Dark Energy

• A. The Supernova Cosmology Project and the High-z Supernova Search Team ✓
• B. The COBE and WMAP collaborations
• C. The LIGO and Virgo collaborations
• D. The Planck and Hubble mission teams

Why: The Supernova Cosmology Project (led by Saul Perlmutter) and the High-z Supernova Search Team (led by Brian Schmidt and Adam Riess) independently studied distant Type Ia supernovae and found they were dimmer than expected, implying the universe's expansion is speeding up.

• A. Red giant stars
• B. Pulsars
• C. Type Ia supernovae ✓
• D. Quasars

Why: Type Ia supernovae have a consistent peak luminosity because they result from the explosion of white dwarfs near a fixed mass limit. Comparing their observed brightness to their known intrinsic brightness reveals their distance.

• A. The expansion was slowing down due to gravity
• B. The expansion was constant with no change over time
• C. The expansion was accelerating over time ✓
• D. The universe was contracting

Why: Distant supernovae appeared fainter than predicted for a decelerating or constant-rate expansion, meaning they were farther away than expected. This indicated that the expansion rate has been increasing over the last several billion years.

• A. Dark matter
• B. Dark energy ✓
• C. Antimatter
• D. Neutrino flux

Why: Dark energy is the hypothesized form of energy that permeates space and exerts a negative pressure, driving the accelerated expansion of the universe. Its exact nature remains unknown.

• A. Perlmutter, Schmidt, and Riess ✓
• B. Hawking, Penrose, and Thorne
• C. Mather and Smoot
• D. Higgs and Englert

Why: Saul Perlmutter, Brian Schmidt, and Adam Riess received the 2011 Nobel Prize in Physics for discovering the accelerating expansion of the universe through observations of distant supernovae.

• A. The rate at which galaxies rotate around their centers
• B. A form of energy density that is uniform across space and causes accelerated cosmic expansion ✓
• C. The total mass of all dark matter in the universe
• D. The temperature of the cosmic microwave background

Why: The cosmological constant represents a uniform energy density of empty space, and its positive value causes the accelerating expansion of the universe observed in the late 1990s.

• A. To explain the redshift of distant galaxies
• B. To allow a static universe that neither expands nor contracts ✓
• C. To account for the rotation curves of spiral galaxies
• D. To predict the existence of black holes

Why: Einstein added the cosmological constant in 1917 to balance gravity and produce a static universe, which was the prevailing assumption at the time before Hubble's discoveries of expansion.

• A. The energy stored in the nuclei of atoms
• B. The energy associated with empty space, arising from quantum fluctuations and field properties ✓
• C. The kinetic energy of photons traveling through space
• D. The heat energy radiated by stars

Why: Vacuum energy is the lowest possible energy of space itself, which quantum field theory predicts is nonzero due to fluctuating virtual particles and field zero-point energy.

• A. It is too large to measure with any telescope
• B. Quantum field theory predicts a vacuum energy many orders of magnitude larger than the observed value ✓
• C. It changes sign every billion years
• D. It cannot be included in Einstein's equations

Why: Naive calculations of vacuum energy from quantum field theory give values around 120 orders of magnitude larger than what is observed, a discrepancy known as the cosmological constant problem.

• A. It causes the universe to collapse into a Big Crunch
• B. It drives accelerated expansion, leading to a cold, dilute future ✓
• C. It stops all star formation immediately
• D. It reverses the direction of time

Why: A positive cosmological constant produces repulsive gravity on cosmic scales, causing accelerated expansion that dilutes matter and radiation over time, a scenario often called heat death or the Big Freeze.

• A. Pressure to energy density ✓
• B. Energy density to pressure
• C. Pressure to temperature
• D. Density to volume

Why: The equation of state parameter is w = p/(ρc²), the ratio of the pressure p to the energy density ρc². It determines how the energy density of a component evolves as the universe expands.

• A. w = 0
• B. w = -1/3
• C. w = -1 ✓
• D. w = +1

Why: A cosmological constant has constant energy density and negative pressure equal in magnitude to its energy density, giving w = -1 exactly. Its energy density does not dilute as the universe expands.

• A. w = -1
• B. w = 0 ✓
• C. w = 1/3
• D. w = -2

Why: Pressureless matter has w = 0. Its energy density scales as a^-3 with the scale factor a, so it dilutes as the volume of the expanding universe increases.

• A. Quintessence
• B. Phantom energy ✓
• C. Radiation-like energy
• D. Dust energy

Why: Dark energy with w < -1 is called phantom energy. Its energy density increases as the universe expands, which leads to exotic behaviour such as a possible future 'Big Rip'. Quintessence, by contrast, has -1 < w < -1/3.

• A. w = a + b z (linear in redshift)
• B. w = w0 + wa(1 - a), the CPL parameterization ✓
• C. w = sin(a)
• D. w = ln(a)/a

Why: The Chevallier-Polarski-Linder (CPL) parameterization, w(a) = w0 + wa(1 - a), is widely used to test whether dark energy evolves over time. Constant w corresponds to wa = 0, and a cosmological constant has w0 = -1 and wa = 0.

• A. They always occur in the same galaxy as the Earth
• B. They reach roughly the same peak luminosity, so their apparent brightness reveals how far away they are ✓
• C. They emit only ultraviolet light, which travels farther than visible light
• D. They are the only objects that produce heavy elements in the universe

Why: Type Ia supernovae reach a consistent peak luminosity because they result from white dwarfs reaching a similar critical mass. Comparing their known intrinsic brightness with their observed brightness allows astronomers to calculate their distance.

• A. The collapse of a massive star's iron core
• B. The merger of two neutron stars
• C. A white dwarf in a binary system gaining mass until it exceeds a critical limit and explodes ✓
• D. A black hole consuming a nearby main-sequence star

Why: A Type Ia supernova occurs when a carbon-oxygen white dwarf accretes matter from a companion star and approaches the Chandrasekhar limit, triggering a runaway thermonuclear explosion.

• A. An object whose intrinsic brightness is known, allowing its distance to be determined ✓
• B. A star that is used to measure the temperature of galaxies
• C. A candle-shaped telescope mirror used for calibration
• D. Any object that glows in the dark

Why: A standard candle is an astronomical object with a known intrinsic luminosity. By comparing its known brightness to how bright it appears from Earth, astronomers can infer its distance.

• A. The supernovae were fainter than expected, implying they were closer than predicted
• B. The supernovae were dimmer than expected, suggesting the universe's expansion is accelerating ✓
• C. The supernovae exploded only in the Milky Way
• D. The supernovae stopped producing light after a few days

Why: Distant Type Ia supernovae appeared dimmer than expected for a decelerating or constantly expanding universe. This indicated that cosmic expansion is speeding up, which led to the discovery of dark energy.

• A. The color of the remnant gas cloud
• B. The duration of the explosion's light curve, which correlates with peak luminosity ✓
• C. The number of neutrinos detected on Earth
• D. The exact time of day the supernova is observed

Why: Brighter Type Ia supernovae fade more slowly after peaking. This light curve width-luminosity relation lets astronomers standardize each supernova's peak brightness before computing its distance.

• A. Gravitational waves produced by merging black holes
• B. Sound waves in the early hot plasma of the universe before recombination
• C. Radio emission from quasars in the early universe
• D. Neutrino flows released during the first few minutes after the Big Bang

Why: BAO are imprints left by sound waves that propagated through the photon-baryon plasma before the universe cooled enough for atoms to form at recombination.

• A. About 1 light-year
• B. About 150 megaparsecs (roughly 500 million light-years)
• C. About 1 parsec
• D. About 10 billion light-years

Why: The sound horizon at the drag epoch sets a characteristic comoving scale of roughly 150 Mpc, which appears as a preferred separation between galaxies in large-scale surveys.

• A. They directly measure the mass of dark energy particles
• B. They act as a standard ruler whose apparent size reveals the expansion history of the universe
• C. They show that dark energy is concentrated inside galaxies
• D. They prove that dark energy does not change over time

Why: Because the BAO scale is known from early-universe physics, measuring its apparent size at different redshifts reveals how distances and the expansion rate have evolved, constraining dark energy.

• A. Measuring the spectra of individual stars in the Milky Way
• B. Mapping the clustering of galaxies or the Lyman-alpha forest across large volumes of the sky
• C. Counting supernovae in nearby dwarf galaxies only
• D. Timing pulsars in globular clusters

Why: Galaxy redshift surveys and Lyman-alpha forest measurements map large-scale structure, revealing the excess clustering at the BAO scale in the correlation function.

• A. The epoch of reionization
• B. The drag epoch, shortly after recombination, when baryons decoupled from photons
• C. The formation of the first stars
• D. The present-day acceleration of the universe

Why: After the drag epoch, baryons were released from photon pressure and the acoustic waves froze in, so the distance the sound traveled up to that time defines the BAO scale.

• A. Radiation emitted by stars in the first billion years after the Big Bang
• B. Thermal radiation left over from the era when the universe became transparent, about 380,000 years after the Big Bang ✓
• C. Light emitted by quasars at the edge of the observable universe
• D. Radio waves produced by supernova explosions throughout galactic history

Why: The CMB is relic thermal radiation released when electrons and protons combined into neutral atoms (recombination), allowing photons to travel freely. This occurred roughly 380,000 years after the Big Bang.

• A. About 3 Kelvin ✓
• B. About 300 Kelvin
• C. About 3,000 Kelvin
• D. About 0.003 Kelvin

Why: The CMB has cooled due to the expansion of the universe to a blackbody temperature of about 2.725 K, close to 3 K. Its original temperature at recombination was around 3,000 K.

• A. They directly detect dark energy particles
• B. They reveal the geometry of the universe and the expansion history, which depend on the amount of dark energy ✓
• C. They show that dark energy does not exist
• D. They measure the mass of individual galaxies

Why: The angular scale of features in the CMB, such as the first acoustic peak, depends on the curvature and total energy content of the universe. This allows cosmologists to constrain the density of dark energy and its equation of state.

• A. The locations of individual stars in the Milky Way
• B. The density variations in the early universe that seeded the formation of galaxies and large-scale structure ✓
• C. The exact age of the Sun
• D. The chemical composition of nearby planets

Why: The tiny anisotropies, on the order of one part in 100,000, reflect primordial density perturbations. These perturbations grew through gravity over time to form galaxies and clusters.

• A. Hubble Space Telescope
• B. Chandra X-ray Observatory
• C. Planck satellite ✓
• D. Kepler Space Telescope

Why: The Planck satellite, operated by the European Space Agency from 2009 to 2013, produced high-precision full-sky maps of CMB anisotropies, greatly refining cosmological parameters including dark energy density. WMAP was another key CMB mission.

• A. To explain why the speed of light is constant in all reference frames
• B. To explain the observed accelerated expansion of the universe without introducing a new energy component ✓
• C. To explain the existence of dark matter halos around galaxies
• D. To explain the cosmic microwave background temperature fluctuations

Why: Modified gravity theories aim to account for the accelerating expansion of the universe by changing how gravity behaves on cosmological scales, rather than adding an unknown dark energy component to the cosmic energy budget.

• A. A time-varying scalar field that couples to matter
• B. A constant energy density of empty space with negative pressure ✓
• C. The curvature of the universe in the spatial dimensions
• D. The mass density of ordinary baryonic matter

Why: The cosmological constant corresponds to a constant vacuum energy density with an equation of state w = -1, meaning its pressure is equal to negative its energy density, which drives accelerated expansion.

• A. A theory in which gravity is replaced by electromagnetism
• B. A modification of general relativity where the Einstein-Hilbert action Ricci scalar R is replaced by a general function f(R) ✓
• C. A theory where gravitons have a nonzero mass
• D. A model in which dark matter interacts only through gravity

Why: f(R) gravity generalizes the Einstein-Hilbert action by replacing the Ricci scalar R with an arbitrary function f(R), which can produce late-time cosmic acceleration without a separate dark energy field.

• A. Measurements of the luminosity of Type Ia supernovae as standard candles at high redshift ✓
• B. Detection of gravitational waves from merging black holes
• C. Discovery of the Higgs boson at the Large Hadron Collider
• D. Measurements of the rotation curves of individual stars in the Milky Way

Why: In 1998, two independent teams used Type Ia supernovae as standard candles and found they were dimmer than expected at high redshift, implying the expansion rate has been accelerating over the last several billion years.

• A. Measuring the mass of the electron
• B. Measuring the growth rate of cosmic structure, such as the growth index, over cosmic time ✓
• C. Counting the number of stars in a single galaxy
• D. Determining the age of the Sun

Why: Modified gravity changes how structures grow under gravity, so it predicts different growth histories for density perturbations compared to a cosmological constant with standard gravity, which can be tested with galaxy surveys and weak lensing.