Search results
Results from the WOW.Com Content Network
The first equation can be derived also from thermodynamical considerations and is equivalent to the first law of thermodynamics, assuming the expansion of the universe is an adiabatic process (which is implicitly assumed in the derivation of the Friedmann–Lemaître–Robertson–Walker metric).
A higher expansion rate would imply a smaller characteristic size of CMB fluctuations, and vice versa. The Planck collaboration measured the expansion rate this way and determined H 0 = 67.4 ± 0.5 (km/s)/Mpc. [24] There is a disagreement between this measurement and the supernova-based measurements, known as the Hubble tension.
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. The metric captures all the geometric and causal structure of spacetime , being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past.
The cosmological principle implies that the metric of the universe must be of the form = where ds 3 2 is a three-dimensional metric that must be one of (a) flat space, (b) a sphere of constant positive curvature or (c) a hyperbolic space with constant negative curvature. This metric is called the Friedmann–Lemaître–Robertson–Walker (FLRW ...
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. [1] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry.
Comoving coordinates separate the exactly proportional expansion in a Friedmannian universe in spatial comoving coordinates from the scale factor () . This example is for the ΛCDM model. The comoving time coordinate is the elapsed time since the Big Bang according to a clock of a comoving observer and is a measure of cosmological time .
The ΛCDM model includes an expansion of metric space that is well documented, both as the redshift of prominent spectral absorption or emission lines in the light from distant galaxies, and as the time dilation in the light decay of supernova luminosity curves.
The mathematical derivation of an idealized Hubble's law for a uniformly expanding universe is a fairly elementary theorem of geometry in 3-dimensional Cartesian/Newtonian coordinate space, which, considered as a metric space, is entirely homogeneous and isotropic (properties do not vary with location or direction). Simply stated, the theorem ...