The Hubble Slow Roll Expansion for Multi Field Inflation

We examine the dynamics of inflation driven by multiple, interacting scalar fields and derive a multi field version of the Hubble slow roll expansion. We show that the properties of this expansion naturally generalize those of the single field case. We present an analogous hierarchy of slow roll parameters, and derive the system of ``flow'' equations that describes their evolution, and show that when this system is truncated at finite order, it can always be solved exactly. Lastly, we express the scalar and tensor perturbation spectra in terms of the slow roll parameters

The seven deadly sins in La vida de Lazarillo de Tormes y de sus fortunas y adversidades

To the modern critic, La vida de Lazarillo de Tormes y de sus aventuras y adversidades poses many problems. One cannot arrive at the book\u27s precise meaning because the author remains unknown. If critics were to know who wrote the book, they would identify similarities between the book and the author\u27s life to approximate the book\u27s moral, or its lack of one. Additionally, some commentators view the book as incomplete or unfinished; although the author developed the first three tratados, the final four tratados seem short and incomplete. Does this diminish the book\u27s purpose? Can the readers still fruitfully discover the book\u27s meaning in an incomplete story? Modern critics have utilized the book\u27s artistic elements, such as its linguistic structure, themes and temporal structure, to arrive at an interpretation of it. Others have compared the book with classical European folklore and other period literary works. This thesis proposes a synthesis of the latter two approaches. This thesis will analyze, using irony and foreshadowing, how the seven tratados correlate or fail to correlate with the seven deadly sins

Spacetime Slices and Surfaces of Revolution

Under certain conditions, a $(1+1)$-dimensional slice $\hat{g}$ of a spherically symmetric black hole spacetime can be equivariantly embedded in $(2+1)$-dimensional Minkowski space. The embedding depends on a real parameter that corresponds physically to the surface gravity $\kappa$ of the black hole horizon. Under conditions that turn out to be closely related, a real surface that possesses rotational symmetry can be equivariantly embedded in 3-dimensional Euclidean space. The embedding does not obviously depend on a parameter. However, the Gaussian curvature is given by a simple formula: If the metric is written $g = \phi(r)^{-1} dr^2 + \phi(r) d\theta^2$, then \K_g=-{1/2}\phi''(r). This note shows that metrics $g$ and $\hat{g}$ occur in dual pairs, and that the embeddings described above are orthogonal facets of a single phenomenon. In particular, the metrics and their respective embeddings differ by a Wick rotation that preserves the ambient symmetry. Consequently, the embedding of $g$ depends on a real parameter. The ambient space is not smooth, and $\kappa$ is inversely proportional to the cone angle at the axis of rotation. Further, the Gaussian curvature of $\hat{g}$ is given by a simple formula that seems not to be widely known.Comment: 15 pages, added reference

On the Suppression of Parametric Resonance and the Viability of Tachyonic Preheating after Multi-Field Inflation

We investigate the feasibility of explosive particle production via parametric resonance or tachyonic preheating in multi-field inflationary models by means of lattice simulations. We observe a strong suppression of resonances in the presence of four-leg interactions between the inflaton fields and a scalar matter field, leading to insufficient preheating when more than two inflatons couple to the same matter field. This suppression is caused by a dephasing of the inflatons that increases the effective mass of the matter field. Including three-leg interactions leads to tachyonic preheating, which is not suppressed by an increase in the number of fields. If four-leg interactions are sub-dominant, we observe a slight enhancement of tachyonic preheating. Thus, in order for preheating after multi-field inflation to be efficient, one needs to ensure that three-leg interactions are present. If no tachyonic contributions exist, we expect the old theory of reheating to be applicable.Comment: v2: reference added, identical with PRD version, 23 pages, 3 figure