Primordial non-Gaussianity in the cosmological perturbations - CBPF

• there is baryonic matter, roughly one baryon per 10 9 photons, but no substantial amount of
antimatter;
• the chemical composition of baryonic matter is about 75% hydrogen, 25% helium, plus trace
amounts of heavier elements;
• baryons contribute only a small percentage of the total energy density; the rest is a dark
component, which appears to be composed of cold dark matter with negligible pressure (25%)
and dark energy with negative pressure (70%).
Observations of the fluctuations in the cosmic microwave background radiation suggest that
• there were only small fluctuations of order 10 −5 in the energy density distribution when the
universe was a thousand times smaller than now.
Any cosmological model worthy of consideration must be consistent with established facts. While
the standard big bang model accommodates most known facts, a physical theory is also judged
by its predictive power. At present, inflationary theory, naturally incorporating the success of the
standard big bang, has no competitor in this regard. Therefore, we will build upon the standard big
bang model, which will be our starting point, until we reach contemporary ideas of inflation. We
will then show how its prediction influences the CMB physics as well as the physics of the matter
perturbations. This set of notes also offers two Appendices about the generation of the baryon
asymmetry of the universe and the phase transitions in the early universe. These subjects will not
be covered during the lectures.
1 The Friedmann-Robertson-Walker metric
As discussed in the previous section, the distribution of matter and radiation in the observable
universe is homogeneous and isotropic. While this by no means guarantees that the entire universe is
smooth, it does imply that a region at least as large as our present Hubble volume is smooth. So long
as the universe is spatially homogeneous and isotropic on scales as large as the Hubble volume, for
purposes of description of our local Hubble volume we may assume the entire universe is homogeneous
and isotropic. While a homogeneous and isotropic region within an otherwise inhomogeneous and
anisotropic universe will not remain so forever, causality implies that such a region will remain
smooth for a time comparable to its light-crossing time. This time corresponds to the Hubble time,
about 10 Gyr. We have determined during the last part of the GR course that the metric of a
maximally symmetric space satisfying the Cosmological Principle is the the metric for a space with
homogeneous and isotropic spatial sections, that is the Friedmann-Robertson-Walker metric, which
can be written in the form
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