Review of Particle Physics (2006)

TLDR: In this article, the authors present a review of the Particle Data Group (PDG) and its role in the development of particle data and its application in particle physics. But the review is limited.

Abstract: A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review. All tables, listings, and reviews (and errata) are also available on the Particle Data Group website: http://pdg.lbl.gov.

Figures

Table 1.1: The basic set of cosmological parameters. We give values as obtained using a fit of a ΛCDM cosmology with a power-law initial spectrum to WMAP3 data alone [2]. Tensors are assumed zero except in quoting a limit on them. We cannot stress too much that the exact values and uncertainties depend on both the precise datasets used and the choice of parameters allowed to vary, and the effects of varying some assumptions will be shown later in Table 1.2. Limits on the cosmological constant depend on whether the Universe is assumed flat, while there is no established convention for specifying the density perturbation amplitude. Uncertainties are one-sigma/68% confidence unless otherwise stated.

Figure 1.2: The angular power spectrum of the cosmic microwave background temperature from WMAP3. The solid line shows the prediction from the best-fitting ΛCDM model [2]. The error bars on the data points (which are tiny for most of them) indicate the observational errors, while the shaded region indicates the statistical uncertainty from being able to observe only one microwave sky, known as cosmic variance, which is the dominant uncertainty on large angular scales. [Figure courtesy NASA/WMAP Science Team.]

Table 1.2: Parameter constraints reproduced from Spergel et al. [2]. All columns assume the ΛCDM cosmology with a power-law initial spectrum, no tensors, spatial flatness, and a cosmological constant as dark energy. Three different data combinations are shown to highlight the extent to which this choice matters. The first column is WMAP3 alone, the second combines this with 2dF, and the third column shows a combination of all datasets considered in Ref. [2]. This last data is not in their paper but can be found online at http://lambda.gsfc.nasa.gov. The parameter A is a measure of the perturbation amplitude; see Ref. 2 for details. Uncertainties are shown at one sigma, and caution is needed in extrapolating them to higher significance levels due to non-Gaussian likelihoods and assumed priors.

Figure 1.1: This shows the preferred region in the Ωm–ΩΛ plane from the compilation of supernovae data in Ref. 17, and also the complementary results coming from some other observations. [Courtesy of the Supernova Cosmology Project.]

Figure 1.3: The galaxy power spectrum from the 2dF galaxy redshift survey [22] compared with that from SDSS [24], each corrected for its survey geometry. The 2dFGRS power spectrum (with distances measured in redshift space) is shown by solid circles with one-sigma errors shown by the shaded area. The triangles and error bars show the SDSS power spectrum. The solid curve shows a linear-theory ΛCDM model with Ωmh = 0.168, Ωb/Ωm = 0.17, h = 0.72, n = 1 and normalization matched to the 2dFGRS power spectrum. The dotted vertical lines indicate the range over which the best-fit model was evaluated. [Figure provided by Shaun Cole and Will Percival; see Ref. 22.]

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The cosmological parameters 2006
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Lahav, O. and Liddle, Andrew (2006) The cosmological parameters 2006. Journal of Physics G,
33 (1). pp. 224-232. ISSN 0954-3899
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arXiv:astro-ph/0601168 v2 18 Oct 2006
1. The Cosmological Paramete rs 2006 1
1. THE COSMOLOGICAL PARAMETERS 2006
Written August 2003, updated May 2006, by O. Lahav (U niversity College London) and
A.R. Liddle (University of Sussex).
1.1. Parametrizing the Universe
Rapid advances in observa tional cosmology are leading to the establishment of the first
precision cosmological model, with many of the key cosmological parameters determined
to one or two significant figure accuracy. Particularly prominent are measurements
of cosmic microwave anisotropies, led by the three-year results from the Wilkinson
Microwave Anisotropy Probe (WMAP) [1,2]. However the most accurate model of the
Universe requires consideration of a wide range of different types of observat ion, with
complementary probes providing consistency checks, lifting parameter degeneracies, and
enabling the strongest constraints to be placed.
The term ‘cosmological parameters’ is forever increasing in its scope, and nowadays
includes the parametrization of some functions, as well as simple numbers describing
properties of t he Universe. The original usage referred to the parameters describing the
global dynamics of the Universe, such as its expansion rate and curvature. Also now of
great interest is how the matter budget of the U niverse is built up from its constituents:
baryons, photons, neutrinos, dark matter, and dark energy. We need to describe the
nature of perturbations in the Universe, through global statistical descriptions such as
the matter and radiation power spectra. There may also be parameters describing the
physical state o f the Universe, such as the ionizatio n fraction as a function of time during
the era since decoupling. Typical comparisons of cosmological models with observational
data now feature between five and ten parameters.
1.1.1. The glo bal description of the Universe:
Ordinarily, the Universe is taken to be a perturbed Robertson–Walker space-time w ith
dynamics governed by Einstein’s equations. This is described in detail by Olive and
Peacock in this volume. Using the density parameters Ω
i
for the various matter species
and Ω
Λ
for the cosmological constant, the Friedmann equation can be written
X
i
Ω
i
+ Ω
Λ
=
k
R
2
H
2
, (1.1)
where the sum is over all the different species of matter in the Universe. This equation
applies at any epoch, but later in this article we will use the symbols Ω
i
and Ω
Λ
to refer
to the present values. A typical collection would be baryons, photons, neutrinos, and
dark matter (given charge neutrality, the electron density is guaranteed to be too small
to be worth considering separately).
The complete present state of the homogeneous Universe can be described by giving
the present values o f all the density parameters and the present Hubble parameter h.
These also allow us to track the history of the Universe back in time, at least until
an epoch where interactions allow interchanges between the densities of the different
species, which is believed to have l ast happened at neutrino decoupling shortly before
nucleosynthesis.
October 19, 2006 08:53

2 1. The Cosmological Pa rameters 2006
To probe further back into the Universe’s history requires assumptions about particle
interactions, and perhaps about the nat ure of physical laws themselves.
1.1.2. Neutrinos:
The standard neutrino sector has three flavors. For neutrinos of mass in the range
5 × 10
−4
eV to 1 MeV, the density parameter in neutrinos is predicted to be
Ω
ν
h
2
=
P
m
ν
94 eV
, (1.2)
where the sum is over all families with mass in that range (higher masses need a more
sophisticated calculation). We use units with c = 1 throughout. Results on atmospheric
and solar neutrino oscillat ions [3] imply non-zero mass-squared differences between the
three neutrino flavors. These oscillation experiments cannot tell us the absolute neutrino
masses, but within the simple assumption of a mass hierarchy suggest a lower limit of
Ω
ν
≈ 0.001 on the neutrino mass density parameter.
For a total mass as small as 0.1 eV, this could have a po tentially observable effect on
the formation of structure, as neutrino free-streaming damps the growth of perturbations.
Present cosmological observations have shown no convincing evidence of any effects
from either neutrino masses or an otherwise non-standard neutrino sector, and impose
quite stringent limits, which we summarize in Section 1.3.4. Consequently, the standard
assumption at present is that the ma sses are too small to have a significant cosmological
impact, but this may change in the near future.
The cosmological effect of neutrinos can also be modified if the neutrinos have decay
channels, or if there is a large asymmetry in the lepton sector manifested as a different
number density of neutrinos versus anti-neutrinos. This latter effect would need to be of
order unity to be significant, rather than the 10
−9
seen in the baryon sector, which may
be in conflict with nucleosynthesis [4].
1.1.3. Inflation and perturbations:
A complete model of the Universe should include a description of deviations from
homogeneity, at least in a statisti cal way. Indeed, some of the most powerful probes o f
the parameters described above come from the evolution of perturbatio ns, so their study
is naturally intertwined in the determination of cosmological parameters.
There are many different notat ions used to describe the perturbations, both in terms
of the quantity used to describe the perturbations and the definition of the statistical
measure. We use the dimensionless power spectrum ∆
2
as defined in Olive and Peacock
(also denoted P in some of the literature). If the perturbations obey Gaussian statistics,
the power spectrum provides a complete description of their properties.
From a theoretical perspective, a useful quantity to describe the perturbations is the
curvature p erturbation R, which measures the spatial curvature of a comoving slicing
of the space-time. A case of particular interest is the Harrison–Zel’dovich spectrum,
which corresponds to a constant sp ectrum ∆
2
R
. More generally, one can approximate the
spectrum by a power-law, writing
∆
2
R
(k) = ∆
2
R
(k
∗
)

k
k
∗

n−1
, (1.3)
October 19, 2006 08:53

1. The Cosmological Pa rameters 2006 3
where n is known as the spectral index, always defined so that n = 1 for the Harrison–
Zel’dovich spectrum, and k
∗
is an arbitrarily chosen scale. The initial spectrum, defined
at some early epoch of the Universe’s history, is usually taken to have a simple form
such as this power-law, and we will see that observations require n clo se to one, which
correspo nds to the perturbations in the curvature being independent of scale. Subsequent
evolution will modify the spectrum from its initial form.
The simplest viable mechanism for generating t he observed perturbatio ns is the
inflationary cosmology, which posits a period of a ccelerated expansion in the Universe’s
early stages [5]. It is a useful working hypot hesis that this is the sole mechanism for
generating perturbations. Co mmonly, it is further assumed to be the simplest class of
inflationary model, where the dynamics are equivalent to that of a single scalar field φ
slowly rolling on a potential V (φ). One aim of cosmology is to verify that this simple
picture can match observa tions, and to determine the properties of V (φ) from the
observati onal data.
Inflation generates perturbations through the amplification o f quantum fluctuations,
which are stretched to astrophysical scales by the rapid expansion. The simplest models
generate two types, density perturbations w hich come from fluctuations in the scalar field
and its corresponding scalar metric perturbation, and gravitational waves which are tensor
metric fluctuations. The former experience gravitational instability and lead to structure
formation, while the latt er can influence the cosmic microwave background anisotropies.
Defining slow-roll parameters, with primes indicating derivatives with respect to the
scalar field, as
ǫ =
m
2
Pl
16π

V
′
V

2
; η =
m
2
Pl
8π
V
′′
V
, (1.4)
which should satisfy ǫ, |η| ≪ 1, the spectra can be computed using the slow-roll
approximation as
∆
2
R
(k) ≃
8
3m
4
Pl
V
ǫ





k= aH
;
∆
2
grav
(k) ≃
128
3m
4
Pl
V





k= aH
. (1.5)
In each case, the expressions on the right-hand side are to be evaluated when the scale
k is equal to the Hubble radius during inflation. The symbol ‘≃’ indicates use of t he
slow-roll approximation, which is expected to be accurate to a few percent or better.
From these expressions, we can compute the spectral indices
n ≃ 1 − 6ǫ + 2η ; n
grav
≃ −2ǫ . (1.6)
Another useful quantity is the ratio of the two spectra, defined by
r ≡
∆
2
grav
(k
∗
)
∆
2
R
(k
∗
)
. (1.7)
October 19, 2006 08:53

4 1. The Cosmological Pa rameters 2006
The literature contains a number of definitions of r; this convention matches that of
recent versions of CMBFAST [6] and that used by WMAP [7], while definitions based o n
the relative effect on the microwave background anisotropies typically differ by tens of
percent. We have
r ≃ 16ǫ ≃ −8n
grav
, (1.8)
which i s known as the consistency equation.
In general one could consider corrections to the power-law approximation, which we
discuss later. However for now we make the wo rking assumption that the spectra can
be approximated by power laws. The consistency equation shows that r and n
grav
are
not independent parameters, and so the simplest inflation models give initial conditions
described by three parameters, usually taken as ∆
2
R
, n, and r, all to be evaluated at some
scale k
∗
, usually the ‘statistical centre’ of the range explored by the data. Alternatively,
one could use the parametri zat ion V , ǫ, a nd η, all evaluated at a point on the putative
inflationary pot ential.
After the perturbations are created in t he early Universe, they undergo a complex
evolution up until the time t hey are observed in the present Universe. While the
perturbations are small, this can be accurately followed using a linear theory numerical
code such as CMBFAST [6]. This works right up to the present for t he cosmic mi crowave
background, but for density perturbations on small scales non-linear evolution is
important and can be addressed by a variety of semi-analy tical and numerical techniques.
However the analysis is made, the outcome of the evolution is in principle determined by
the cosmological model, and by the parameters describing the initial perturbations, and
hence can be used to determine them.
Of particular interest are cosmic microwave background anisotropies. Both the total
intensity and two independent polarization modes are predicted to have anisotropies.
These can be described by the radiation angular power spectra C
ℓ
as defined in the
article of Scott and Smoot in this volume, and again provide a complete description i f t he
density perturbations are Gaussian.
1.1.4. The stand a rd cosmological mod el:
We now have most of the ingredients in place to describe the cosmological model.
Beyond t hose of the previous subsections, there a re two parameters which are essential
— a measure of the ionization state of the Universe and the galaxy bias parameter.
The Universe is known to be highly ionized at low redshifts (otherwise radiation from
distant quasars wo uld be heavily absorbed in the ultra-violet), and the ionized electrons
can scatter microwave photons altering the pattern of observed anisotropies. The most
convenient parameter to describe this is the optical depth to scattering τ (i.e. the
probability that a given photon scatters once); in the approximatio n of instantaneous and
complete re-ionization, this could equivalently be described by the redshift of re-ionization
z
ion
. The bias parameter, described fully later, is needed to relate the observed galaxy
power spectrum to the predicted dark matter power spectrum.
The basic set of cosmological parameters is therefore as shown in Table 1.1. The
spatial curvature does not appear in the list, because it can be determined from the other
October 19, 2006 08:53