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cosmic microwave background

θ < θ0 will escape the trap, i.e., they thermalize in the ambient plasma before they bounce.

corotating interaction region

See helio-

spheric stream structure.

 

correlation length In phase transitions, topological defects may arise when growing spatial domains with different orientations (phases) of the correlated field fail to match smoothly. Hence, fluctuations in the phase of the field (determined by local physics only) will be uncorrelated on scales larger than a given correlation length ξ, whose details depend on the transition taking place.

The tendency of the field configuration after the transition will be to homogenize, and thus ξ will grow in time. Causality imposes an upper limit, as information cannot propagate faster than light. Hence, in cosmology the correlation length must be smaller than the distance signals can have traveled since the Big Bang, which for both radiationand matter-dominated eras im-

plies ξ

<

t, with t the cosmic time.

The correlation length is of utmost importance for the subsequent evolution of a cosmic defect network. In fact, the initial length scale of the network will be determined by the probability of defect formation out of the coalescence of different domains.

coseismic deformation Displacement such as uplift and subsidence that occurs during an earthquake. The term is used particularly to describe static displacement and not vibration associated with seismic wave propagation. Depending on the means of measurement, the term may represent displacements that occur within a fraction of a second to a period of several years.

cosine collector A radiant energy detector whose effective light collection area is proportional to the cosine of the angle between the incident light and the normal to the detector surface; used to measure plane irradiances.

cosmic abundance The relative abundance of elements in the universe. Hydrogen provides approximately 75% of the mass density of the universe. 4H e provides about 24%. Lithium, beryllium and boron are each at the 1012 to

1010 level. These elements are thought to have been produced in the Big Bang.

Heavier elements were produced in stars or supernovae. Carbon, nitrogen, oxygen, and neon are present at parts greater than 104. Silicon and iron are abundant at the 104 level. Elements with atomic number exceeding approximately 30 are present at the 1010 to 1011 level. There is strong “odd-even” effect; even atomic numbers (numbers of protons) or even numbers of neutrons make the isotope much more abundant than nearby isotopes.

cosmic censorship The conjecture put forward by R. Penrose that the formation of naked singularities (singularities visible from infinitely far away) is evaded in nature because singularities in space-time are always surrounded by an event horizon which prevents them from being observed and from influencing the outside world. In this simple formulation the hypothesis was proven false by counterexamples, i.e., models of spacetime whose metrics obey Einstein’s equations, but in which naked singularities exist. According to proponents of cosmic censorship, these examples are not generic. Some of the spacetimes in question are highly symmetric or require tuning of parameters. In others, the gravitational fields in the neighborhood of those singularities are, in a well-defined mathematical sense, too weak (i.e., produce too weak tidal forces) to be considered genuinely singular. There is as yet no well-formulated statement of cosmic censorship or a proof of its holding in general relativity.

cosmic microwave background Single component of cosmic origin that dominates the electromagnetic background at wavelengths in the millimeters to centimeters range. It was serendipitously discovered by Penzias and Wilson in 1965. The cosmic microwave background radiation has the spectrum of a black body at temperature To = 2.728 ± 0.002 K. It can be detected in any direction of the sky. Its high degree of isotropy is an observational evidence that on the largest scale, the universe is homogeneous and isotropic.

The Planckian spectrum of the cosmic microwave background is a strong vindication of the Big Bang picture. Since the universe at

© 2001 by CRC Press LLC

cosmic microwave background, dipole component

present is transparent to radiation (radiogalaxies at redshifts z < 1 are observed at microwave frequencies), a thermal spectrum could not have been produced recently, i.e., at redshifts smaller than unity as would be required by the steady state cosmological model. In the Big Bang model, the effect of the expansion is to decrease the cosmic microwave background temperature, so in the past the universe was hotter. At redshift z, the temperature would be T = To(1+z). At z 1000 matter and radiation would have achieved thermal equilibrium. In the 1940s, Gamow, Alpher, Herman, and Follin predicted that, as the universe expands and temperature drops, the interactions that kept matter and radiation in thermal equilibrium cease to exist. The radiation that would then propagate freely is the one observed today.

On scales up to a few tens of Mpc, the universe is not homogeneous. The presence of inhomogeneities induces temperature anisotropies on the background radiation. Irregularities in the matter distribution at the moment of recombination, our peculiar motions with respect to the Hubble flow, the effect of hot plasma on clusters of galaxies (see Sunyaev– Zel’dovich effect), and several other contributions, induced anisotropies at the level of one part in 103 (dipole) and at 105 on smaller angular scales. These effects convert the CBR into an excellent probe of the history of structure formation (galaxies, clusters of galaxies) in the evolving universe. See cosmic microwave back- ground, dipole; quadrupole; temperature fluctuations; spectral distortions.

cosmic microwave background, dipole component Dipole variation in the thermodynamic temperature as a function of direction. It is the largest anisotropy present in the cosmic microwave background radiation. The motion of an observer with velocity v with respect to a reference frame where a radiation field (of temperature To) is isotropic produces a Doppler-shifted temperature T (θ) = To(1 +

(v/c)2)1/2/(1(v/c) cos(θ)) where θ is the angle between the direction of observation and the direction of motion, and c is the speed of light. Immediately after the discovery of the cosmic microwave background, the search started for the Doppler anisotropy described above, and

the first results were obtained at the end of the 1960s. The best-fit of the dipole amplitude is 3.358 ± 0.023 mK in the direction (l, b) = (264.31 ± 0.16, 48.05 ± 0.09) in galactic coordinates. The current understanding is that the largest contribution to the dipole anisotropy comes from the motion of the Earth. All other contributions are negligible. Under this assumption, the data quoted above corresponds to a sun velocity, with respect to the cosmic microwave background, of v = 369.0 ± 2.5 km/s towards the constellation Leo, and the velocity of the local group is vLG = 627 ± 22 km/s in the direction (l, b) = (276o ± 3, 30o ± 2). See peculiar motion.

cosmic microwave background, quadrupole component Quadrupole variation of the temperature pattern of the cosmic microwave background across the sky. It was first measured in 1992 by the Differential Microwave Radiometer (DMR) experiment on board the COBE satellite, launched by NASA in 1989. The cosmic microwave background temperature fluctuations were measured at an angular resolution of 7o at frequencies of 31.5, 53, and 90 GHz. The r.m.s. quadrupole anisotropy amplitude is

defined through Q2rms/To2 = m |a2m|2/4π, with To the cosmic microwave background tem-

perature and a2m the five (l = 2) multipoles of the spherical harmonic expansion of the temperature pattern (see cosmic microwave background temperature anisotropies, Sachs–Wolfe effect). The observed cosmic microwave background quadrupole amplitude is Qrms = 10.7± 3.6±7.1µ K, where the quoted errors reflect the 68% confidence uncertainties from statistical errors and systematic errors associated to the modeling of the galactic contribution, respectively.

More interesting for cosmological purposes is the quadrupole obtained from a power law

fit to the

entire

radiation

power spectrum,

QrmsP S.

The data indicates that the spec-

tral

index

of matter density perturbations is

n

=

1.2

± 0.3 and the

quadrupole normaliza-

 

 

 

 

3.8

µ K. For n

 

1,

tion Q

rms

P S =

15.3+

 

=

 

 

 

 

2.8

 

=

the best-fit normalization is QrmsP S|(n=1)

18 ± 1.6µ K. The difference between the two definitions reflects the statistical uncertainty associated with the large sampling variance of

© 2001 by CRC Press LLC

cosmic microwave background, temperature fluctuations

Qrms since it is obtained from only five independent measurements.

cosmic microwave background, spectral distortions The cosmic microwave background is well characterized by a 2.728 ± 0.002 K black body spectrum over more than three decades in frequency. Spectral distortions could have been produced by energy released by decaying of unstable dark matter particles or other mechanisms. Free-free processes (bremsstrahlung and free-free absorption) become ineffective to thermalize the radiation below redshift zff 105(IB h2)6/5, where IB is the baryon fraction of the total density in units of the critical density, and h is the dimensionless Hubble constant. Any processes releasing energy later than zff will leave a distinctive imprint on the spectrum of the cosmic microwave background. After zff , Compton scattering between the radiation and electron gas is the only process than can redistribute the photon energy density, but as it conserves photon number, it does not lead to a Planckian spectrum. The lack of any distortion on the cosmic microwave background spectrum sets a very strict upper limit on the fractional energy released in the early universe: ?E/Ecmb < 2 × 104 for redshifts between 5 × 106 and recombination. The only distortion detected up to now is a temperature deficit in the direction of clusters of galaxies due to inverse Compton scattering of cosmic microwave background photons by hot electrons in the cluster atmosphere. See Sunyaev–Zeldovich effect.

cosmic microwave background, temperature fluctuations Variation on the cosmic microwave background temperature across the sky. Current observations show that the cosmic microwave background has a dipole anisotropy at the 103 level and smaller scale anisotropies at the 105 level in agreement with the expectations of the most widely accepted models of structure formation. It is customary to express the cosmic microwave background temperature anisotropies on the sky in a spherical harmonic expansion,

?T

 

 

(θ, φ) = almYlm(θ, φ) .

T

 

lm

The dipole (l = 1) is dominated by the Doppler shift caused by the Earth’s motion relative to the nearly isotropic blackbody field (see cosmic microwave background dipole component). The lower order multipoles (2 l 30), corresponding to angular scales larger than the horizon at recombination, are dominated by variations in the gravitational potential across the last scattering surface (see Sachs–Wolfe effect). On smaller angular scales, peculiar motions associated with the oscillation in the baryon-photon plasma dominate the contribution, giving rise to variations in power between l 100 and l 1000 known as Doppler peaks. Together, other physical processes can contribute to increase the intrinsic anisotropies along the photon trajectory such as integrated Sachs–Wolfe, Sunyaev–Zeldovich, Vishniac or Rees–Sciama effects. The pattern of temperature anisotropies and the location and relative amplitude of the different Doppler peaks depend on several cosmological parameters: Hubble constant, baryon fraction, dark matter and cosmological constant contributions to the total energy density, geometry of the universe, spectral index of matter density perturbations at large scales, existence of a background of gravitational waves, etc. In this respect, the cosmic microwave background is an excellent cosmological probe and a useful test of models of galaxy and structure formation. The character of the fluctuations is usually described by the best fitting index n and QrmsP S, the mean r.m.s. temperature fluctuations expected in the quadrupole component of the anisotropy averaged over all cosmic observers.

A cosmological model does not predict the exact cosmic microwave background temperature that would be observed in our sky, but rather predicts a statistical distribution of anisotropy parameters, such as spherical harmonic amplitudes: Cl =< |alm|2 > where the average is over all cosmic observers. In the context of these models, the true cosmic microwave background temperature observed in our sky is only a single realization from a statistical distribution. If the statistical distribution is Gaussian, and the spectral index of matter density perturbation spectrum is n = 1, as favored by inflation, then Cl = 6C2/l(l+1). The figure displays the mean temperature offset δTl = (l(l + 1)Cl/2π)1/2To of several experiments carried out to measure

© 2001 by CRC Press LLC

cosmic nucleosynthesis

temperature anisotropies on all angular scales. The data indicate a plateau at l 20, suggesting a spectral index close to n = 1 and a rise from l = 30 to 200, as it would correspond to the first Doppler peak if I = 1. Error bars in the vertical direction give 68% confidence uncertainty. In the horizontal direction indicate the experiments angular sensitivity. We have supersoped the predictions of three flat models: Icdm = 0.95 h = 0.65, Icdm = 0.95, IU = 0.7 and h = 0.7, and Ihdm = 0.95 h = 0.65 to show the agreement between data and theory. In both cases the baryon fraction was IB = 0.05, in units of the critical density. Icdm represents the fraction of cold dark matter, Ihdm of hot dark matter, and IU the contribution of the cosmological constant to the total energy density.

Experimental results as to January 1999. Measurements of anisotropies have been converted into temperature offsets. The predictions of two models are superposed with: cold dark matter (ICDM = 0.95, IB h2 = 0.02, h = 0.65) and cold dark matter with

cosmological constant (to = 14×109 yr, IU = 0.7,

ICDM = 0.25, IB h2 = 0.02).

cosmic nucleosynthesis

Big Bang nucle-

osynthesis.

 

cosmic phase transition

The idea that phase

transitions would occur in the early universe, originally borrowed from condensed matter and statistical physics. Examples of such cosmic transitions are the quark to hadron (confinement) phase transition, which quantum chromodynamics (QCD, the theory of strongly interacting particles) predicts at an energy around 1 GeV, and the electroweak phase transition at

about 250 GeV. Within grand unified theories, aiming to describe the physics beyond the standard model, other phase transitions are predicted to occur at energies of order 1015 GeV.

In cosmic phase transitions, the system is the expanding, cooling down universe, and the role of the order parameter is commonly assigned to the vacuum expectation value |φ| of hypothetical scalar Higgs fields (denoted φ in what follows), which characterize the ground state of the theory. In the transition the expected value of the field goes from zero (the high temperature symmetric phase) to a nonvanishing value (in the low temperature broken symmetry phase, which does not display all the symmetries of the Hamiltonian).

The evolution of the order parameter (φ in our case) can be a continuous process (for secondorder transitions). It can also proceed by bubble nucleation or by spinoidal decomposition (firstorder transition), in which case φ changes from zero to its low temperature value abruptly. Typical effective potentials are shown on the figures.

V(φ)

V(φ)

T>Tc

T>Tc

 

φ

φ

T=0

T=0

a

b

Effective potentials used to describe cosmic phase transitions: (a) for a second-order phase transition and (b) for a first-order phase transition. In both cases, the potential has a minimum value for φ = 0 at high temperatures (i.e., T Tc, dotted lines), while its shape is modified at low temperatures (solid lines). First-order transitions are characterized by the fact that there exist two qualitatively distinct types of minima at low temperature, the symmetric phase (φ = 0) being metastable instead of unstable as is the case for a second-order transition.

© 2001 by CRC Press LLC

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