Evolution of superhorizon perturbations in early Universe with anisotropic solid remnant
Peter Mészáros, Daniel Račko
TL;DR
This work analyzes the evolution of superhorizon perturbations in an early radiation-dominated Universe containing a small anisotropic solid remnant from solid inflation, realized on a Bianchi type-I background with residual $SO(2)$ symmetry. The authors construct a two-fluid model with radiation plus a solid remnant described by a Lagrangian $\mathcal{L}_m = \lambda f(\Theta,\Omega)$, taking $f(\Theta,\Omega) = K \Theta^P \Omega^Q$ and performing a perturbative expansion in $\lambda$, focusing on the special case $P+Q=2$ to keep anisotropy under control. They derive background solutions and the superhorizon perturbation dynamics, finding that scalar and vector modes acquire growing solutions while tensor perturbations behave as in standard radiation; a growth exponent $\mathcal{Y}_1 \approx 3.85$ governs the vector sector, and a stability bound constrains the duration of the anisotropic phase. The observational implications are significant: the tensor-to-scalar ratio $r$ is suppressed and the vector-to-scalar ratio $s$ can be enhanced relative to the isotropic case, potentially improving agreement with Planck data in the simplified solid-inflation framework, while nonlinear effects and stabilization mechanisms offer avenues for further exploration.
Abstract
We study effects of presence of a small amount of so-called anisotropic solid remnant in the early post-inflationary Universe dominated by radiation. This model is inspired by solid inflation and its generalizations with matter described through a triplet of fields. In our model, the internal full global Euclidean symmetry of this triplet is broken, which leads to an anisotropic expansion of the Universe. Superhorizon scalar and vector perturbations grow, while behavior of tensor perturbations remains the same as in the standard case with Universe filled with only radiation. We also find a very interesting case within the limit of a very small amount of the anisotropic solid remnant and the longest possible duration of its presence, where size of vector perturbations decreases with a different power of scale factor as in the standard scenario. The obtained results improve agreement between the observational data and the theoretical predictions of solid inflation in a case with suppressed non-linear effects.