims to deploy hundreds of thousands of detectors across multiple telescopes at sites in Chile and Antarctica, covering a wide range of frequencies and angular scales
• The experiment will measure the CMB polarization with unprecedented sensitivity, aiming to detect or constrain primordial B-modes, measure the sum of neutrino masses, and constrain dark energy and the physics of the early universe

Primordial gravitational waves

• Detecting primordial gravitational waves through their imprint on the CMB B-modes is a major goal of future CMB experiments
• The amplitude of primordial B-modes depends on the tensor-to-scalar ratio $r$, which is related to the energy scale of inflation
• Measuring or constraining $r$ will test inflationary models and provide insights into the physics of the early universe at energy scales far beyond those accessible to particle accelerators

Neutrino masses and properties

• The CMB is sensitive to the sum of neutrino masses through their effect on the growth of structure and the suppression of small-scale fluctuations
• Future CMB experiments, combined with large-scale structure surveys, aim to measure the sum of neutrino masses with a sensitivity of about 20 meV, which could distinguish between different neutrino mass hierarchies
• The CMB may also be sensitive to other neutrino properties, such as their effective number and possible non-standard interactions

Cosmic inflation tests

• Future CMB observations will provide stringent tests of inflationary models and help constrain the physics of the early universe
• Measuring the spectral index $n_s$ and its running with scale, as well as the tensor-to-scalar ratio $r$, will discriminate between different inflationary models and probe the shape of the inflaton potential
• The CMB may also be sensitive to non-Gaussian features in the primordial fluctuations, which could arise from complex inflationary dynamics or alternative theories of the early universe