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R. Brandenberger
to the expanding phase of Standard Big Bang cosmology (see e.g. [16] for a review).
In the emergent scenario, the horizon is infinite, and scales which are observed
today are trivially sub-Hubble in the emergent phase (since the Hubble radius is
infinite in the limit that the emergent phase is static). As discovered in [17], the
spectrum of cosmological perturbations originating from thermal fluctuations of the
string gas is nearly scale-invariant. A prediction with which String Gas Cosmology
can be distinguished from simple inflationary models is the tilt of the spectrum
of primordial gravitational waves. Whereas inflationary models based on a matter
content which satisfies the usual energy conditions predict a slight red tilt of the
spectrum, String Gas Cosmology predicts a blue tilt n t satisfying a consistency
relation n t = n s −1, where n s −1 is the tilt of the spectrum of curvature fluctuations
[18].
None of the early universe scenarios discussed above is without problems. In
the case of inflationary cosmology we can point to the trans-Planckian problem for
fluctuations: if the period of inflation is much longer than the minimal period which
inflation has to last in order to enable a causal generation mechanism of fluctuations,
the length scale of all modes which are currently observed today was smaller than
the Planck length at the beginning of inflation [19]. Thus, new physics must enter to
give the initial conditions for the fluctuations.
As discussed in [20], the matter bounce scenario is not a local attractor in initial
condition space: initial anisotropies blow up during the contracting phase. The
Ekpyrotic scenario does better in this respect: initial anisotropies decay and the
homogeneous Ekpyrotic contracting trajectory is a local attractor in initial condition
space [21]. Note that in the case of large field inflation, the inflationary slow-roll
trajectory is also a local attractor [22]. A key challenge for bouncing scenarios is that
new physics is required to yield the cosmological bounce. An important problem for
the emergent scenario is to obtain dynamical equations which describe the emergent
phase.
Both inflationary and Ekpyrotic models are obtained in the context of Einstein
gravity by taking the dominant component of matter to be given by a scalar field ϕ
with a potential V (ϕ). To obtain slow-roll inflation the potential has to be very flat
V
V
λ m
−1
pl ,
(1)
where the prime indicates a derivative with respect to ϕ, and where m pl is the Planck
mass. For models free of an initial condition fine tuning problem the field ϕ must roll
over a field range |Δϕ| > m pl during inflation. In contrast, the Ekpyrotic scenario
is based on scalar field matter with a negative and steep exponential potential. V /V
is large in Planck units, and the scalar field rolls a distance smaller than m pl .
I highlight this point in connection with the constraints on effective field theories
involving scalar fields which emerge from the considerations based on fundamental
physics to be discussed in the following section.
R. Brandenberger
to the expanding phase of Standard Big Bang cosmology (see e.g. [16] for a review).
In the emergent scenario, the horizon is infinite, and scales which are observed
today are trivially sub-Hubble in the emergent phase (since the Hubble radius is
infinite in the limit that the emergent phase is static). As discovered in [17], the
spectrum of cosmological perturbations originating from thermal fluctuations of the
string gas is nearly scale-invariant. A prediction with which String Gas Cosmology
can be distinguished from simple inflationary models is the tilt of the spectrum
of primordial gravitational waves. Whereas inflationary models based on a matter
content which satisfies the usual energy conditions predict a slight red tilt of the
spectrum, String Gas Cosmology predicts a blue tilt n t satisfying a consistency
relation n t = n s −1, where n s −1 is the tilt of the spectrum of curvature fluctuations
[18].
None of the early universe scenarios discussed above is without problems. In
the case of inflationary cosmology we can point to the trans-Planckian problem for
fluctuations: if the period of inflation is much longer than the minimal period which
inflation has to last in order to enable a causal generation mechanism of fluctuations,
the length scale of all modes which are currently observed today was smaller than
the Planck length at the beginning of inflation [19]. Thus, new physics must enter to
give the initial conditions for the fluctuations.
As discussed in [20], the matter bounce scenario is not a local attractor in initial
condition space: initial anisotropies blow up during the contracting phase. The
Ekpyrotic scenario does better in this respect: initial anisotropies decay and the
homogeneous Ekpyrotic contracting trajectory is a local attractor in initial condition
space [21]. Note that in the case of large field inflation, the inflationary slow-roll
trajectory is also a local attractor [22]. A key challenge for bouncing scenarios is that
new physics is required to yield the cosmological bounce. An important problem for
the emergent scenario is to obtain dynamical equations which describe the emergent
phase.
Both inflationary and Ekpyrotic models are obtained in the context of Einstein
gravity by taking the dominant component of matter to be given by a scalar field ϕ
with a potential V (ϕ). To obtain slow-roll inflation the potential has to be very flat
V
V
λ m
−1
pl ,
(1)
where the prime indicates a derivative with respect to ϕ, and where m pl is the Planck
mass. For models free of an initial condition fine tuning problem the field ϕ must roll
over a field range |Δϕ| > m pl during inflation. In contrast, the Ekpyrotic scenario
is based on scalar field matter with a negative and steep exponential potential. V /V
is large in Planck units, and the scalar field rolls a distance smaller than m pl .
I highlight this point in connection with the constraints on effective field theories
involving scalar fields which emerge from the considerations based on fundamental
physics to be discussed in the following section.