104 An introduction to the physics of cosmology
n= 1. 01 ± 0. 09.The only parameter left undetermined by the CMB is the Hubble constant,h.
Recent work (e.g. Mouldet al2000) suggests that this is now determined to an
rms accuracy of 10%, and we adopt a central value ofh= 0 .70. This completes
the cosmological model, requiring a total matter density parameterc+b=
0. 35 ± 0 .14, very nicely consistent with what is required to be consistent with
σ 8 for exactly scale-invariant fluctuations. The predicted fluctuation shape is also
very sensible for this model:= 0 .18.
The fact that such a ‘vanilla’ model matches the main cosmological data
so well is a striking achievement, but it raises a number of issues. One is that
the baryon density inferred from the data exceeds that determined via primordial
nucleosynthesis by about a factor 1.5. This may sound like good agreement, but
both the CMB and nucleosynthesis are now impressively precise areas of science,
and neither can easily accommodate the other’s figure. The boring solution is that
small systematics will eventually be identified that allow a compromise figure.
Alternatively, this inconsistency could be the first sign that something is rotten
in the basic framework. However, it is too early to make strong claims in this
direction.
Of potentially greater significance is the fact that this successful fit has been
achieved using scalar fluctuations alone; indeed, the tensor modes are not even
mentioned by Jaffeet al(2000). To a certain extent, the presence of tensor modes
can be hidden by adjustments in the other parameters. There can be no acoustic
peak in the tensor contribution, so that the addition of tensors would require larger
peak in the scalar component to compensate, pushing in the direction of universes
that are of lower density, with larger baryon fractions. However, this would make
it harder to keep higher harmonics of the acoustic oscillations low – and it is
the lack of detection of any second and third peaks that forces the high baryon
density in this solution. There would also be the danger of spoiling the very good
agreement with other constraints, such as theσ 8 normalization. We therefore have
to face the unpalatable fact that there is as yet no sign of the two generic signatures
expected from inflationary models: tilt and a significant tensor contribution. It
may be that the next generation of CMB experiments will detect such features
at a low level. If they do not, and the initial conditions for structure formation
remain as they presently seem to be (scale-invariant adiabatic scalar modes), then
the heroic vision of using cosmology to probe physics near the Planck scale may
not be achieved. The stakes are high.
References
Abramowitz M and Stegun I A 1965Handbook of Mathematical Functions(New York:
Dover)
Adelberger K, Steidel C, Giavalisco M, Dickinson M, Pettini M and Kellogg M 1998
Astrophys. J. 50518