Inflation over the hill

We calculate the power spectrum of curvature perturbations when the inflaton field is rolling over the top of a local maximum of a potential. We show that the evolution of the field can be decomposed into a late-time attractor, which is identified as the slow roll solution, plus a rapidly decaying non-slow roll solution, corresponding to the field rolling ``up the hill'' to the maximum of the potential. The exponentially decaying transient solution can map to an observationally relevant range of scales because the universe is also expanding exponentially. We consider the two branches separately and we find that they are related through a simple transformation of the slow roll parameter $\eta$ and they predict identical power spectra. We generalize this approach to the case where the inflaton field is described by both branches simultaneously and find that the mode equation can be solved exactly at all times. Even though the slow roll parameter $\eta$ is evolving rapidly during the transition from the transient solution to the late-time attractor solution, the resultant power spectrum is an exact power-law spectrum. Such solutions may be useful for model-building on the string landscape.Comment: 11 pages, 1 figure (V3: Version accepted by PRD, title changed by journal

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

Spectroscopy of the quantum black hole

We develop the idea that, in quantum gravity where the horizon fluctuates, a black hole should have a discrete mass spectrum with concomitant line emission. Simple arguments fix the spacing of the lines, which should be broad but unblended. Assuming uniformity of the matrix elements for quantum transitions between near levels, we work out the probabilities for the emission of a specified series of quanta and the intensities of the spectral lines. The thermal character of the radiation is entirely due to the degeneracy of the levels, the same degeneracy that becomes manifest as black hole entropy. One prediction is that there should be no lines with wavelength of order the black hole size or larger. This makes it possible to test quantum gravity with black holes well above Planck scale.Comment: RevTeX, 9 page

On Adiabatic Renormalization of Inflationary Perturbations

We discuss the impact of adiabatic renormalization on the power spectrum of scalar and tensor perturbations from inflation. We show that adiabatic regularization is ambiguous as it leads to very different results, for different adiabatic subtraction schemes, both in the range v\equiv k/(aH) \gsim 0.1 and in the infrared regime. All these schemes agree in the far ultraviolet, $v\gg 1$. Therefore, we argue that in the far infrared regime, $v\ll 1$, the adiabatic expansion is no longer valid, and the unrenormalized spectra are the physical, measurable quantities. These findings cast some doubt on the validity of the adiabatic subtraction at horizon exit, $v=1$, to determine the perturbation spectra from inflation which has recently advocated in the literature.Comment: 7 pages, 3 figures, revtex. New version with more results and modified plot

Path Integral Quantization of Cosmological Perturbations

We derive the first order canonical formulation of cosmological perturbation theory in a Universe filled by a few scalar fields. This theory is quantized via well-defined Hamiltonian path integral. The propagator which describes the evolution of the initial (for instance, vacuum) state, is calculated.Comment: 16 pages, ETH-TH/94-0

Nucleosynthesis Without a Computer

I derive completely analytically the time evolution and final abundances of the light elements (up to Be-7) formed in the big-bang nucleosynthesis.This highlights an interesting physics taking place during the formation of light elements in the early universe.Comment: 3 figures; uses tcilate