Analytical $poly\Lambda$CDM dynamics

Abstract

We develop a novel analytical dynamical analysis to derive precise energy density ratio evolutions for the $\varphi$CDM and $poly\Lambda$CDM models, comparing them to the standard $\Lambda$CDM model and validating against numerical solutions. Analytical solutions for the quintessence, i.e. $\varphi$CDM, show sub percent agreement with $\Lambda$CDM with greater reliability than numerical integration of stiff systems. The $poly\Lambda$CDM model, a phenomenological modified gravity framework, captures radiation, matter, dark energy, and exotic epochs, offering a streamlined yet comprehensive alternative to existing studies. Its dynamics reveal a global transition from a dark energy-dark matter exchange reflector, through saddle points of matter, radiation, curvature, and modified gravity, to an SVT modified gravity attractor-saddle, and finally to a cosmological constant attractor in the far future, with saddle transitions between modified gravity components. The $poly\Lambda$CDM model integrates modified gravity models, using dynamical analysis to distinguish observationally viable critical points and differentiate gravity epochs. All three models align with observed cosmic evolution, but $poly\Lambda$CDM richer phenomenology provides deeper insights into modified gravity dynamics. Code available at GitHub.

46 pages, 10 figures, preprint version of the one accepted in PDU

References in corpus (21)

• Dynamics of dark energy
• The Effective Field Theory of Cosmological Large Scale Structures
• Euclid. I. Overview of the Euclid mission
• Teleparallel Gravity: From Theory to Cosmology
• The $H_0$ Olympics: A fair ranking of proposed models
• A Parameterized Post-Friedmann Framework for Modified Gravity
• The Parameterized Post-Friedmann Framework for Theories of Modified Gravity: Concepts, Formalism and Examples
• $Euclid$ preparation: XV. Forecasting cosmological constraints for the $Euclid$ and CMB joint analysis
• Testing the theory of gravity with DESI: estimators, predictions and simulation requirements
• Non-Local Gravity Cosmology: an Overview
• Phenomenology of theories of gravity without Lorentz invariance: the preferred frame case
• Dark energy beyond quintessence: Constraints from the swampland
• Cosmological perturbations in modified teleparallel gravity models: Boundary term extension
• Observational Constraints in Metric-Affine Gravity
• Diagnostic of Horndeski Theories
• Non-Local Curvature Gravity Cosmology via Noether Symmetries
• Cosmological Perturbation Theory in Metric-Affine Gravity
• A comparison between axion-like and power law potentials in cosmological background
• The Homogeneity Scale of the universe
• Advanced manifold-metric pairs
• Simple $\varphi \Lambda$ CDM dynamics