10.5 Cosmological probes

Cosmological probes are essential tools for understanding the universe's structure, composition, and evolution. These methods, including standard candles, rulers, and redshift measurements, allow scientists to map cosmic distances and study large-scale structures.

The cosmic microwave background, large-scale structure, and Type Ia supernovae are key probes that provide crucial insights. These tools, along with Hubble parameter measurements and primordial nucleosynthesis, help constrain cosmological models and reveal the universe's fundamental properties.

Cosmological distance measurements

• Cosmological distance measurements are crucial for understanding the size, age, and evolution of the universe
• Various techniques are employed to measure distances on cosmological scales, each with its own strengths and limitations

Standard candles

Top images from around the web for Standard candles

• 

  Type Ia supernova - Wikipedia View original

  Is this image relevant?

• 

  Type Ia supernova - Wikipedia View original

  Is this image relevant?

1 of 1

Top images from around the web for Standard candles

• 

  Type Ia supernova - Wikipedia View original

  Is this image relevant?

• 

  Type Ia supernova - Wikipedia View original

  Is this image relevant?

1 of 1

• Astronomical objects with known luminosity used to determine distances
• Cepheid variables pulsate with a period-luminosity relation, allowing distance estimation (Type Ia supernovae)
• Supernovae Type Ia have consistent peak luminosity, making them excellent standard candles for measuring distances to distant galaxies
• Tully-Fisher relation correlates the luminosity of a spiral galaxy with its rotation velocity, enabling distance measurements

Standard rulers

• Objects or structures with known physical size used as a reference to measure angular size and infer distance
• Baryon acoustic oscillations (BAO) are a standard ruler originating from sound waves in the early universe
  • BAO appear as a peak in the galaxy correlation function at a characteristic scale of ~150 Mpc
• Sunyaev-Zel'dovich effect measures the apparent angular size of galaxy clusters, serving as a standard ruler

Redshift-distance relation

• Redshift measures the stretching of light due to cosmic expansion, with higher redshifts indicating greater distances
• Hubble-Lemaître law relates the recessional velocity (redshift) of a galaxy to its distance
  • $v = H_0 \times d$, where $v$ is velocity, $H_0$ is the Hubble constant, and $d$ is distance
• Cosmological redshift is caused by the expansion of space itself, not by Doppler effect
• Redshift-distance relation is a key tool for mapping the large-scale structure and evolution of the universe

Cosmic microwave background

• The cosmic microwave background (CMB) is the oldest observable light in the universe, originating ~380,000 years after the Big Bang
• CMB provides a snapshot of the early universe and encodes valuable information about cosmological parameters

Temperature anisotropies

• CMB temperature fluctuations on the order of 1 part in 100,000 across the sky
• Anisotropies arise from density fluctuations in the early universe, which grew into the large-scale structure observed today
• Primary anisotropies originate from the last scattering surface, while secondary anisotropies are caused by interactions along the line of sight (Sunyaev-Zel'dovich effect, gravitational lensing)

Polarization

• CMB photons are polarized due to Thomson scattering off free electrons in the early universe
• E-mode polarization is caused by density fluctuations and is curl-free
• B-mode polarization is a signature of primordial gravitational waves and tensor perturbations, potentially providing evidence for cosmic inflation

Power spectrum

• The CMB power spectrum quantifies the amplitude of temperature fluctuations as a function of angular scale (multipole moment $\ell$)
• Acoustic peaks in the power spectrum correspond to the sound horizon scale at the time of recombination
  • Position and height of peaks depend on cosmological parameters (curvature, baryon density, dark matter density)
• Large-scale (low $\ell$) plateau is the Sachs-Wolfe plateau, sensitive to the primordial power spectrum

Cosmological parameters from CMB

• CMB measurements tightly constrain key cosmological parameters, such as the age, curvature, and composition of the universe
• Planck satellite results (2018): Hubble constant $H_0 = 67.4 \pm 0.5$ km/s/Mpc, matter density $\Omega_m = 0.315 \pm 0.007$, dark energy density $\Omega_\Lambda = 0.685 \pm 0.007$
• CMB supports the inflationary $\Lambda$CDM model, with a flat universe dominated by dark energy and cold dark matter
• Tension between CMB and other measurements (e.g., $H_0$ from local distance ladders) may hint at new physics beyond the standard model

Large-scale structure

• Large-scale structure refers to the distribution of galaxies and galaxy clusters on scales larger than individual galaxies
• Studying the large-scale structure provides insights into the growth of structure, the nature of dark matter, and the effects of dark energy

Galaxy clustering

• Galaxies are not randomly distributed in the universe but form a complex web-like structure
• Two-point correlation function measures the excess probability of finding galaxy pairs at a given separation compared to a random distribution
• Higher-order correlation functions (three-point, four-point) capture additional information about the clustering hierarchy

Baryon acoustic oscillations

• BAO are a preferred scale in the distribution of galaxies, originating from sound waves in the baryon-photon fluid before recombination
• BAO provide a standard ruler for measuring cosmological distances and constraining the expansion history of the universe
• BAO peak appears as a bump in the galaxy correlation function at a scale of ~150 Mpc, corresponding to the sound horizon at the drag epoch

Redshift-space distortions

• Peculiar velocities of galaxies cause apparent distortions in their spatial distribution when observed in redshift space
• On large scales, galaxies exhibit coherent infall towards overdense regions, leading to a flattening of the clustering pattern (Kaiser effect)
• On small scales, random motions within galaxy clusters cause elongation along the line of sight (Fingers of God effect)
• Redshift-space distortions can be used to measure the growth rate of structure and test gravity on cosmological scales

Weak gravitational lensing

• Gravitational lensing is the deflection of light by massive structures, such as galaxies and galaxy clusters
• Weak lensing refers to the subtle distortions in the shapes of background galaxies caused by foreground mass distributions
• Cosmic shear is the coherent distortion pattern induced by the large-scale structure, which can be measured statistically from galaxy shape correlations
• Weak lensing tomography, where galaxies are divided into redshift bins, provides a 3D map of the matter distribution and constrains cosmological parameters

Type Ia supernovae

• Type Ia supernovae (SNe Ia) are powerful explosions that occur when a white dwarf in a binary system accretes matter from its companion, triggering a thermonuclear runaway
• SNe Ia have remarkably consistent peak luminosities, making them excellent standardizable candles for measuring cosmological distances

Luminosity vs redshift

• The relationship between the observed brightness (apparent magnitude) and the redshift of SNe Ia encodes information about the expansion history of the universe
• In a decelerating universe, SNe Ia should appear fainter at a given redshift compared to a coasting or accelerating universe
• Observations of SNe Ia at high redshifts ($z > 0.5$) revealed that they appear dimmer than expected in a matter-dominated universe

Accelerating universe

• The dimming of high-redshift SNe Ia provided the first direct evidence for the accelerating expansion of the universe
• Acceleration implies the presence of a new form of energy with negative pressure, dubbed dark energy
• The discovery of the accelerating universe by two independent teams (Riess et al., Perlmutter et al.) was awarded the Nobel Prize in Physics in 2011

Dark energy constraints

• SNe Ia measurements constrain the properties of dark energy, particularly its equation of state parameter $w = P/\rho$
• For a cosmological constant ($\Lambda$), $w = -1$, while other dark energy models predict different values or evolution of $w$ with time
• Combined with other cosmological probes (CMB, BAO), SNe Ia data support a dark energy component consistent with a cosmological constant
• Future surveys (e.g., LSST, WFIRST) will observe thousands of SNe Ia to high redshifts, providing tighter constraints on the nature of dark energy

Hubble parameter measurements

• The Hubble parameter $H(z)$ describes the expansion rate of the universe as a function of redshift
• Measuring $H(z)$ at different cosmic epochs provides a direct probe of the expansion history and the properties of dark energy

Cosmic distance ladder

• The cosmic distance ladder is a series of methods used to measure distances on progressively larger scales
• Each rung of the ladder is calibrated using the previous one, starting from nearby objects (parallax) and extending to cosmological distances (SNe Ia, BAO)
• Cepheid variables and tip of the red giant branch (TRGB) stars are key rungs in the distance ladder, used to calibrate the luminosity of SNe Ia

Time delays in gravitational lenses

• Strong gravitational lensing occurs when a massive foreground object (e.g., galaxy, cluster) creates multiple images of a background source
• The light travel time for each image path differs due to the geometry and gravitational potential of the lens
• Measuring the time delays between the images and modeling the lens mass distribution allows the determination of the Hubble constant $H_0$
• Time delay cosmography provides an independent measure of $H_0$, complementing other methods (distance ladder, CMB)

Age of the oldest stars

• The age of the oldest stars in the Milky Way provides a lower limit on the age of the universe
• Globular clusters contain some of the oldest known stars, with ages estimated from stellar evolution models and chemical abundances
• The age of the universe can be inferred from the Hubble parameter and the density parameters ($\Omega_m$, $\Omega_\Lambda$) in the context of a cosmological model
• Consistency between the age of the oldest stars and the cosmological age is a test of the standard $\Lambda$CDM model

Primordial nucleosynthesis

• Primordial nucleosynthesis, or Big Bang nucleosynthesis (BBN), refers to the production of light elements (deuterium, helium-3, helium-4, lithium-7) in the early universe
• BBN occurred within the first few minutes after the Big Bang when the universe was dense and hot enough for nuclear fusion reactions to take place

Abundance of light elements

• The primordial abundance of light elements depends on the baryon-to-photon ratio $\eta$ and the number of relativistic species (e.g., neutrinos) at the time of BBN
• Deuterium is the most sensitive probe of the baryon density, as its abundance decreases rapidly with increasing $\eta$
• Helium-4 is the second most abundant element produced in BBN, with a primordial mass fraction of $\sim$25%
• Lithium-7 is produced in trace amounts and is sensitive to the baryon density and the cosmic expansion rate

Baryon density

• BBN predictions for the light element abundances depend on the baryon density parameter $\Omega_b$
• Comparing the observed primordial abundances with BBN calculations constrains the value of $\Omega_b$
• BBN measurements are consistent with a low-density universe, with $\Omega_b \sim 0.04$, in agreement with CMB and large-scale structure results

Neutrino species

• The expansion rate during BBN is sensitive to the number of relativistic species, particularly the number of light neutrino species $N_\nu$
• Standard model predicts $N_\nu = 3$ for the three known neutrino flavors (electron, muon, tau)
• Deviations from $N_\nu = 3$ would affect the primordial helium abundance, allowing BBN to constrain physics beyond the standard model
• Current BBN and CMB measurements are consistent with $N_\nu \approx 3$, placing limits on the existence of additional light species or non-standard neutrino properties

Cosmological simulations

• Cosmological simulations are computational methods used to study the formation and evolution of structure in the universe
• Simulations follow the gravitational collapse of matter from initial conditions motivated by CMB observations and solve the equations of motion for dark matter, gas, and stars

N-body simulations

• N-body simulations model the evolution of a large number of particles (typically dark matter) under the influence of gravity
• Particles are discretized on a grid or using adaptive techniques (e.g., tree codes) to efficiently calculate the gravitational forces
• N-body simulations have been instrumental in understanding the hierarchical growth of structure, the properties of dark matter halos, and the cosmic web

Hydrodynamical simulations

• Hydrodynamical simulations include the effects of gas dynamics, radiative cooling, star formation, and feedback processes in addition to gravity
• Gas is typically modeled using smoothed particle hydrodynamics (SPH) or grid-based methods (e.g., adaptive mesh refinement)
• Subgrid models are employed to capture physical processes below the resolution limit, such as star formation, supernova feedback, and black hole accretion
• Hydrodynamical simulations aim to reproduce the observed properties of galaxies, clusters, and the intergalactic medium

Comparison with observations

• Cosmological simulations are compared with observations to test our understanding of structure formation and the underlying cosmological model
• Dark matter-only simulations are used to interpret galaxy clustering, weak lensing, and velocity field measurements
• Hydrodynamical simulations are compared with the observed properties of galaxies (e.g., luminosity functions, color-magnitude diagrams, scaling relations)
• Discrepancies between simulations and observations can highlight missing physics or the need for modified cosmological models
• Simulations also guide the interpretation of current observations and make predictions for future surveys

Future cosmological probes

• Upcoming cosmological surveys and experiments will provide new opportunities to test the standard cosmological model and explore physics beyond it
• Future probes will combine multiple tracers and techniques to achieve unprecedented precision and probe new regimes

21cm cosmology

• The 21cm line of neutral hydrogen can be used to map the distribution of matter in the early universe, before and during the epoch of reionization
• 21cm intensity mapping surveys will measure the large-scale structure at redshifts $z > 6$, complementing galaxy surveys at lower redshifts
• Experiments like the Square Kilometre Array (SKA) and the Hydrogen Epoch of Reionization Array (HERA) aim to detect the 21cm signal and constrain the reionization history and cosmological parameters

Gravitational waves

• Gravitational waves are ripples in the fabric of spacetime predicted by Einstein's general relativity
• Primordial gravitational waves, generated during cosmic inflation, leave an imprint on the CMB polarization (B-modes)
• Detection of primordial gravitational waves would provide direct evidence for inflation and constrain the energy scale and physics of the inflationary epoch
• Gravitational waves from merging compact objects (black holes, neutron stars) serve as standard sirens for measuring cosmological distances and the Hubble constant

Cosmic voids

• Cosmic voids are large underdense regions in the galaxy distribution, occupying a significant fraction of the universe's volume
• Voids are sensitive probes of dark energy and modified gravity, as their growth and shape are affected by the expansion history and gravitational law
• Void statistics, such as the void size function and void-galaxy cross-correlation, can constrain cosmological parameters and test alternative gravity models
• Future galaxy surveys (e.g., DESI, Euclid, LSST) will provide large samples of voids for cosmological analysis

Intensity mapping

• Intensity mapping is a technique that measures the integrated emission from unresolved sources, such as galaxies or neutral hydrogen, in large volumes of the universe
• Intensity mapping surveys can efficiently map the large-scale structure at high redshifts, complementing traditional galaxy surveys
• Examples include the CII intensity mapping experiment (TIME), which targets the 158μm line of singly ionized carbon at $z \sim 5-9$, and the Lyman-alpha intensity mapping experiment (HETDEX)
• Intensity mapping can constrain the galaxy power spectrum, the cosmic expansion history, and the growth of structure, providing tests of dark energy and modified gravity models