At multipoles ,
the CMB anisotropies become sensitive
to fundamental cosmological parameters, such as the spatial curvature
of the Universe, the baryon density and the Hubble constant. Some
specific examples have been shown in Figure 1.9a. With the high
sensitivity, angular resolution and large sky coverage afforded by
PLANCK it is possible, with certain general assumptions,
to determine these fundamental parameters to a precision
of a few percent (see eg,
Bond, Efstathiou & Tegmark 1997,
Zaldarriaga, Spergel & Seljak 1997,
Efstathiou & Bond 1999).
The unique ability of Planck to distinguish between theoretical models
with very similar cosmological parameters is illustrated in
figure 1.9a. In this figure, we compare CMB power spectra for
spatially flat adiabatic CDM models with different parameters and compare the
ability of MAP and Planck to differentiate between them.


Figure 1.9a: Simulations of the CMB power spectrum of a cold dark matter model
illustrating how Planck can determine cosmological parameters to high
precision. The solid curves in the upper panel shows the CMB power spectrum
for an adiabatic CDM model with baryon density
_{b} =
_{b} h^{2}= 0.0125$,
CDM density _{c}=
_{c} h^{2}=0.2375,
zero cosmological constant,
Hubble constant H_{0} = 50 km s^{1} Mpc^{1},
scaleinvariant spectra, n_{s} = 1, n_{t}=0,
and a ratio of r=0.2 for the
tensor to scalar amplitudes. The dashed lines (barely distinguishable from
the solid lines) show spatially flat models with the parameters listed above
each figure. The differences in these power spectra are plotted on an
expanded scale in the lower panels. The points show simulated observations and
1 errors for the original specifications of MAP,
the current
improved MAP design (designated MAP+) and for the current design
specifications of Planck HFI. These models are marginally distinguishable
by MAP but are easily distinguishable by Planck high significance
levels.
The Table below displays the 1 errors
in estimates of cosmological parameters
(assuming a spatially flat universe) expected from MAP and Planck.
It is important to emphasise that the examples shown in the Table
ignore any systematic errors from Galactic foregrounds,
extragalactic point sources, sidelobe leakage, etc. As already demonstrated in
in the Phase A report, Planck has been carefully
designed to minimise these sources of systematic error. In particular, the
wide frequency coverage provided by the Planck LFI and HFI instruments
allows accurate
subtraction of the Galaxy and extragalactic foregrounds from the primordial
cosmological signal. Furthermore, LFI and HFI the have different beam
profiles, noise characteristics and both sample the 100 GHz frequency range
at comparable sensitivities. The Planck instruments have been designed to
allow a large number of crosschecks of the data. Such consistency checks are
essential for a comprehensive and convincing analysis of cosmological
parameters.
Parameter  MAP  MAP+  PLANCK LFI  PLANCK HFI 
_{b}/
_{b}  0.11  0.05
 0.016 
0.0068  
_{c}/
_{c}  0.21  0.11 
0.04 
0.0063 
_{} 
0.15  0.081  0.035 
0.0049 
Q  0.014  0.0046 
 0.00139 
r  0.81  0.67
 0.13  0.49 
n_{s}  0.066  0.032
 0.01 
0.005  
n_{t}  0.74
 0.72   0.57 

0.22  0.19  0.18  
1 errors in estimates of cosmological parameters
(spatially flat universe). We use the notation
_{i} =
_{i} h^{2} to
denote physical densities
( _{b}, _{c}
and _{}
are the baryon, CDM and cosmological constant densities, respectively).
Q denotes the quadrupole amplitude,
n_{s} (n_{t}) stands for the scalar (tensor) spectral index,
while is the
Thomson optical depth back to the redshift at which the universe reionized.
Determining fundamental cosmological parameters with high accuracy would lead
to a profound change in our understanding of cosmology. For example:
 PLANCK promises the first accurate geometrical estimate
of the spatial curvature of the Universe. Will it be compatible with
the inflationary prediction of ? How will it compare
with dynamical estimates of the mean mass density derived from
galaxy peculiar velocities?
 Will CMB estimates of the Hubble constant be compatible
with estimates from more traditional techniques, such as from
Cepheid distances to galaxies in the Virgo cluster (e.g.
Freedman et al. 1994) or from Type Ia supernova light curves
(Riess et al. 1995)? Will the values of and H_{0}
be compatible with the ages of stars in globular clusters?
 PLANCK can set tight limits on the value of a
cosmological constant . With an angular resolution of
, the error on the dimensionless quantity
is expected to be , well
below the dynamically interesting values of proposed by
some authors (e.g. Ostriker and Steinhardt) to solve the
ageHubble constant problem and observed largescale structure in the
Universe. Such a stringent limit on (or perhaps a detection
of a nonzero value), will be of fundamental significance to particle
physics since there is, at present, no accepted theoretical
explanation of why the cosmological constant is 120 orders of
magnitude smaller than the natural value set by the Planck scale.
 Will estimates of the baryon density and Hubble
constant be compatible with the predictions of primordial
nucleosynthesis? The PLANCK limits on will
be about 30 times smaller than the range derived from
primordial nucleosynthesis (e.g.
Walker et al. 1991),
and will serve as a stimulus for more accurate measurements
of primordial element abundances and for theoretical
investigations of deviations in the predicted abundances
caused by physics beyond the Standard Model of particle physics
(e.g. massive neutrinos, singlet neutrinos etc).
 Do we require dark baryonic matter in the present Universe?
Luminous stars in galaxies contribute only to the density parameter in the Universe. The net baryon content is
very poorly constrained at present and it is not known, for example,
how much remains as hot ionized gas, or whether a significant fraction
of the baryons are locked up in lowmass stars below the nuclear
burning threshold of .
These and many other questions will, for the first time, be
open to quantitative analysis. PLANCK would truly revolutionize
cosmology, turning it from a qualitative science fraught with systematic
errors and uncertainties, into a quantitative science in which most of
the key parameters are constrained to high precision.
Figure 1.9b shows examples of the correlations between some of these
parameters. In Figure 1.9b we have assumed a universe with ,h = 0.5, , spectral index n_{s}=1, r=1, ,and a normalization of K to match the amplitude of the
second year COBE measurements at large angular scales. The figure
shows likelihood contours for representative pairs of parameters
marginalized over all other parameters for CMB experiments at two
angular resolutions, and .In both cases we have assumed that 1/3 of the sky is
mapped at a sensitivity of per resolution element.
Figure 1.9b: The contours show 50, 5, 2 and 0.1 percentile likelihood contours
for pairs of parameters determined from fits to the CMB power spectrum.
The figures to the left show results for an experiment with resolution
_{FWHM} = 1°. Those to the
right for a higher resolution resolution experiment with
_{FWHM} = 10' plotted with the
same scales (central column) and with expanded scales (rightmost column).
Notice how the accuracy of parameter estimation increases dramatically at the
higher angular resolution. In these examples, we have assumed that 1/3 of the
sky is observed at a sensitivity of
T/T = 2x10^{6} per resolution element.
(See Figure 1.5 for simulations of the CMB power spectra for these
experimental configurations.)
This figure shows that: (1) the parameters , h and are
relatively weakly coupled with each other and that the accuracy with which
these parameters can be measured is strongly dependent on angular resolution;
(2) some parameters are strongly coupled, for example the amplitude Q_{rms}
and spectral index n_{s}, but again with the angular resolution of PLANCK
the uncertainty on each parameter can be reduced to a few percent; (3) the
uncertainty on the amplitude of the gravitational wave component of the
fluctuations, r, depends only weakly on angular resolution because it is
determined by low order multipoles (cf. e.g. Knox 1995).
In summary, the analysis of this section shows that observations of
the CMB anisotropies with PLANCK are capable of determining
fundamental cosmological parameters to high precision. The only assumptions
involved are that the primordial fluctuations are adiabatic and characterized
by an approximately powerlaw spectral index, assumptions which themselves
can be verified from the PLANCK maps of the CMB anisotropies.
The physics underlying these predictions is extremely well
understood, involving only linear perturbation theory, and hence
the theoretical predictions presented here should be realistic. The
analysis provided in
From Observations to Scientific Information
shows that the frequency coverage and high sensitivity
of PLANCK will allow subtraction of foregrounds and discrete sources,
so that the CMB anisotropies should be retrieved over at least
1/3 of the sky with a sensitivity of , as assumed in this Section. No other technique is
capable of yielding results of such precision for parameters that have
yet to be measured reliably, despite many decades of research.
[last update: 1 August 1999 by P. Fosalba]