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--- courses:ast403:baryon-acoustic-oscillation [2026/04/04 00:51] – [Observational Signatures: The Standard Ruler] shuvo
+++ courses:ast403:baryon-acoustic-oscillation [2026/04/06 09:58] (current) – [Observational Signatures: The Standard Ruler] shuvo
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-Baryon Acoustic Oscillations (BAO) refer to the regular, periodic fluctuations in the density of the visible baryonic matter of the universe. Much like how sound waves travel through the air, these acoustic waves traveled through the primordial plasma of the early universe. Today, BAO provides a robust "standard ruler" for cosmology, allowing us to measure the expansion history of the universe and constrain the properties of Dark Energy.
+Baryon Acoustic Oscillations (BAO) refer to the regular, periodic fluctuations in the density of the visible baryonic matter of the Universe. Much like how sound waves travel through the air, these acoustic waves traveled through the primordial plasma of the early universe. Today, BAO provides a robust "standard ruler" for cosmology, allowing us to measure the expansion history of the Universe and constrain the properties of Dark Energy.
 ===== The Physics of the Early Universe =====
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 **Photon-Baryon Fluid:** Electrons and photons were tightly coupled via Thomson scattering, and protons were coupled to electrons via Coulomb interactions. This created a single, relativistic photon-baryon fluid.
-When a dark matter overdensity collapsed under gravity, it pulled the photon-baryon fluid with it. However, the immense radiation pressure of the photons strongly resisted this compression, driving the fluid outward. This competition between gravity and radiation pressure generated spherical acoustic waves propagating away from the initial overdensities.
+When a dark matter overdensity collapsed under gravity, it pulled the photon-baryon fluid with it. However, the immense radiation pressure of the photons strongly resisted this compression, driving the fluid outward. **This competition between gravity and radiation pressure generated spherical acoustic waves propagating away from the initial overdensities.**
-[{{ :courses:ast403:bao.png?600 | Fig 1: Artist's impression of BAO signature. Credit: ESA and the Planck Collaboration / Gabriela Secara / Perimeter Institute}}]
 ===== Mathematical Formalism of the Acoustic Waves =====
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 $$c_s = \frac{c}{\sqrt{3(1+R)}}$$
-In the very early universe, radiation dominates ($R \to 0$), and the sound speed approaches the relativistic limit $c/\sqrt{3}$. As the universe expands and baryons begin to contribute more to the inertia of the fluid, $c_s$ drops.
+In the very early Universe, radiation dominates ($R \to 0$), and the sound speed approaches the relativistic limit $c/\sqrt{3}$. As the Universe expands and baryons begin to contribute more to the inertia of the fluid, $c_s$ drops.
+[{{ :courses:ast403:bao_wave.gif | Fig 1: A gif animation showing the effect two opposing effect.}}]
 **The Comoving Sound Horizon:
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 ===== Recombination and the Relic Signature =====
-At recombination, the temperature of the universe dropped sufficiently for electrons and protons to form neutral hydrogen. Thomson scattering ceased.\\
+At recombination, the temperature of the Universe dropped sufficiently for electrons and protons to form neutral hydrogen. Thomson scattering ceased.\\
 The **photons** streamed away freely, carrying the imprint of these temperature fluctuations to us as the Cosmic Microwave Background (CMB).\\
 The **baryons**, having lost the radiation pressure driving them outward, stalled. They formed a spherical shell of slight overdensity at exactly the radius of the sound horizon ($r_s \approx 147$ Mpc) surrounding the central dark matter halo.\\
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 Over billions of years, both the central dark matter peak and the spherical baryonic shell acted as gravitational seeds for structure formation. Therefore, for any given galaxy, there is a slightly enhanced probability of finding another galaxy exactly $147$ Mpc away.
+[{{ :courses:ast403:bao.png?600 | Fig 2: Artist's impression of BAO signature. Credit: ESA and the Planck Collaboration / Gabriela Secara / Perimeter Institute}}]
 ===== Observational Signatures: The Standard Ruler =====
-Because the scale of the sound horizon $r_s$ is firmly rooted in the well-understood physics of the early universe, it serves as a cosmological Standard Ruler. By observing the apparent size of the BAO scale in the clustering of galaxies at different redshifts, we can measure the geometry and expansion rate of the universe.
+Because the scale of the sound horizon $r_s$ is firmly rooted in the well-understood physics of the early Universe, it serves as a cosmological Standard Ruler. By observing the apparent size of the BAO scale in the clustering of galaxies at different redshifts, we can measure the geometry and expansion rate of the Universe.
 We measure the BAO signal in two directions relative to our line of sight:
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-[{{ :courses:ast403:standard-rulers.jpg | Fig 2: BAO standard rular.}}]
+[{{ :courses:ast403:desi_bao.jpg?600 | Fig 3: Large-scale structure from DESI redshift survey}}]
+An animation of the formation of BAO: [[https://www.youtube.com/watch?v=jpXuYc-wzk4]]