Baryon acoustic oscillations (BAO) are cosmic sound waves that left their mark on the universe's structure. These frozen ripples from the early cosmos now serve as a cosmic ruler, helping us measure vast distances and understand the universe's expansion.

BAO measurements provide crucial insights into the universe's composition and evolution. By studying these primordial echoes, scientists can constrain key cosmological parameters and test theories about dark energy, shedding light on the mysterious force driving cosmic acceleration.

Baryon Acoustic Oscillations

Origin of baryon acoustic oscillations

• In the early universe, baryons and photons were tightly coupled forming a baryon-photon fluid due to high temperature and density
• Primordial density fluctuations in the universe caused acoustic waves in the baryon-photon fluid seeded by quantum fluctuations during cosmic inflation
• Competition between gravity and radiation pressure in the baryon-photon fluid led to oscillations
  • Gravity compressed the fluid into potential wells
  • Radiation pressure resisted this compression
• At the time of recombination ($z \approx 1100$), the universe cooled enough for neutral atoms to form
  • Decoupling of baryons and photons caused the oscillations to freeze leaving an imprint on the matter distribution (similar to sound waves in air)

BAO imprint on galaxy distribution

• Frozen baryon acoustic oscillations left an imprint on the distribution of matter in the universe manifesting as a slight excess of galaxies separated by a characteristic scale (BAO peak)
• Characteristic scale of BAO is determined by the sound horizon at the time of decoupling
  • Sound horizon is the maximum distance a sound wave could travel in the baryon-photon fluid before decoupling (∼150 Mpc)
• In the galaxy correlation function, BAO appears as a peak at a scale of approximately 150 comoving Mpc
  • Correlation function measures the excess probability of finding galaxy pairs at a given separation compared to a random distribution
• In the matter power spectrum, BAO appears as a series of oscillations with a characteristic wavelength
  • Power spectrum is the Fourier transform of the correlation function and describes the clustering of matter at different scales (similar to a musical score)

BAO as cosmic standard ruler

• Characteristic scale of BAO serves as a "standard ruler" for measuring cosmic distances because the BAO scale is determined by well-understood physics in the early universe and is not affected by later cosmic evolution
• By measuring the apparent size of the BAO scale at different redshifts, cosmologists can infer the angular diameter distance $D_A(z)$
  • Angular diameter distance relates the apparent angular size of an object to its physical size and depends on the expansion history of the universe
• By measuring the BAO scale along the line of sight (in the redshift direction), cosmologists can infer the Hubble parameter $H(z)$
  • Hubble parameter describes the expansion rate of the universe as a function of redshift
• Combining measurements of $D_A(z)$ and $H(z)$ from BAO at different redshifts provides a powerful probe of the universe's geometry and expansion history (similar to using a ruler to measure distances on a map)

BAO in cosmological constraints

• BAO measurements provide independent constraints on key cosmological parameters, complementing other probes such as cosmic microwave background (CMB) and Type Ia supernovae
• By measuring the BAO scale at different redshifts, cosmologists can constrain:
  1. Matter density parameter $\Omega_m$
  2. Dark energy equation of state parameter $w$
     • These parameters govern the expansion history and geometry of the universe
• BAO measurements have helped to establish the standard $\Lambda$CDM cosmological model
  • Universe is dominated by cold dark matter (CDM) and a cosmological constant $\Lambda$, which drives the accelerated expansion
• Consistency between BAO measurements and other cosmological probes has strengthened the evidence for dark energy and the accelerating universe
• Future galaxy surveys (DESI, Euclid) will measure BAO with unprecedented precision, enabling stringent tests of cosmological models and shedding light on the nature of dark energy