Physical cosmology

Age of the universe Big Bang Comoving distance Cosmic microwave background Dark energy Dark matter FLRW metric Friedmann equations Galaxy formation Hubble's law Inflation Large-scale structure Lambda-CDM model Metric expansion of space Nucleosynthesis Observable universe Redshift Shape of the universe Structure formation Timeline of the Big Bang Timeline of cosmology Ultimate fate of the universe Universe

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Astrophysics General relativity Particle physics Quantum gravity

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Cosmic variance is the idea that we are only able to observe one universe at one particular time, so it is difficult to make statistical statements about cosmology on the scale of the entire universe. Cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ... Image File history File links Download high resolution version (2198x1274, 1278 KB)WMAP map of CMB anisotropy, from NASA.gov File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Nothing is certain as to the extent of either the age or size of the universe, but the age of the Universe, according to the Big Bang theory, is defined as the largest possible value of proper time integrated along a timelike curve from the Earth at the present epoch... According to the Big Bang theory, the universe emerged from an extremely dense and hot state (bottom). ... The comoving distance or conformal distance of two objects in the universe is the distance divided by a time-varying scale factor representing the expansion of the universe. ... In cosmology, the cosmic microwave background radiation (most often abbreviated CMB but occasionally CMBR, CBR or MBR) is a form of electromagnetic radiation discovered in 1965 that fills the entire universe. ... In physical cosmology, dark energy is a hypothetical form of energy which permeates all of space and has strong negative pressure. ... In astrophysics, dark matter refers to matter that does not emit or reflect enough electromagnetic radiation (such as light, x-rays and so on) to be detected directly, but whose presence may be inferred from its gravitational effects on visible matter. ... The Friedmann-Lemaître-Robertson-Walker (FLRW) metric describes a homogeneous, isotropic expanding/contracting universe. ... The Friedmann equations relate various cosmological parameters within the context of general relativity. ... REDIRECT [[ --68. ... Hubbles law is the statement in physical cosmology that the redshift in light coming from distant galaxies is proportional to their distance. ... Astronomy and cosmology examine the universe to understand the large-scale structure of the cosmos. ... A pie chart indicating the proportional composition of different energy-density components of the universe. ... The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ... In cosmology, Big Bang nucleosynthesis (or primordial nucleosynthesis) refers to the production of nuclei other than H-1, the normal, light hydrogen, during the early phases of the universe, shortly after the Big Bang. ... The observable Universe is a term used in cosmology to describe a ball-shaped region of space surrounding the Earth that is close enough that we might observe objects in it. ... Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared to that of the Sun (left). ... The shape of the Universe is a subject of investigation within cosmology. ... It has been suggested that this article or section be merged into Large-scale structure of the cosmos. ... A graphical timeline is available here: Graphical timeline of the Big Bang This timeline of the Big Bang describes the events that have occurred and will occur according to the scientific theory of the Big Bang. ... The timeline of cosmology lists the sequence of cosmological theories and discoveries in chronological order. ... The ultimate fate of our universe is a topic in physical cosmology. ... The deepest visible-light image of the cosmos, the Hubble Ultra Deep Field. ... Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature and chemical composition) of celestial objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... Particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... Cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ...

The standard big bang model is usually supplemented with cosmic inflation. In inflationary models, we only see a tiny fraction of the whole universe, much less than a billionth (1/10⁹) of the volume of the universe postulated in inflation. So the observable universe (the so-called particle horizon of the universe) is the result of processes that follow some general physical laws, including quantum mechanics and general relativity. Some of these processes are random: for example, the distribution of galaxies throughout the universe can only be described statistically and cannot be derived from first principles. According to the Big Bang theory, the universe emerged from an extremely dense and hot state (bottom). ... Cosmic inflation is the idea, first proposed by Alan Guth in 1981, that the nascent universe passed through a phase of exponential expansion (the inflationary epoch) that was driven by a negative pressure vacuum energy density. ... The deepest visible-light image of the cosmos, the Hubble Ultra Deep Field. ... The particle horizon in cosmology is the distance from which particles (of positive mass or of zero mass) can have travelled to the observer in the age of the Universe. ... A physical law or a law of nature is a scientific generalization based on empirical observations. ... Fig. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... // About Bees This article is about completely random and illogical things. ... This article is about a celestial body. ... A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ...

This raises philosophical problems: suppose that random physical processes happen on length scales both smaller than and bigger than the horizon. A physical process (such as an amplitude of a primordial perturbation in density) that happens on the horizon scale only gives us one observable realization. A physical process on a larger scale gives us zero observable realizations. A physical process on a slightly smaller scale gives us a small number of realizations. To meet Wikipedias quality standards, this article may require cleanup. ... Perturbation is a term used in astronomy to describe alterations to an objects orbit caused by gravitational interactions with other bodies. ...

In the case of only one realization it is difficult to draw statistical conclusions about its significance. For example, if the underlying model of a physical process implies that the observed property should occur only 1% of the time, does that really mean that the model is excluded? Consider the physical model of the citizenship of human beings in the early 21st century, where about 30% are Indian and Chinese citizens, about 5% are American citizens, about 1% are French citizens, and so on. For an observer who has only one observation - of his/her own citizenship- and who happens to be French and cannot make any external observations, the model can be rejected at the 99% significance level. Yet we, the external observers with more information unavailable to the first observer, know that the model is correct.

In other words, even if the bit of the universe we observe is the result of a statistical process, we can only observe one realization of that process, so our observation is statistically insignificant for saying much about the model, unless we are careful to include the variance. This variance is called the cosmic variance and is separate from other sources of experimental error: a very accurate measurement of only one value drawn from a distribution still leaves considerable uncertainty about the underlying model. Variance is normally plotted separately from other sources of uncertainty. Because it is necessarily a large fraction of the signal, workers must be very careful in interpreting the statistical significance of measurements on scales close to the horizon. In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are. ... In mathematics and statistics, a probability distribution, more properly called a probability density, assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ... The particle horizon in cosmology is the distance from which particles (of positive mass or of zero mass) can have travelled to the observer in the age of the Universe. ...

In physical cosmology, the common way of dealing with this on the horizon scale and on slightly sub-horizon scales (where the number of occurrences is greater than one but still quite small), is to explicitly include the variance of very small statistical samples (Poisson distribution) when calculating uncertainties. This is important in describing the low multipoles of the cosmic microwave background and has been the source of much controversy in the cosmology community since the COBE and WMAP measurements. Cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ... In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are. ... In probability theory and statistics, the Poisson distribution is a discrete probability distribution. ... // Relation between uncertainty, probability and risk In his seminal work Risk, Uncertainty, and Profit, Frank Knight (1921) established the important distinction between risk and uncertainty: … Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated. ... In mathematics, the spherical harmonics are an orthogonal set of solutions to Laplaces equation represented in a system of spherical coordinates. ... WMAP image of the CMB anisotropy,Cosmic microwave background radiation(June 2003) The cosmic microwave background radiation (CMB) is a form of electromagnetic radiation that fills the whole of the universe. ... The Cosmic Background Explorer (COBE), also referred to as Explorer 66, was the first satellite built dedicated to cosmology. ... Artist depiction of the WMAP satellite at the L2 point The Wilkinson Microwave Anisotropy Probe (WMAP) is a NASA satellite whose mission is to survey the sky to measure the temperature of the radiant heat left over from the Big Bang. ...

A similar problem is faced by evolutionary biologists. Just as cosmologists have a sample size of one universe, biologists have a sample size of one fossil record. The problem is closely related to the anthropic principle. Evolutionary biology is a subfield of biology concerned with the origin and descent of species, as well as their change, multiplication, and diversity over time. ... A sample is that part of a population which is actually observed. ... In cosmology, the anthropic principle in its most basic form states the truism that any valid theory of the universe must be consistent with our existence as carbon-based human beings at this particular time and place in the universe. ...

References

• Stephen Hawking (2003). Cosmology from the Top Down. Proceedings of the Davis Meeting on Cosmic Inflation. (online)

Cosmic variance is also the name of a collaborative weblog discussing astrophysics and fundamental physics, written by JoAnne Hewett, Clifford Johnson, Mark Trodden, Sean Carroll and Risa Wechsler. [1] A weblog (now more commonly known as a blog) is a web-based publication consisting primarily of periodic articles (normally, but not always, in reverse chronological order). ... Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature and chemical composition) of celestial objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ... Sean M. Carroll is a senior research associate in the Department of Physics at the California Institute of Technology. ...