Analytical $polyΛ$CDM dynamics
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arXiv
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| Format: | Preprint |
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2026
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| author | Ntelis, Pierros Said, Jackson Levi |
| author_facet | Ntelis, Pierros Said, Jackson Levi |
| contents | We develop a novel analytical dynamical analysis to derive precise energy density ratio evolutions for the $ϕ$CDM and $polyΛ$CDM models, comparing them to the standard $Λ$CDM model and validating against numerical solutions. Analytical solutions for the quintessence, i.e. $ϕ$CDM, show sub percent agreement with $Λ$CDM with greater reliability than numerical integration of stiff systems. The $polyΛ$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 $polyΛ$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 $polyΛ$CDM richer phenomenology provides deeper insights into modified gravity dynamics. Code available at GitHub. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_22361 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analytical $polyΛ$CDM dynamics Ntelis, Pierros Said, Jackson Levi General Relativity and Quantum Cosmology We develop a novel analytical dynamical analysis to derive precise energy density ratio evolutions for the $ϕ$CDM and $polyΛ$CDM models, comparing them to the standard $Λ$CDM model and validating against numerical solutions. Analytical solutions for the quintessence, i.e. $ϕ$CDM, show sub percent agreement with $Λ$CDM with greater reliability than numerical integration of stiff systems. The $polyΛ$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 $polyΛ$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 $polyΛ$CDM richer phenomenology provides deeper insights into modified gravity dynamics. Code available at GitHub. |
| title | Analytical $polyΛ$CDM dynamics |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.22361 |