Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. The unexpected result was that objects in the universe are moving away from one another at an accelerated rate. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred the Hubble law established that the farther an object is from us, the faster it is receding. The idea was that as type Ia supernovae have almost the same intrinsic brightness (a standard candle), and since objects that are farther away appear dimmer, we can use the observed brightness of these supernovae to measure the distance to them. The accelerated expansion of the universe was discovered during 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which both used distant type Ia supernovae to measure the acceleration. Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The timeline in this schematic diagram extends from the Big Bang/inflation era 13.7 billion years ago to the present cosmological time. We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect primordial non-Gaussianity is little compromised.Lambda-CDM, accelerated expansion of the universe. We show that in an all-sky galaxy redshift survey at low redshift the velocity term can be measured at a few sigma if one can utilize halos of mass M ≥ 10 12 h − 1 M ⊙ (this can increase to 10 − σ or more in some more optimistic scenarios), while the gravitational potential term itself can only be marginally detected. To detect these terms one must resort to the recently developed methods to reduce sampling variance and shot noise. We perform a Fisher matrix analysis of detectability of these terms and show that in a single tracer survey they are completely undetectable. We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing to velocity effect. Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales.
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