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 ζ\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

δN\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