Cosmic variance

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The term cosmic variance is the statistical uncertainty inherent in observations of the universe at extreme distances. It has three different but closely related meanings:

Contents

This most widespread use of the term is based on the idea that it is only possible to observe part of the universe at one particular time, so it is difficult to make statistical statements about cosmology on the scale of the entire universe, [1] [2] as the number of observations (sample size) must be not too small.

Background

The standard Big Bang model is usually supplemented with cosmic inflation. In inflationary models, the observer only sees 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.

Philosophical issues

This raises philosophical problems: suppose that random physical processes happen on length scales both smaller than and bigger than the particle 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.

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 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 observed is the result of a statistical process, the observer can only view one realization of that process, so our observation is statistically insignificant for saying much about the model, unless the observer is 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 particle horizon.

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. [3] 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.

Similar problems

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.

Another problem of limited sample sizes in astronomy, here practical rather than essential, is in the Titius–Bode law on spacing of satellites in an orbital system. Originally observed for the Solar System, the difficulty in observing other solar systems has limited data to test this.

Related Research Articles

<span class="mw-page-title-main">Big Bang</span> Theory on how the universe expanded

The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. It was first proposed in 1927 by Roman Catholic priest and physicist Georges Lemaître. Various cosmological models of the Big Bang explain the evolution of the observable universe from the earliest known periods through its subsequent large-scale form. These models offer a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The overall uniformity of the Universe, known as the flatness problem, is explained through cosmic inflation: a sudden and very rapid expansion of space during the earliest moments. However, physics currently lacks a widely accepted theory of quantum gravity that can successfully model the earliest conditions of the Big Bang.

<span class="mw-page-title-main">Physical cosmology</span> Branch of cosmology which studies mathematical models of the universe

Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fundamental questions about its origin, structure, evolution, and ultimate fate. Cosmology as a science originated with the Copernican principle, which implies that celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed those physical laws to be understood.

In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch is believed to have lasted from 10−36 seconds to between 10−33 and 10−32 seconds after the Big Bang. Following the inflationary period, the universe continued to expand, but at a slower rate. The acceleration of this expansion due to dark energy began after the universe was already over 7.7 billion years old.

<span class="mw-page-title-main">Cosmic microwave background</span> Trace radiation from the early universe

The cosmic microwave background is microwave radiation that fills all space in the observable universe. It is a remnant that provides an important source of data on the primordial universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dark. However, a sufficiently sensitive radio telescope detects a faint background glow that is almost uniform and is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The accidental discovery of the CMB in 1965 by American radio astronomers Arno Penzias and Robert Wilson was the culmination of work initiated in the 1940s.

<span class="mw-page-title-main">Wilkinson Microwave Anisotropy Probe</span> NASA satellite of the Explorer program

The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe, was a NASA spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic microwave background (CMB) – the radiant heat remaining from the Big Bang. Headed by Professor Charles L. Bennett of Johns Hopkins University, the mission was developed in a joint partnership between the NASA Goddard Space Flight Center and Princeton University. The WMAP spacecraft was launched on 30 June 2001 from Florida. The WMAP mission succeeded the COBE space mission and was the second medium-class (MIDEX) spacecraft in the NASA Explorer program. In 2003, MAP was renamed WMAP in honor of cosmologist David Todd Wilkinson (1935–2002), who had been a member of the mission's science team. After nine years of operations, WMAP was switched off in 2010, following the launch of the more advanced Planck spacecraft by European Space Agency (ESA) in 2009.

A non-standard cosmology is any physical cosmological model of the universe that was, or still is, proposed as an alternative to the then-current standard model of cosmology. The term non-standard is applied to any theory that does not conform to the scientific consensus. Because the term depends on the prevailing consensus, the meaning of the term changes over time. For example, hot dark matter would not have been considered non-standard in 1990, but would be in 2010. Conversely, a non-zero cosmological constant resulting in an accelerating universe would have been considered non-standard in 1990, but is part of the standard cosmology in 2010.

<span class="mw-page-title-main">Observable universe</span> All of space observable from the Earth at the present

The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time; the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. Initially, it was estimated that there may be 2 trillion galaxies in the observable universe. That number was reduced in 2021 to only several hundred billion based on data from New Horizons. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe is a spherical region centered on the observer. Every location in the universe has its own observable universe, which may or may not overlap with the one centered on Earth.

<span class="mw-page-title-main">Plasma cosmology</span> Non-standard model of the universe; emphasizes the role of ionized gases

Plasma cosmology is a non-standard cosmology whose central postulate is that the dynamics of ionized gases and plasmas play important, if not dominant, roles in the physics of the universe at interstellar and intergalactic scales. In contrast, the current observations and models of cosmologists and astrophysicists explain the formation, development, and evolution of large-scale structures as dominated by gravity.

The particle horizon is the maximum distance from which light from particles could have traveled to the observer in the age of the universe. Much like the concept of a terrestrial horizon, it represents the boundary between the observable and the unobservable regions of the universe, so its distance at the present epoch defines the size of the observable universe. Due to the expansion of the universe, it is not simply the age of the universe times the speed of light, but rather the speed of light times the conformal time. The existence, properties, and significance of a cosmological horizon depend on the particular cosmological model.

<span class="mw-page-title-main">Horizon problem</span> Cosmological fine-tuning problem

The horizon problem is a cosmological fine-tuning problem within the Big Bang model of the universe. It arises due to the difficulty in explaining the observed homogeneity of causally disconnected regions of space in the absence of a mechanism that sets the same initial conditions everywhere. It was first pointed out by Wolfgang Rindler in 1956.

The Lambda-CDM, Lambda cold dark matter or ΛCDM model is a mathematical model of the Big Bang theory with three major components:

  1. a cosmological constant denoted by lambda (Λ) associated with dark energy,
  2. the postulated cold dark matter, and
  3. ordinary matter.
<span class="mw-page-title-main">Flatness problem</span> Cosmological fine-tuning problem

The flatness problem is a cosmological fine-tuning problem within the Big Bang model of the universe. Such problems arise from the observation that some of the initial conditions of the universe appear to be fine-tuned to very 'special' values, and that small deviations from these values would have extreme effects on the appearance of the universe at the current time.

In physical cosmology, structure formation is the formation of galaxies, galaxy clusters and larger structures from small early density fluctuations. The universe, as is now known from observations of the cosmic microwave background radiation, began in a hot, dense, nearly uniform state approximately 13.8 billion years ago. However, looking at the night sky today, structures on all scales can be seen, from stars and planets to galaxies. On even larger scales, galaxy clusters and sheet-like structures of galaxies are separated by enormous voids containing few galaxies. Structure formation attempts to model how these structures were formed by gravitational instability of small early ripples in spacetime density or another emergence.

<span class="mw-page-title-main">History of the Big Bang theory</span> History of a cosmological theory

The history of the Big Bang theory began with the Big Bang's development from observations and theoretical considerations. Much of the theoretical work in cosmology now involves extensions and refinements to the basic Big Bang model. The theory itself was originally formalised by Father Georges Lemaître in 1927. Hubble's Law of the expansion of the universe provided foundational support for the theory.

A cosmological horizon is a measure of the distance from which one could possibly retrieve information. This observable constraint is due to various properties of general relativity, the expanding universe, and the physics of Big Bang cosmology. Cosmological horizons set the size and scale of the observable universe. This article explains a number of these horizons.

The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion; the universe does not expand "into" anything and does not require space to exist "outside" it. To any observer in the universe, it appears that all but the nearest galaxies recede at speeds that are proportional to their distance from the observer, on average. While objects cannot move faster than light, this limitation only applies with respect to local reference frames and does not limit the recession rates of cosmologically distant objects.

<span class="mw-page-title-main">Boltzmann brain</span> Philosophical thought experiment

The Boltzmann brain thought experiment suggests that it might be more likely for a single brain to spontaneously form in a void, complete with a memory of having existed in our universe, rather than for the entire universe to come about in the manner cosmologists think it actually did. Physicists use the Boltzmann brain thought experiment as a reductio ad absurdum argument for evaluating competing scientific theories.

In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe. Assuming that the lambda-CDM model of cosmology is correct, dark energy is the dominant component of the universe, contributing 68% of the total energy in the present-day observable universe while dark matter and ordinary (baryonic) matter contribute 26% and 5%, respectively, and other components such as neutrinos and photons are nearly negligible. Dark energy's density is very low: 6×10−10 J/m3, much less than the density of ordinary matter or dark matter within galaxies. However, it dominates the universe's mass–energy content because it is uniform across space.

<span class="mw-page-title-main">Steady-state model</span> Model of the universe – alternative to the Big Bang model

In cosmology, the steady-state model or steady state theory is an alternative to the Big Bang theory of evolution of the universe. In the steady-state model, the density of matter in the expanding universe remains unchanged due to a continuous creation of matter, thus adhering to the perfect cosmological principle, a principle that says that the observable universe is always the same at any time and any place.

References

  1. Somerville; Lee, Kyoungsoo; Ferguson, Henry C.; Gardner, Jonathan P.; Moustakas, Leonidas A.; Giavalisco, Mauro; et al. (2004). "Cosmic Variance in the Great Observatories Origins Deep Survey". The Astrophysical Journal Letters. 600 (2): L171–L174. arXiv: astro-ph/0309071 . Bibcode:2004ApJ...600L.171S. CiteSeerX   10.1.1.255.7912 . doi:10.1086/378628. S2CID   16650601.
  2. Keremedjiev, M. S.; MacDonald, E. C.; Dey, A.; Jannuzi, B. T. (2005). "Quantifying the Effects of Cosmic Variance Using the NOAO Deep-Wide Field Survey". American Astronomical Society Meeting Abstracts. 207: 170.06. Bibcode:2005AAS...20717006K. Archived from the original on 2008-01-02. Retrieved 2007-09-18.
  3. Portsmouth, Jamie (2004). "Analysis of the Kamionkowski-Loeb method of reducing cosmic variance with CMB polarization". Physical Review D. 70 (6): 063504. arXiv: astro-ph/0402173 . Bibcode:2004PhRvD..70f3504P. doi:10.1103/PhysRevD.70.063504. S2CID   119349882.

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