Wikiversity

Talk:PlanetPhysics/Cosmic Microwave Background Radiation

< Talk:PlanetPhysics

Original TeX Content from PlanetPhysics Archive

edit

%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: cosmic microwave background radiation %%% Primary Category Code: 98.80.-k %%% Filename: CosmicMicrowaveBackgroundRadiation.tex %%% Version: 1 %%% Owner: bloftin %%% Author(s): bloftin %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

\setlength{\topmargin}{0.00in} \setlength{\headsep}{0.00in} \setlength{\headheight}{0.00in} \setlength{\evensidemargin}{0.00in} \setlength{\oddsidemargin}{0.00in} \setlength{\textwidth}{6.5in} \setlength{\textheight}{9.00in} \setlength{\voffset}{0.00in} \setlength{\hoffset}{0.00in} \setlength{\marginparwidth}{0.00in} \setlength{\marginparsep}{0.00in} \setlength{\parindent}{0.00in} \setlength{\parskip}{0.15in}

\usepackage{html}

% this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners.

% almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts}

% used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic}

% there are many more packages, add them here as you need them

% define commands here

\begin{document} 

\section{Cosmic Microwave Background Radiation}

In cosmology, the cosmic microwave background radiation (most often abbreviated CMB but occasionally CMBR, CBR or MBR) is a form of electromagnetic \htmladdnormallink{radiation}{http://planetphysics.us/encyclopedia/Cyclotron.html} discovered in 1965 that fills the entire \htmladdnormallink{Universe}{http://planetphysics.us/encyclopedia/MultiVerses.html}. It has a thermal 2.725 kelvin black body \htmladdnormallink{spectrum}{http://planetphysics.us/encyclopedia/CohomologyTheoryOnCWComplexes.html} which peaks in the \htmladdnormallink{microwave}{http://planetphysics.us/encyclopedia/FluorescenceCrossCorrelationSpectroscopy.html} range at a frequency of 160.4 GHz, corresponding to a wavelength of 1.9 mm. Most cosmologists consider this radiation to be the best evidence for the hot big bang model of the universe.

\subsection{Features}

The cosmic microwave background is isotropic to roughly one part in 100,000: the root mean \htmladdnormallink{square}{http://planetphysics.us/encyclopedia/PiecewiseLinear.html} variations are only 18 µK.[1] The Far-Infrared Absolute Spectrophotometer (FIRAS) instrument on the NASA COsmic Background Explorer (COBE) satellite has carefully measured the spectrum of the cosmic microwave background. FIRAS compared the CMB with a reference black body and no difference could be seen in their spectra. Any deviations from the black body form that might still remain undetected in the CMB spectrum over the wavelength range from 0.5 to 5 mm must have a weighted rms value of at most 50 parts per million (0.005%) of the CMB peak \htmladdnormallink{brightness}{http://planetphysics.us/encyclopedia/AbsoluteMagnitude.html}.[2] This made the CMB spectrum the most precisely measured black body spectrum in nature.

The cosmic microwave background is a prediction of the Big Bang. In the theory, the early universe was made up of a hot \htmladdnormallink{plasma}{http://planetphysics.us/encyclopedia/PlasmaDisplayPanel.html} of photons, electrons and \htmladdnormallink{baryons}{http://planetphysics.us/encyclopedia/QuarkAntiquarkPair.html}. The photons were constantly interacting with the plasma through Thomson scattering. As the universe expanded, the cosmological redshift caused the plasma to cool until it became favorable for electrons to combine with protons and form hydrogen atoms. This happened at around 3,000 K or when the universe was approximately 380,000 years old (z=1088). At this point, the photons did not scatter off of the now neutral atoms and began to travel freely through space. This process is called recombination or decoupling (referring to electrons combining with nuclei and to the decoupling of matter and radiation respectively).

The photons continued cooling until they reached their present 2.725 K \htmladdnormallink{temperature}{http://planetphysics.us/encyclopedia/BoltzmannConstant.html}. Accordingly, the radiation from the sky we measure today comes from a spherical surface, called the surface of last scattering, from which the photons that decoupled from interaction with matter in the early universe, 13.7 billion years ago, are just now reaching observers on Earth. The big bang suggests that the cosmic microwave background fills all of \htmladdnormallink{observable}{http://planetphysics.us/encyclopedia/QuantumSpinNetworkFunctor2.html} space, and that most of the radiation \htmladdnormallink{energy}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} in the universe is in the cosmic microwave background, which makes up a fraction of roughly 5\OE{}10-5 of the total density of the universe.[3]

Two of the greatest successes of the big bang are its prediction of its almost perfect black body spectrum and its detailed prediction of the anisotropies in the cosmic microwave background. The recent Wilkinson Microwave Anisotropy Probe has precisely measured these anisotropies over the whole sky down to angular scales of 0.2 degrees.[4] These can be used to estimate the \htmladdnormallink{parameters}{http://planetphysics.us/encyclopedia/Parameter.html} of the standard Lambda-CDM model of the big bang. Some information, such as the shape of the Universe, can be obtained straightforwardly from the cosmic microwave background, while others, such as the Hubble constant, are not constrained and must be inferred from other measurements.[5]

\subsection{History}

The cosmic microwave background was predicted by George Gamow, Ralph Alpher, and Robert Herman in 1948. Moreover, Alpher and Herman were able to estimate the temperature of the cosmic microwave background to be 5 K.[9] Although there were several previous estimates of the temperature of space (see timeline), these suffered from two flaws. First, they were measurements of the effective temperature of space, and did not suggest that space was filled with a thermal Planck spectrum: Second, they are dependent on our special place at the edge of the Milky Way galaxy and did not suggest the radiation is isotropic. Moreover, they would yield very different predictions if Earth happened to be located elsewhere in the universe.[10]

The results of Gamow were not widely discussed. However, they were rediscovered by Robert Dicke and Yakov Zel'dovich in the early 1960s. In 1964, this prompted David Todd Wilkinson and Peter Roll, Dicke's colleagues at Princeton University, to begin constructing a Dicke radiometer to measure the cosmic microwave background[11]. In 1965, Arno Penzias and Robert Woodrow Wilson at Bell Telephone Laboratories in nearby Holmdel, New Jersey had built a Dicke radiometer that they intended to use for radio astronomy and satellite communication experiments. Their instrument had an excess 3.5 K antenna temperature which they could not account for. After receiving a telephone call from Holmdel, Dicke famously quipped: "Boys, we've been scooped."[12] A meeting between the Princeton and Holmdel \htmladdnormallink{groups}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} determined that the antenna temperature was indeed due to the microwave background. Penzias and Wilson received the 1978 Nobel Prize in Physics for their discovery.

The interpretation of the cosmic microwave background was a controversial issue in the 1960s with some proponents of the steady state theory arguing that the microwave background was the result of scattered starlight from distant galaxies. Using this model, and based on the study of narrow \htmladdnormallink{absorption}{http://planetphysics.us/encyclopedia/FluorescenceCrossCorrelationSpectroscopy.html} line features in the spectra of stars, the astronomer Andrew McKellar wrote in 1941: "It can be calculated that the 'rotational temperatureˡ of interstellar space is 2 K."[13] However, during the 1970s the consensus was established that the cosmic microwave background is a remnant of the big bang. This was largely because new measurements at a range of frequencies showed that the spectrum was a thermal, black body spectrum, a result that the steady state model was unable to reproduce.

Harrison, Peebles and Yu, and Zel'dovich realized that the early universe would have to have inhomogeneities at the level of 10-4 or 10−5.[14] Rashid Sunyaev later calculated the observable imprint that these inhomogeneities would have on the cosmic microwave background.[15] Increasingly stringent limits on the anisotropy of the cosmic microwave background were set by ground based experiments, but the anisotropy was first detected by the Differential Microwave Radiometer instrument on the COBE satellite.[16]

Inspired by the COBE results, a series of ground and balloon-based experiments measured cosmic microwave background anisotropies on smaller angular scales over the next decade. The primary goal of these experiments was to measure the scale of the first acoustic peak, which COBE did not have sufficient resolution to resolve. The first peak in the anisotropy was tentatively detected by the Toco experiment and the result was confirmed by the BOOMERanG and MAXIMA experiments.[17]. These measurements demonstrated that the Universe is flat and were able to rule out cosmic strings as a theory of cosmic structure formation, and suggested cosmic inflation was the right theory of structure formation.

The second peak was tentatively detected by several experiments before being definitively detected by WMAP, which has also tentatively detected the third peak. Several experiments to improve measurements of the \htmladdnormallink{Polarization}{http://planetphysics.us/encyclopedia/FluorescenceCrossCorrelationSpectroscopy.html} and the microwave background on small angular scales are ongoing. These include DASI, WMAP, BOOMERanG and the Cosmic Background Imager. Forthcoming experiments include the Planck satellite, Atacama Cosmology Telescope and the South Pole Telescope.

\subsection{Relationship to the Big Bang}

The standard hot big bang model of the universe requires that the initial conditions for the universe are a Gaussian random \htmladdnormallink{field}{http://planetphysics.us/encyclopedia/CosmologicalConstant2.html} with a nearly scale invariant or Harrison-Zel'dovich spectrum. This is, for example, a prediction of the cosmic inflation model. This means that the initial state of the universe is random, but in a clearly specified way in which the amplitude of the primeval inhomogeneities is 10-5. Therefore, meaningful statements about the inhomogeneities in the universe need to be statistical in nature. This leads to cosmic variance in which the uncertainties in the variance of the largest scale fluctuations observed in the universe are difficult to accurately compare to theory.

\subsection{Temperature}

The cosmic microwave background radiation and the cosmological red shift are together regarded as the best available evidence for the Big Bang (BB) theory. The discovery of the CMB in the mid-1960s curtailed interest in alternatives such as the steady state theory. The CMB gives a snapshot of the Universe when, according to standard cosmology, the temperature dropped enough to allow electrons and protons to form hydrogen atoms, thus making the universe transparent to radiation. When it originated some 400,000 years after the Big Bang — this time period is generally known as the "time of last scattering" or the period of recombination or decoupling — the temperature of the Universe was about 3,000 K. This corresponds to an energy of about 0.25 eV, which is much less than the 13.6 eV ionization energy of hydrogen. Since then, the temperature of the radiation has dropped by a factor of roughly 1100 due to the expansion of the Universe. As the universe expands, the CMB photons are redshifted, making the radiation's temperature inversely proportional to the Universe's scale length. For details about the reasoning that the radiation is evidence for the Big Bang, see Cosmic background radiation of the Big Bang.

\subsection{Primary Anisotropy} The anisotropy of the cosmic microwave background is divided into two sorts: primary anisotropy – which is due to effects which occur at the last scattering surface and before – and secondary anisotropy – which is due to effects, such as interactions with hot gas or gravitational potentials, between the last scattering surface and the observer.

The structure of the cosmic microwave background anisotropies is principally determined by two effects: acoustic oscillations and diffusion damping (also called collisionless damping or Silk damping). The acoustic oscillations arise because of a competition in the photon-baryon plasma in the early universe. The pressure of the photons tends to erase anisotropies, whereas the gravitational attraction of the baryons – which are moving at \htmladdnormallink{speeds}{http://planetphysics.us/encyclopedia/Velocity.html} much less than the \htmladdnormallink{speed of light}{http://planetphysics.us/encyclopedia/CosmologicalConstant2.html} – makes them tend to collapse to form dense haloes. These two effects compete to create acoustic oscillations which give the microwave background its characteristic peak structure. The peaks correspond, roughly, to \htmladdnormallink{resonances}{http://planetphysics.us/encyclopedia/WavePhenomena.html} in which the photons decouple when a particular mode is at its peak amplitude. The peaks contain interesting physical signatures. The first peak determines the shape of the Universe. The second peak – truly the ratio of the odd peaks to the even peaks – determines the reduced baryon density. The third peak can be used to extract information about the \htmladdnormallink{dark matter}{http://planetphysics.us/encyclopedia/PlasmaDisplayPanel.html} density.

Collisionless damping is caused by two effects, when the treatment of the primordial plasma as a fluid begins to break down:

These effects contribute about equally to the supression of anisotropies on small scales, and give rise to the characteristic exponential damping tail seen in the very small angular scale anisotropies.

\subsection{Late Time Anisotropy} After the creation of the CMB, it is modified by several physical processes collectively referred to as late-time anisotropy or secondary anisotropy. After the emission of the CMB, ordinary matter in the universe was mostly in the form of neutral hydrogen and helium atoms, but from observations of galaxies it seems that most of the \htmladdnormallink{volume}{http://planetphysics.us/encyclopedia/Volume.html} of the intergalactic medium (IGM) today consists of ionized material (since there are few absorption lines due to hydrogen atoms). This implies a period of reionization in which the material of the universe breaks down into hydrogen ions.

The CMB photons scatter off free \htmladdnormallink{charges}{http://planetphysics.us/encyclopedia/Charge.html} such as electrons that are not bound in atoms. In an ionized universe, such electrons have been liberated from neutral atoms by ionizing (ultraviolet) radiation. Today these free charges are at sufficiently low density in most of the volume of the Universe that they do not measurably affect the CMB. However, if the IGM was ionized at very early times when the universe was still denser, then there are two main effects on the CMB:

1. Small scale anisotropies are erased (just as when looking at an \htmladdnormallink{object}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} through fog, details of the object appear fuzzy). 2. The physics of how photons scatter off free electrons (Thomson scattering) induces polarization anisotropies on large angular scales. This large angle polarization is correlated with the large angle temperature perturbation.

Both of these effects have been observed by the WMAP satellite, providing evidence that the universe was ionized at very early times, at a redshift of larger than 17. The detailed provenance of this early ionizing radiation is still a matter of scientific debate. It may have included starlight from the very first population of stars (population III stars), supernovae when these first stars reached the end of their lives, or the ionizing radiation produced by the accretion disks of massive \htmladdnormallink{black holes}{http://planetphysics.us/encyclopedia/BlackHoles.html}.

The period after the emission of the cosmic microwave background and before the observation of the first stars is semi-humorously referred to by cosmologists as the dark age, and is a period which is under intense study by astronomers (See 21 centimeter radiation).

Other effects that occur between reionization and our observation of the cosmic microwave background which cause anisotropies include the Sunyaev-Zel'dovich effect, in which a cloud of high energy electrons scatters the radiation, transferring some energy to the CMB photons, and the Sachs-Wolfe effect, which causes photons from the cosmic microwave background to be gravitationally redshifted or blue shifted due to changing gravitational fields.

\subsection{Polarization} The cosmic microwave background is polarized at the level of a few microkelvins. There are two \htmladdnormallink{types}{http://planetphysics.us/encyclopedia/Bijective.html} of polarization, called E-modes and B-modes. This is in analogy to electrostatics, in which the \htmladdnormallink{Electric Field}{http://planetphysics.us/encyclopedia/ElectricField.html} (E-field) has a vanishing \htmladdnormallink{curl}{http://planetphysics.us/encyclopedia/Curl.html} and the \htmladdnormallink{magnetic field}{http://planetphysics.us/encyclopedia/NeutrinoRestMass.html} (B-field) has a vanishing \htmladdnormallink{divergence}{http://planetphysics.us/encyclopedia/DivergenceOfAVectorField.html}. The E-modes arise naturally from Thomson scattering in an inhomogeneous plasma. The B-modes, which have not been measured and are thought to have an amplitude of at most a 0.1 µK, are not produced from the plasma physics alone. They are a signal from cosmic inflation and are determined by the density of primordial gravitational \htmladdnormallink{waves}{http://planetphysics.us/encyclopedia/CosmologicalConstant2.html}. Detecting the B-modes will be extremely difficult, particularly given that the degree of foreground contamination is unknown, and the weak \htmladdnormallink{gravitational lensing}{http://planetphysics.us/encyclopedia/GravitationalLensing.html} signal mixes the relatively strong E-mode signal with the B-mode signal.[18]

\subsection{Microwave Background Observations}

The design of cosmic microwave background experiments is a very challenging task. The greatest problems are:

  • Detectors The challenge of observing differences of a few microkelvins on top of a 2.7 K signal is difficult. Many improved microwave detector technologies have been designed for microwave background applications. Some technologies used are HEMT, MMIC, SIS (Superconductor-Insulator-Superconductor) and bolometers. Experiments generally use elaborate cryogenic \htmladdnormallink{systems}{http://planetphysics.us/encyclopedia/SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence.html} to keep the detectors cool. Often, experiments are interferometers which only measure the spatial fluctuations in signals on the sky, and are insensitive to the average 2.7 K background. Another problem is the 1/f noise intrinsic to all detectors. Usually the experimental scan strategy is designed to minimize the effect of such noise.
  • Optics To minimize side lobes, microwave optics usually utilize elaborate lenses and feed horns.
  • Water vapor Because water absorbs microwave radiation (a fact that is used to build microwave ovens), it is rather difficult to observe the microwave background with ground-based instruments. CMB research therefore makes increasing use of air and space-borne experiments. Ground-based observations are usually made from dry, high altitude locations such as the Chilean Andes and the South Pole.

\subsection{Analyses}

The analysis of cosmic microwave background data to produce maps, an angular \htmladdnormallink{power}{http://planetphysics.us/encyclopedia/Power.html} spectrum and ultimately cosmological parameters is a complicated, computationally difficult problem. Although computing a power spectrum from a map is in principle a simple \htmladdnormallink{Fourier transform}{http://planetphysics.us/encyclopedia/FourierTransforms.html}, decomposing the map of the sky into spherical harmonics, in practice it is hard to take the effects of noise and foregrounds into account. Constraints on many cosmological parameters can be obtained from their effects on the power spectrum, and results are often calculated using Markov Chain Monte Carlo sampling techniques.

\subsection{Low Multipoles}

With the increasingly precise data provided by WMAP, there have been a number of claims that the CMB suffers from anomalies, such as non-gaussianity. The most longstanding of these is the low-l multipole controversy. Even in the COBE map, it was observed that the quadrupole (l = 2 spherical harmonic) has a low amplitude compared to the predictions of the big bang. Some observers have pointed out that the anisotropies in the WMAP data did not appear to be consistent with the big bang picture. In particular, the quadrupole and octupole (l = 3) modes appear to have an unexplained alignment with each other and with the ecliptic plane.[19] A number of groups have suggested that this could be the signature of new physics at the largest observable scales. Ultimately, due to the foregrounds and the cosmic variance problem, the largest modes will never be as well measured as the small angular scale modes. The analyses were performed on two maps that have had the foregrounds removed as best as is possible: the "internal linear combination" map of the WMAP collaboration and a similar map prepared by Max Tegmark and others.[20] Later analyses have pointed out that these are the modes most susceptible to foreground contamination from synchrotron, dust and free-free emission, and from experimental uncertainty in the monopole and dipole. While the low quadrupole does appear to be robust (The measured value has a likelihood of roughly 2–4% in the Lambda-CDM model.), carefully accounting for the procedure used to remove the foregrounds from the full sky map reduces the significance of the alignment, and may suggest that it is due to foreground contamination.[21]

\subsection{References}

[1] This ignores the dipole anisotropy, which is due to the Doppler shift of the microwave background radiation due to our peculiar \htmladdnormallink{velocity}{http://planetphysics.us/encyclopedia/Velocity.html} relative to the comoving cosmic rest frame. This feature is consistent with the Earth moving at some 380 km/s towards the constellation Virgo.

[2] D. J. Fixen et al., "The Cosmic Microwave Background Spectrum from the full COBE FIRAS data set", Astrophysical Journal 473, 576–587 (1996).

[3] The energy density of a black-body spectrum is $\pi k_B^2T^4/15(\hbar c)^3$, where $T$ is the temperature, $kB$ is the \htmladdnormallink{Boltzmann constant}{http://planetphysics.us/encyclopedia/BoltzmannConstant.html}, $\hbar$ is the Planck constant and c is the speed of light. This can be related to the critical density of the universe using the parameters of the Lambda-CDM model.

[4] Astrophysical Journal Supplement, 148 (2003). In particular, G. Hinshaw et al. "First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: the angular power spectrum", 135–159.

[5] D. N. Spergel et al., "First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: determination of cosmological parameters", Astrophysical Journal Supplement 148, 175–194 (2003).

[6] Helge Kragh, Cosmology and Controversy: The Historical Development of Two Theories of the Universe (1999) ISBN 0-691-00546-X

[7] George Gamow, The Creation Of The Universe p.50 (Dover reprint of revised 1961 edition) ISBN 0-486-43868-6

[8] J. Kovac et al., "\htmladdnormallink{detection}{http://planetphysics.us/encyclopedia/MolecularOrbitals.html} of polarization in the cosmic microwave background using DASI", Nature 420, 772-787 (2002).

[9] G. Gamow, "The Origin of Elements and the Separation of Galaxies," Physical Review 74 (1948), 505. G. Gamow, "The evolution of the universe", Nature 162 (1948), 680. R. A. Alpher and R. Herman, "On the Relative Abundance of the Elements," Physical Review 74 (1948), 1577.

[10] A. K. T. Assis, M. C. D. Neves, "History of the 2.7 K Temperature Prior to Penzias and Wilson," (1995, \htmladdnormallink{pdf}{http://planetphysics.us/encyclopedia/LebesgueMeasure.html} | HTML) but see also N. Wright, "Eddington did not predict the CMB", [1].

[11] R. H. Dicke, "The measurement of thermal radiation at microwave frequencies", Rev. Sci. Instrum. 17, 268 (1946). This basic design for a radiometer has been used in most subsequent cosmic microwave background experiments.

[12] A. A. Penzias and R. W. Wilson, "A Measurement of Excess Antenna Temperature at 4080 \htmladdnormallink{MC/}{http://planetphysics.us/encyclopedia/LQG2.html}," Astrophysical Journal 142 (1965), 419. R. H. Dicke, P. J. E. Peebles, P. G. Roll and D. T. Wilkinson, "Cosmic Black-Body Radiation," Astrophysical Journal 142 (1965), 414. The history is given in P. J. E. Peebles, Principles of physical cosmology (Princeton Univ. Pr., Princeton 1993).

[13] A. McKellar, Publ. Dominion Astrophys. Obs. 7, 251.

[14] E. R. Harrison, "Fluctuations at the threshold of classical cosmology," Phys. Rev. D1 (1970), 2726. P. J. E. Peebles and J. T. Yu, "Primeval adiabatic perturbation in an expanding universe," Astrophysical Journal 162 (1970), 815. Ya. B. Zel'dovich, "A hypothesis, unifying the structure and \htmladdnormallink{entropy}{http://planetphysics.us/encyclopedia/ThermodynamicLaws.html} of the universe," Monthly Notices of the Royal Astronomical Society 160 (1972).

[15] R. A. Sunyaev, "Fluctuations of the microwave background radiation," in Large Scale Structure of the Universe ed. M. S. Longair and J. Einasto, 393. Dordrecht: Reidel 1978. While this is the first paper to discuss the detailed observational imprint of density inhomogeneities as anisotropies in the cosmic microwave background, some of the groundwork was laid in Peebles and Yu, above.

[16] G. F. Smoot et al. "Structure in the COBE DMR first year maps", Astrophysical Journal 396 L1–L5 (1992). C. L. Bennett et al. "Four year COBE DMR cosmic microwave background observations: maps and basic results.", Astrophysical Journal 464 L1–L4 (1996).

[17] A. D. Miller et al., "A measurement of the angular power spectrum of the cosmic microwave background from l = 100 to 400", Astrophysical Journal 524, L1–L4 (1999). A. E. Lange et al., "Cosmological parameters from the first results of Boomerang". P. de Bernardis et al., "A flat universe from high-resolution maps of the cosmic microwave background", Nature 404, 955 (2000). S. Hanany et al. "MAXIMA-1: A measurement of the cosmic microwave background anisotropy on angular scales of 10'-5°", Astrophysical Journal 545 L5–L9 (2000).

[18] A. Lewis and A. Challinor (2006). "Weak gravitational lensing of the CMB". Phys. Rep.. (to appear)

[19.] A. de Oliveira-Costa, M. Tegmark, M. Zaldarriga and A. Hamilton (2004). "The significance of the largest scale CMB fluctuations in WMAP". Phys. Rev. D69: 063516. arXiv:astro-ph/0307282. D. J. Schwarz, G. D. Starkman, D. Huterer and C. J. Copi (2004). "Is the low-l microwave background cosmic?". Phys. Rev. Lett. 93: 221301. arXiv:astro-ph/0403353. P. Bielewicz, K. M. Gorski and A. J. Banday (2004). "Low-order multipole maps of CMB anisotropy derived from WMAP". Mon. Not. Roy. Astron. Soc. 355: 1283. arXiv:astro-ph/0405007.

[20] C. L. Bennett et al. (WMAP collaboration) (2003). "First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: preliminary maps and basic results". Astrophysical Journal Supplement 148: 1. arXiv:astro-ph/0302207. G. Hinshaw et al. (WMAP collaboration) (March 2006). "Three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: temperature analysis". preprint. M. Tegmark, A. de Oliveira-Costa and A. Hamilton (2003). "A high resolution foreground cleaned CMB map from WMAP". Phys. Rev. D68: 123523. arXiv:astro-ph/0302496. The first year WMAP paper warns: "the statistics of this internal linear combination map are complex and inappropriate for most CMB analyses." The third year paper states: "Not surprisingly, the two most contaminated multipoles are [the quadrupole and octopole], which most closely \htmladdnormallink{trace}{http://planetphysics.us/encyclopedia/Trace.html} the galactic plane morphology."

[21] A. Slosar and U. Seljak (2004). "Assessing the effects of foregrounds and sky removal in WMAP". Phys. Rev. D70: 083002. arXiv:astro-ph/0404567. P. Bielewicz, H. K. Eriksen, A. J. Banday, K. M. Gorski and P. B. Lilije (2005). "Multipole \htmladdnormallink{vector}{http://planetphysics.us/encyclopedia/Vectors.html} anomalies in the first-year WMAP data: a cut-sky analysis". Astrophys. J. 635: 750–60. arXiv:astro-ph/0507186. C. J. Copi, D. Hueterer, D. J. Schwarz and G. D. Starkman (2006). "On the large-angle anomalies of the microwave sky". Mon. Not. Roy. Astron. Soc. 367: 79–102. arXiv:astro-ph/0508047. A. de Oliveira-Costa and M. Tegmark (2006). "CMB multipole measurements in the presence of foregrounds". preprint. arXiv:astro-ph/0603369.


This entry is a derivative of the cosmic microwave background radiation article \htmladdnormallink{from Wikipedia, the Free Encyclopedia}{http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation}. Authors of the orginial article include: TexMurphy, Peripitus, Wdanwatts, Kungfuadam and Profero. History page of the original is \htmladdnormallink{here}{http://en.wikipedia.org/w/index.php\?title=Cosmic_microwave_background_radiation\&action=history}

\end{document}

Add topic
Retrieved from "https://en.wikiversity.org/w/index.php?title=Talk:PlanetPhysics/Cosmic_Microwave_Background_Radiation&oldid=2589717"
Return to "PlanetPhysics/Cosmic Microwave Background Radiation" page.