Unveiling the physics behind the accelerating expansion of the Universe, which was discovered in 1998, is one of the most challenging tasks in modern sciences. In theory, the cosmic acceleration may result from the fact that approximately two thirds energy density of the Universe is provided by Dark Energy, a yet unknown energy component, or imply that general relativity, the most successful theory of gravity within the solar system established by Einstein, may need to be extended on cosmological scales. In principle, the scenarios of energy and modified gravity can yield identical cosmic expansion history, but predict different structure growth. Therefore, this dark degeneracy can be broken by studying the evolution history of the cosmic structure with large galaxy surveys. Galaxy surveys is one of the key probes for energy and gravity, which can be used to reconstruct the history of cosmic expansion and structure growth using baryonic acoustic oscillations (BAO) and redshift space distortions (RSD) respectively. BAO is a specific three-dimensional clustering pattern of galaxies due to interactions between photons and baryons in the early Universe. Back in the early cosmic epochs, photons scattered with electrons and electrons interacted with protons, making photons and protons (baryonic matter) glued together. There are two opposite forces exerting on this tightly coupled plasma: the pressure of photons and gravity acting on baryons. Similar to what happens to a vibrating spring vertically fixed on the ground, the photon-baryon plasma underwent Oscillations, propagating waves in the same way as the sound does. Therefore, this physical process is called Baryonic Acoustic Oscillations. The effect of the BAO is to push galaxies apart until at a specific time, called the cosmic recombination, when the temperature of the Universe becomes so low that no more photon-baryon interaction can happen. Since then, the separation among galaxies is frozen at a characteristic scale, which is about 150 Mpc depending on the energy content of the Universe, making it a standard ruler to be used to infer the expansion history of the Universe, thus BAO is one of the key probes for the nature of energy. RSD is another special three-dimensional clustering pattern of galaxies, but it is due to local motions of the galaxies under gravity. Suppose galaxies only co-move with the cosmic background without moving locally, the clustering of galaxies should be isotropic, in other words, there are same number of galaxy pairs along or across lines of sight of the observer. However, this is not the case in the real world. Galaxies move towards nearby galaxies due to gravity, thus they have velocities. As we infer galaxies positions from their line-of-sight velocities in astronomy, the peculiar velocities can distort galaxies positions, which results in a distortion, called Redshift Space Distortions, in the 3D clustering of galaxies. RSD plays a key role in cosmology as it can directly be used to infer the nature of gravity (remember the peculiar motion is caused by gravity!). The Baryonic Oscillation Spectroscopic Survey (BOSS) program, part of the Sloan Digital Sky Survey (SDSS)-III project, is the largest completed galaxy survey in the world. BOSS has enabled us to investigate energy and gravity to a unprecedented precision, which has implied a 3.5 sigma evidence for the dynamics of energy. Ongoing and forthcoming galaxy surveys including the extended Baryonic Oscillation Spectroscopic Survey (eBOSS), Dark Energy Spectroscopic Instrument (DESI) and Prime Focus Spectrograph (PFS), will be able to probe the Universe at higher redshifts with much higher precision, which will be providing key observational support for the study of cosmic acceleration.
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