Artur Alho

Spherical linear waves in de Sitter spacetime

We apply Christodoulous framework, developed to study the Einstein-scalar field equations in spherical symmetry, to the linear wave equation in de Sitter spacetime, as a first step towards the Einstein-scalar field equations with positive cosmological constant. We obtain an integro-differential evolution equation, which we solve by taking initial data on a null cone. As a corollary, we obtain elementary derivations of expected properties of linear waves in de Sitter spacetime: boundedness in terms of (characteristic) initial data, and a Price law establishing uniform exponential decay, in Bondi time, to a constant.

Scalar field deformations of

This paper treats nonrelativistic matter and a scalar field phi with a monotonically decreasing potential minimally coupled to gravity in flat Friedmann-Lemaitre-Robertson-Walker cosmology. The fie ...

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We study flat Friedmann-Lemaitre-Robertson-Walker alpha-attractor E- and T-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimension ...

CDM cosmology

We derive a set of equations monitoring the evolution of covariant and gauge-invariant linear scalar perturbations of Friedman-Lema^itre-Robertson-Walker models with multiple interacting non-linear scalar fields. We use a dynamical systems approach in order to perform a stability analysis for some classes of scalar field potentials. In particular, using a recent approximation for the inflationary dynamics of the background solution, we derive conditions under which homogenization occurs for chaotic (quadratic and quartic potentials) and new inflation. We also prove a cosmic no-hair result for power-law inflation and its generalisation for two scalar fields with independent exponential potentials (assisted power-law inflation).

Inflationary alpha-attractor cosmology : A global dynamical systems perspective

We study the Einstein-scalar field system with positive cosmological constant and spherically symmetric characteristic initial data given on a truncated null cone. We prove well-posedness, global existence and exponential decay in (Bondi) time, for small data. From this, it follows that initial data close enough to de Sitter data evolves to a causally geodesically complete spacetime (with boundary), which approaches a region of de Sitter asymptotically at an exponential rate; this is a non-linear stability result for de Sitter within the class under consideration, as well as a realization of the cosmic no-hair conjecture.

Covariant and gauge-invariant linear scalar perturbations in multiple scalar field cosmologies

Nonlinear scalar fields have been important to model the presently observed accelerated cosmological expansion as well as the inflationary phase of the early universe. An underlying mathematical property is common to these two epochs: The presently observed universe is approximately homogeneous on sufficiently large scales and, in turn, inflation requires a pre-existing homogeneous patch over a horizon volume, in general. So, both at early and late times, spatial homogeneity plays an important role in cosmology. Given that generic initial conditions contain inhomogeneities, an interesting question is under what conditions will those inhomogeneities die out to the future. This question can be studied using linear perturbation theory on the spatially homogeneous and isotropic backgrounds of Friedman-Lemaitre-RobertsonWalker (FLRW). On a FLRW background, linear scalar perturbations Δ(x, τ) satisfy a partial differential equation (PDE) of the form

The Problem of a Self-Gravitating Scalar Field with Positive Cosmological Constant

We review recent work on the study of the wave equation in a fixed de Sitter background. This is to be seen as a first step in the direction of the full Einstein-Λ-scalar field system in spherical symmetry.

Homogenization of scalar field cosmologies

We review recent progress concerning the study of the Einstein-scalar field system with positive cosmological constant in spherical symmetry. We focus on the associated uncoupled wave equations and discuss how such linear case can shed light on the non-liner problem.

Towards the Einstein-Α-scalar field system in spherical symmetry

We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.

Linear and non-linear waves in de Sitter

We study covariant and gauge-invariant linear scalar perturbations of a scalar-field with positive exponential potential in a flat Robertson-Walker background. By applying a dynamical systems approach we investigate how the phase of the perturbations evolves, finding bounds on the wave-number in terms of the slope parameter, for which the perturbations decays when approaching the inflationary solution.