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R. Brandenberger
the distribution of matter and radiation, most spectacularly the high precision all
sky maps of the cosmic microwave background (CMB) radiation [1]. The angular
power spectrum of these anisotropies shows that the fluctuations are scale-invariant
on large scales and are characterized by acoustic oscillations on smaller scales.
What is the origin of these fluctuations?
The physics which yields the abovementioned acoustic oscillations in the angular
power spectrum of CMB fluctuations was discussed in two pioneering papers
[2, 3]. These authors assumed the existence of a roughly scale-invariant spectrum
of curvature fluctuations on super-Hubble scales (the Hubble radius is H −1 (t),
where H is the Hubble expansion rate) at a time before recombination. These
fluctuations are standing waves which are frozen in until the time when the Hubble
radius becomes larger than the length scale of the fluctuations (in the linear regime
fluctuations have constant wavelength in comoving coordinates; hence, in the
matter-dominated epoch their physical wavelength grows as t 2/3 while the Hubble
radius grows at the faster rate ∼t). After they enter they begin to oscillate. Modes
which have performed an even (odd) number of half oscillations by the time of
recombination yield maxima (local minima) in the power spectrum. The papers
[2, 3] date back to 10 years before the development of inflationary cosmology. Both
the CMB acoustic oscillations and the baryon acoustic oscillations in the power
spectrum of matter fluctuations were predicted already then.
The question which was not addressed in [2, 3] is the origin of the superHubble fluctuations at early times. In Standard Big Bang cosmology the Hubble
radius equals the horizon, and hence having super-Hubble fluctuations appears to be
acausal. Inflationary cosmology [4] was the first scenario to propose an origin [5]
for these fluctuations, but now we know that it is not the only one. In the following
I will develop necessary criteria for an early universe scenario to be able to explain
the near homogeneity of the universe and the origin of the observed cosmological
perturbations. I will then introduce a couple of early universe scenarios which satisfy
the criteria. In Sect. 3 I will turn to the question of which early universe scenario
might emerge from superstring theory.
2 Early Universe Scenarios
The first criterion which a successful early universe scenario must satisfy is that the
horizon (the radius of the forward light cone of a point on the initial value surface)
is much larger than the Hubble radius H −1 (t) at late times. This is necessary to be
able to address the horizon problem of Standard Big Bang cosmology. In order to
admit the possibility of a causal mechanism to generate the primordial fluctuations,
comoving scales which are probed with current cosmological observations must
originate inside the Hubble radius at early times. This is the second criterion. If
the fluctuations emerge as quantum vacuum perturbations (as they are postulated
to in inflationary cosmology), then scales we observe today must evolve for a long
time on super-Hubble scales in order to obtain the squeezing of the fluctuations
R. Brandenberger
the distribution of matter and radiation, most spectacularly the high precision all
sky maps of the cosmic microwave background (CMB) radiation [1]. The angular
power spectrum of these anisotropies shows that the fluctuations are scale-invariant
on large scales and are characterized by acoustic oscillations on smaller scales.
What is the origin of these fluctuations?
The physics which yields the abovementioned acoustic oscillations in the angular
power spectrum of CMB fluctuations was discussed in two pioneering papers
[2, 3]. These authors assumed the existence of a roughly scale-invariant spectrum
of curvature fluctuations on super-Hubble scales (the Hubble radius is H −1 (t),
where H is the Hubble expansion rate) at a time before recombination. These
fluctuations are standing waves which are frozen in until the time when the Hubble
radius becomes larger than the length scale of the fluctuations (in the linear regime
fluctuations have constant wavelength in comoving coordinates; hence, in the
matter-dominated epoch their physical wavelength grows as t 2/3 while the Hubble
radius grows at the faster rate ∼t). After they enter they begin to oscillate. Modes
which have performed an even (odd) number of half oscillations by the time of
recombination yield maxima (local minima) in the power spectrum. The papers
[2, 3] date back to 10 years before the development of inflationary cosmology. Both
the CMB acoustic oscillations and the baryon acoustic oscillations in the power
spectrum of matter fluctuations were predicted already then.
The question which was not addressed in [2, 3] is the origin of the superHubble fluctuations at early times. In Standard Big Bang cosmology the Hubble
radius equals the horizon, and hence having super-Hubble fluctuations appears to be
acausal. Inflationary cosmology [4] was the first scenario to propose an origin [5]
for these fluctuations, but now we know that it is not the only one. In the following
I will develop necessary criteria for an early universe scenario to be able to explain
the near homogeneity of the universe and the origin of the observed cosmological
perturbations. I will then introduce a couple of early universe scenarios which satisfy
the criteria. In Sect. 3 I will turn to the question of which early universe scenario
might emerge from superstring theory.
2 Early Universe Scenarios
The first criterion which a successful early universe scenario must satisfy is that the
horizon (the radius of the forward light cone of a point on the initial value surface)
is much larger than the Hubble radius H −1 (t) at late times. This is necessary to be
able to address the horizon problem of Standard Big Bang cosmology. In order to
admit the possibility of a causal mechanism to generate the primordial fluctuations,
comoving scales which are probed with current cosmological observations must
originate inside the Hubble radius at early times. This is the second criterion. If
the fluctuations emerge as quantum vacuum perturbations (as they are postulated
to in inflationary cosmology), then scales we observe today must evolve for a long
time on super-Hubble scales in order to obtain the squeezing of the fluctuations