353 research outputs found

### Perturbations in k-inflation

We extend the theory of cosmological perturbations to the case when the
``matter'' Lagrangian is an arbitrary function of the scalar field and its
first derivatives. In particular, this extension provides a unified description
of known cases such as the usual scalar field and the hydrodynamical perfect
fluid. In addition, it applies to the recently proposed k-inflation, which is
driven by non-minimal kinetic terms in the Lagrangian. The spectrum of quantum
fluctuations for slow-roll and power law k-inflation is calculated. We find,
for instance, that the usual ``consistency relation'' between the tensor
spectral index and the relative amplitude of scalar and tensor perturbations is
modified. Thus, at least in principle, k-inflation is phenomenologically
distinguishable from standard inflation.Comment: 12 pages, LaTe

### Holographic inflation and the conservation of $\zeta$

In a holographic description of inflation, cosmological time evolution in the
bulk is expected to correspond to the renomalization group (RG) flow in a dual
boundary theory. Here, we analyze this expectation by computing the correlation
functions of the curvature perturbation $\zeta$ holographically. For this
purpose, we use a deformed conformal field theory at the boundary, with a
single deformation operator. In standard single field models of inflation,
$\zeta$ is known to be conserved at large scales under very general conditions.
However, we find that this is not generically the case in the dual description.
The requirement that higher correlators of $\zeta$ should be conserved severely
restricts the possibilities for the RG flow. With such restriction, the power
spectrum $P_\zeta$ must follow an exact power law, at least within the regime
of validity of conformal perturbation theory.Comment: 27 pages, 1 figure; v2: version to appear in JHE

### Cosmological perturbations in the 5D Big Bang

Bucher [Bucher2001] has recently proposed an interesting brane-world
cosmological scenario where the ``Big Bang'' hypersurface is the locus of
collision of two vacuum bubbles which nucleate in a five dimensional flat
space. This gives rise to an open universe, where the curvature can be very
small provided that $d/R_0$ is sufficiently large. Here, d is the distance
between bubbles and $R_0$ is their size at the time of nucleation. Quantum
fluctuations develop on the bubbles as they expand towards each other, and
these in turn imprint cosmological perturbations on the initial hypersurface.
We present a simple formalism for calculating the spectrum of such
perturbations and their subsequent evolution. We conclude that, unfortunately,
the spectrum is very tilted, with spectral index $n_s=3$. The amplitude of
fluctuations at horizon crossing is given by $\sim
(R_0/d)^2 S_E^{-1} k^2$, where $S_E\gg 1$ is the Euclidean action of the
instanton describing the nucleation of a bubble and k is the wavenumber in
units of the curvature scale. The spectrum peaks on the smallest possible
relevant scale, whose wave-number is given by $k\sim d/R_0$. We comment on the
possible extension of our formalism to more general situations where a Big Bang
is ignited through the collision of 4D extended objects.Comment: 7 page

### $\delta N$ formalism from superpotential and holography

We consider the superpotential formalism to describe the evolution of scalar
fields during inflation, generalizing it to include the case with non-canonical
kinetic terms. We provide a characterization of the attractor behaviour of the
background evolution in terms of first and second slow-roll parameters (which
need not be small). We find that the superpotential is useful in justifying the
separate universe approximation from the gradient expansion, and also in
computing the spectra of primordial perturbations around attractor solutions in
the $\delta N$ formalism. As an application, we consider a class of models
where the background trajectories for the inflaton fields are derived from a
product separable superpotential. In the perspective of the holographic
inflation scenario, such models are dual to a deformed CFT boundary theory,
with $D$ mutually uncorrelated deformation operators. We compute the bulk power
spectra of primordial adiabatic and entropy cosmological perturbations, and
show that the results agree with the ones obtained by using conformal
perturbation theory in the dual picture.Comment: 37 page

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