Reconstructing the parameter space of non-analytical cosmological fixed points

Abstract

Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a set of autonomous first-order differential equations. The fixed points of this autonomous set encode the asymptotic evolution of the model. Usually, these points can be written as analytical expressions for the variables in terms of the parameters of the model, which allows a complete characterization of the corresponding parameter space. However, a thoroughly analytical treatment is impossible in some cases. In this work, we give an example of a dark energy model, a scalar field coupled to a vector field in an anisotropic background, where not all the fixed points can be analytically found. Then, we put forward a general scheme that provides a numerical description of the parameter space. This allows us to find interesting accelerated attractors of the system with no analytical representation. This work may serve as a template for the numerical analysis of highly complicated dynamical systems.

13 pages, 13 figures, 1 table. Changes match the published version

References in corpus (40)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Dynamics of dark energy
• Cosmological parameters from SDSS and WMAP
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team
• In the Realm of the Hubble tension $-$ a Review of Solutions
• The High-Z Supernova Search: Measuring Cosmic Deceleration and Global Cur vature of the Universe Using Type Ia Supernovae
• Cosmological Constraints from the SDSS Luminous Red Galaxies
• Challenges for $\Lambda$CDM: An update
• Measuring the Baryon Acoustic Oscillation scale using the SDSS and 2dFGRS
• KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints
• Cosmological implications of baryon acoustic oscillation (BAO) measurements
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Are There Cosmic Microwave Background Anomalies?
• Measurements of the Hubble Constant: Tensions in Perspective
• Cosmology with tachyon field as dark energy
• Planck 2018 results. VII. Isotropy and Statistics of the CMB
• Dynamical systems applied to cosmology: dark energy and modified gravity
• Can interacting dark energy solve the $H_0$ tension?
• CMB Anomalies after Planck
• A Lower Growth Rate from Recent Redshift Space Distortion Measurements than Expected from Planck
• Cosmological dynamics of the tachyon with an inverse power-law potential
• Early-universe constraints on a Primordial Scaling Field
• Cosmology in generalized Proca theories
• Can the $H_0$ tension be resolved in extensions to $\Lambda$CDM cosmology?
• Tension between the power spectrum of density perturbations measured on large and small scales
• Tracking solutions in tachyon cosmology
• Testing the Isotropy of the Universe with Type Ia Supernovae
• Anisotropic power-law k-inflation
• Some Aspects of Tachyon Field Cosmology
• Introduction to the application of the dynamical systems theory in the study of the dynamics of cosmological models of dark energy
• Dynamical system analysis at background and perturbation levels: Quintessence in severe disadvantage comparing to $\Lambda$CDM
• Dynamical analysis of cosmological models with non-Abelian gauge vector fields
• Einstein Yang-Mills Higgs dark energy revisited
• Anisotropic Einstein Yang-Mills Higgs Dark Energy
• Anisotropic solid dark energy
• Anisotropic $k$-essence
• Dynamics of generalized tachyon field
• Recent Results from the MAXIMA Experiment

Cited by in corpus (3)

• Late-Time Anisotropy Sourced by a 2-Form Field Non-Minimally Coupled to Cold Dark Matter
• Dynamical Shortcomings in the Generalized SU(2) Proca Theory: Challenges for Cosmic Acceleration
• Horndeski in motion