Superpotential method for chiral cosmological models connected with modified gravity

Abstract

We consider the Chiral Cosmological Models (CCMs) and modified gravity theories associated with them. Generalization of the superpotential method for a general CCM with several scalar fields is performed, and the method of construction CCMs admitting exact solutions is developed. New classes of exact solutions in the two-component CCM connected with an $f(R)$ gravity model with an additional scalar field have been constructed. We construct new cosmological solutions for a diagonal metric of the target space, including modified power-law solutions. In particular, we propose the reconstruction procedure based on the superpotential method and present examples of kinetic part reconstruction for periodic and hyperbolic Hubble parameters. We also focus on a cyclic type of Universe dubbed the Quasi-Steady State (QSS) model, with the aim of constructing single- and double-field potentials for one and the same behaviour of the Hubble parameter using the developed superpotential method for the CCM. The realization of this task includes a new set of solutions for a CCM with a scale factor characterized by the QSS theory. We also propose a method for reducing the two-field CCM to the single scalar field model.

27 pages, minor clarifications added, typos corrected, revised version to appear in Phys. Rev. D

References in corpus (25)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The Standard Model Higgs boson as the inflaton
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey
• Can dark energy evolve to the Phantom?
• Inflation scenario via the Standard Model Higgs boson and LHC
• Conformal Transformations with Multiple Scalar Fields
• Quintom cosmologies admitting either tracking or phantom attractors
• Quintom cosmologies with arbitrary potentials
• Curvature Perturbation Spectrum in Two-field Inflation with a Turning Trajectory
• Hamilton-Jacobi method for Domain Walls and Cosmologies
• Universality classes for models of inflation
• Observational Constraints on New Exact Inflationary Scalar-field Solutions
• Some like it hot: $R^2$ heals Higgs inflation, but does not cool it
• Global stability analysis for cosmological models with non-minimally coupled scalar fields
• Reconstruction of Scalar Potentials in Modified Gravity Models
• Cosmological Solutions in Multiscalar Field Theory
• Hamilton-Jacobi Mechanics from Pseudo-Supersymmetry
• Reconstruction of scalar potentials in two-field cosmological models
• First-order formalism for dark energy and dust
• An Emergent Universe supported by chiral cosmological fields in Einstein--Gauss--Bonnet gravity
• Cosmological Model of Interacting Tachyon Field
• Unified dark matter and dark energy description in a chiral cosmological model
• First-order formalism for the quintom model of dark energy
• Testing Two-Field Inflation

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• Classical and quantum exact solutions for a FRW in chiral like cosmology
• Superpotential method for $F(R)$ cosmological models
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• Quintom fields from chiral K-essence cosmology
• Asymptotic behavior of $N$-fields Chiral Cosmology
• New conservation laws and exact cosmological solutions in Brans-Dicke cosmology with an extra scalar field
• Anisotropic chiral cosmology: exact solutions
• Dynamical system analysis in modified Galileon cosmology
• Quintom fields from chiral anisotropic cosmology
• New method of exponential potentials reconstruction based on given scale factor in phantonical two-field models
• New exact solutions in multi-scalar field cosmology
• Primordial Black Holes in Induced Gravity Inflationary Models with Two Scalar Fields
• Multiscalar field cosmological model and possible solutions using Noether symmetry approach
• Anisotropic solutions for $R^2$ gravity model with a scalar field
• Primordial black holes formation in inflationary $F(R)$ models with scalar fields
• New Integrable Chiral Cosmological Models with Two Scalar Fields
• Integrable Cosmological Models with an Arbitrary Number of Scalar Fields