arXiv subjects

D. Varela

Publications and source records attributed to D. Varela.

3 recordsLinked to original sources

arXiv2020

Inflationary Twin Models

We introduce the concept of inflationary twin models, that is, a class of generalized (kinetic or "K-inflation") field theories which lead exactly to the same cosmological evolution during the inflationary period as a given standard scalar field theory of inflation. The twin concept permits to introduce generalized, K-inflation theories in a controlled manner, maintaining some inflationary predictions unaltered. Further, this concept allows to extend analytical tools like the slow-roll expansion to the realm of K-inflation theories, facilitating their investigation. Twins of a standard scalar field model of inflation still may result in different results for some inflationary observables, because of their nontrivial scalar speed of sound. This implies that non-standard twins may lead to completely viable models of inflation, even if their standard twin is ruled out by observations. We provide some explicit examples of this possibility, including the physical case of a dilaton--Dirac-Born-Infeld theory.

hep-th↗

arXiv2019

The superpotential method in cosmological inflation

Scalar field cosmological inflation has a first integral relating the Hubble function and the lagrangian of the scalar field(s), which is known under the names of "Hamilton-Jacobi approach" or "superpotential equation". Here we exploit the simplicity of this superpotential equation and use it as an alternative but equivalent cosmological evolution equation during inflation, replacing the Friedman-Robertson-Walker (FRW) equations. It turns out that all inflationary observables can be calculated directly from its solution (the superpotential). Further, the superpotential equation allows for a simple and direct calculation of the slow-roll expansion to arbitrary order and, in many cases, for an exact determination of the slow-roll attractor. It also allows for a power series expansion in the inflaton field which permits to estimate the radius of convergence of the slow-roll expansion. We consider several examples of single-field inflationary models to demonstrate the simplicity and usefulness of the method.

gr-qc↗

arXiv2010

The Cauchy-Schlomilch transformation

The Cauchy-Schlömilch transformation states that for a function $f$ and $a, \, b > 0$, the integral of $f(x^{2})$ and $af((ax-bx^{-1})^{2}$ over the interval $[0, \infty)$ are the same. This elementary result is used to evaluate many non-elementary definite integrals, most of which cannot be obtained by symbolic packages. Applications to probability distributions is also given.

math.CA↗