Cosmological probes are essential tools for understanding the universe's structure, composition, and evolution. These methods, including , rulers, and measurements, allow scientists to map cosmic distances and study large-scale structures.
The cosmic microwave background, , and 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
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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
(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=H0×d, where v is velocity, H0 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
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, )
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
Power spectrum
The CMB power spectrum quantifies the amplitude of temperature fluctuations as a function of angular scale (multipole moment ℓ)
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 ℓ) 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 H0=67.4±0.5 km/s/Mpc, matter density Ωm=0.315±0.007, density ΩΛ=0.685±0.007
CMB supports the inflationary ΛCDM model, with a flat universe dominated by dark energy and cold dark matter
Tension between CMB and other measurements (e.g., H0 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
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/ρ
For a cosmological constant (Λ), 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 H0
Time delay cosmography provides an independent measure of H0, 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 (Ωm, ΩΛ) 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 ΛCDM 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 η 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 η
Helium-4 is the second most abundant element produced in BBN, with a primordial mass fraction of ∼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 Ωb
Comparing the observed primordial abundances with BBN calculations constrains the value of Ωb
BBN measurements are consistent with a low-density universe, with Ωb∼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 Nν
Standard model predicts Nν=3 for the three known neutrino flavors (electron, muon, tau)
Deviations from Nν=3 would affect the primordial helium abundance, allowing BBN to constrain physics beyond the standard model
Current BBN and CMB measurements are consistent with Nν≈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
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∼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
Key Terms to Review (18)
Accelerating Universe: The accelerating universe refers to the phenomenon where the expansion of the universe is speeding up over time, rather than slowing down due to gravitational attraction. This discovery, made in the late 1990s through observations of distant supernovae, indicates that there is an unknown force driving this acceleration, often attributed to dark energy. Understanding this concept is crucial for exploring cosmological probes, the nature of dark energy, and the implications of a cosmological constant.
Alan Guth: Alan Guth is a theoretical physicist and cosmologist best known for proposing the theory of cosmic inflation, which describes a rapid expansion of the universe in its earliest moments. His work laid the groundwork for understanding how the universe evolved from a hot, dense state to its current large-scale structure, influencing concepts like the cosmic microwave background radiation and the formation of galaxies.
Baryon Acoustic Oscillations: Baryon acoustic oscillations refer to the periodic fluctuations in the density of visible baryonic matter (normal matter) in the universe, which were produced by sound waves in the early universe. These oscillations are critical as they provide evidence of the distribution of matter and energy in the cosmos, influencing structures like galaxy clusters, superclusters, and voids.
Big bang: The big bang is the leading explanation for the origin of the universe, proposing that it began as an extremely hot and dense point approximately 13.8 billion years ago and has been expanding ever since. This event marks not only the birth of space and time but also sets the stage for understanding cosmic evolution, including the formation of galaxies, stars, and the large-scale structure of the universe.
Cosmic inflation: Cosmic inflation is a theory that proposes a rapid expansion of the universe at an exponential rate during the first moments after the Big Bang. This concept explains several key features of our universe, such as its large-scale structure, uniformity, and the distribution of cosmic microwave background radiation. By addressing certain problems in cosmology, cosmic inflation helps to connect the early universe's conditions to the formation of galaxies and structures we observe today.
Cosmic Microwave Background Radiation: Cosmic microwave background radiation (CMB) is the faint glow of microwave radiation that fills the universe, a relic from the early stages of the universe shortly after the Big Bang. This radiation provides critical evidence for various cosmological theories, serving as a key element in understanding dark matter, cosmic inflation, primordial nucleosynthesis, and the expansion of the universe.
Cosmic Web: The cosmic web is the large-scale structure of the universe, characterized by a vast network of galaxies, clusters, and superclusters interconnected by filaments of dark matter and gas, along with vast voids in between. This intricate structure highlights the distribution of matter and energy in the universe and plays a crucial role in understanding its formation and evolution.
Dark energy: Dark energy is a mysterious form of energy that makes up about 68% of the universe and is responsible for the accelerated expansion of the cosmos. It plays a crucial role in shaping the universe's large-scale structure, influencing phenomena like voids, the cosmological principle, and Hubble's law.
Edwin Hubble: Edwin Hubble was an American astronomer who played a pivotal role in establishing the field of extragalactic astronomy and is best known for Hubble's law, which describes the expansion of the universe. His work not only led to the classification of galaxies but also revolutionized our understanding of the cosmos, connecting various concepts like the cosmic web and the cosmological principle.
Gravitational Lensing: Gravitational lensing is a phenomenon that occurs when a massive object, such as a galaxy or a cluster of galaxies, bends the light from a more distant object due to its gravitational field. This effect not only magnifies and distorts the image of the background object but can also provide crucial information about the mass and distribution of dark matter in the lensing object, connecting it to various cosmic structures and dynamics.
Hubble's Law: Hubble's Law states that the velocity at which a galaxy is receding from us is directly proportional to its distance from us. This fundamental observation supports the idea that the universe is expanding, linking it to various phenomena like galaxy formation and the structure of the cosmos.
Inflationary theory: Inflationary theory proposes that the universe underwent a rapid exponential expansion just after the Big Bang, driven by a high-energy field known as 'inflaton.' This theory helps explain several observations about the universe, such as its large-scale structure, uniformity, and the distribution of galaxies, connecting it to concepts like the cosmic web, voids, cosmological probes, and large-scale structure surveys.
Lambda-cdm model: The lambda-cdm model is a cosmological model that describes the large-scale structure and evolution of the universe, incorporating dark energy (represented by lambda) and cold dark matter (cdm). This model explains how galaxies form and evolve over time while considering the effects of both dark matter halos and cosmic expansion influenced by dark energy.
Large-scale structure: Large-scale structure refers to the organization and distribution of matter in the universe on scales larger than individual galaxies, encompassing clusters, superclusters, and the cosmic web. This framework helps us understand how galaxies and other cosmic structures form and evolve under the influence of gravitational forces and dark matter.
Recombination Epoch: The recombination epoch refers to a critical period in the early universe, approximately 380,000 years after the Big Bang, when electrons and protons combined to form neutral hydrogen atoms. This event marked a significant transition from a hot, dense plasma state to a transparent gas, allowing photons to travel freely through space and leading to the decoupling of matter and radiation, which is essential for understanding the cosmic microwave background radiation.
Redshift: Redshift is the phenomenon where light from an object is shifted towards longer wavelengths, typically observed as a shift toward the red end of the spectrum. This effect occurs when an object moves away from the observer, providing key insights into the expansion of the universe and the nature of celestial bodies.
Standard candles: Standard candles are astronomical objects with a known intrinsic brightness, allowing astronomers to determine their distance from Earth by comparing their known brightness to their observed brightness. This property makes them essential for measuring distances in the universe, contributing significantly to the cosmological distance ladder and serving as powerful probes of the cosmos.
Type Ia supernovae: Type Ia supernovae are a class of stellar explosions that occur in binary systems where one star is a white dwarf. These supernovae are critical for measuring astronomical distances and understanding the expansion of the universe due to their consistent peak brightness. Their predictable luminosity allows astronomers to use them as 'standard candles' in cosmology, linking them to various concepts in cosmic distance measurements, dark energy, and the cosmological constant.