[Paper Review] Chiral Cosmological Models: Dark Sector Fields Description

S. V. Chervon|arXiv (Cornell University)|Mar 28, 2014

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper proposes a chiral cosmological model (CCM) based on a self-gravitating nonlinear sigma model with interacting dark sector fields to describe both early inflation and late-time accelerated expansion. By analyzing a two-component system of a phantom field and a canonical scalar field, the authors derive exact solutions, generalize quintom models, and show that dark sector perturbations significantly alter gravitational perturbations, leading to deviations from standard inflationary predictions in long-wavelength approximations.

ABSTRACT

The present review is devoted to a Chiral Cosmological Model as the self-gravitating nonlinear sigma model with the potential of (self)interactions employed in cosmology. The chiral cosmological model has successive applications in descriptions of the inflationary epoch of the Universe evolution; the present accelerated expansion of the Universe also can be described by the chiral fields multiplet as the dark energy in wide sense. To be more illustrative we are often addressed to the two-component chiral cosmological model. Namely, the two-component chiral cosmological model describing the phantom field with interaction to a canonical scalar field is analyzed in details. New generalized model of quintom character is proposed and exact solutions are founded out. In the review we represented the perturbation theory for chiral cosmological model with the aim to describe the structure formation using the progress achieved in the inflation theory. It was shown that cosmological perturbations from chiral fields can be decomposed for inflaton and the dark sector perturbations. The two-component model is investigated in details, the general solution for shortwave approximation is obtained and analyzed for power law Universe expansion. New issue for understanding the features of Universe evolution is proposed by consideration of the dark sector fields on the inflaton background. The results are illustrated for the solutions in the long-wave approximation.

Motivation & Objective

• To develop a unified framework for describing both inflationary and dark energy epochs using a chiral cosmological model based on nonlinear sigma models.
• To address the limitations of single-field models by incorporating interacting dark sector fields, including phantom and canonical scalar fields.
• To generalize quintom-type models by introducing new interaction structures and deriving exact solutions.
• To investigate cosmological perturbations in the presence of dark sector fields, particularly their decomposition into inflaton and dark sector components.
• To analyze the impact of dark sector fields on structure formation by solving perturbation equations in power-law and long-wavelength approximations.

Proposed method

• Formulate the chiral cosmological model as a self-gravitating nonlinear sigma model (NSM) with a target space metric and self-interaction potential.
• Use conformal time parametrization and power-law scale factor ansatz $ a( au) \propto \tau^{\alpha} $ to simplify the field equations.
• Apply the isometric embedding method to solve the NSM equations for cosmological metrics, including Friedmann-Robertson-Walker and anisotropic cases.
• Derive the gravitational perturbation equation $ \Phi^{\prime\prime} - \nabla^2\Phi + 2\Phi'\left(\frac{\alpha+1}{\eta}\right) + \kappa W = 0 $, incorporating dark sector interactions.
• Introduce a kinetic interaction $ h_{22} = \psi^2 $ and a double-power-law potential $ W = -K_1^2\psi^{\lambda_1} + K_2^2\psi^{\lambda_2} + W_0 $ to model dark sector dynamics.
• Solve the perturbation equations in the long-wavelength limit by neglecting $ \nabla^2\Phi $, yielding exact expressions for $ \Phi $ in terms of conformal time.

Experimental results

Research questions

• RQ1 How can the chiral cosmological model with interacting dark sector fields describe both early inflation and late-time accelerated expansion?
• RQ2 What are the exact solutions for a two-component chiral model with a phantom field coupled to a canonical scalar field?
• RQ3 How do dark sector fields modify cosmological perturbations compared to standard single-field inflation?
• RQ4 What is the role of the dark sector potential $ W $ in shaping gravitational perturbations in the long-wavelength limit?
• RQ5 Can the chiral model be generalized into a quintom-like framework with exact solutions and observable consequences for structure formation?

Key findings

• The chiral cosmological model successfully describes both inflationary and late-time accelerated expansion using a single nonlinear sigma model framework.
• Exact solutions for the two-component model are derived, with $ \psi = \beta\eta $ and $ \chi = \chi_0 - \frac{1}{(2\alpha+1)}\eta^{-(2\alpha+1)} $, valid in power-law expansion.
• The dark sector potential is found to be $ W = -\frac{1}{a_s^2\beta}\psi^3 + \frac{C_1^2}{2a_s^2\beta^9}\psi^4 + W_0 $ for $ m=3 $, corresponding to $ \alpha = 2 $.
• Gravitational perturbations in the long-wavelength limit are given by $ \Phi = \frac{\kappa\beta^2}{15a_s^2}\eta^5 - \frac{\kappa C_1^2}{48a_s^2\beta^5}\eta^6 + \frac{C_2}{2\eta^2} $, deviating from standard $ \Phi^{(0)} \propto \eta^{1+\alpha} $.
• The inclusion of dark sector fields leads to non-standard perturbation behavior, with no terms matching the standard solution (116) for any $ \alpha $, indicating a crucial departure from conventional inflation.
• The model provides a new mechanism for structure formation by showing that dark sector fields significantly alter the growth of gravitational potential perturbations, especially in the long-wavelength regime.