Adventures in Friedmann Cosmology: An Educationally Detailed Expansion of the Cosmological Friedmann Equations

Abstract

The general relativistic cosmological Friedmann equations which describe how the scale factor of the universe evolves are expanded explicitly to include energy forms not usually seen. The evolution of the universe as predicted by the Friedmann equations when dominated by a single, isotropic, stable, static, perfect-fluid energy form is discussed for different values of its gravitational pressure to density ratio $w$. These energy forms include phantom energy ($w<-1$), cosmological constant ($w=-1$), domain walls ($w=-2/3$), cosmic strings ($w=-1/3$), normal matter ($w=0$), radiation and relativistic matter ($w=1/3$), and a previously little-discussed form of energy called "ultralight" ($w>1/3$). A brief history and possible futures of Friedmann universes dominated by a single energy form are discussed.

32 pages, 4 tables; modified version accepted for publication in the American Journal of Physics

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Cited by in corpus (16)

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• Explicit Integration of Friedmann's Equation with Nonlinear Equations of State
• The Apparent (Gravitational) Horizon in Cosmology
• An exposition on Friedmann Cosmology with Negative Energy Densities
• Friedmann-Lemaitre Cosmologies via Roulettes and Other Analytic Methods
• A critical discussion on the $H_0$ tension
• Qualitative study of perfect-fluid Friedmann-Lema\^ıtre-Robertson-Walker models with a cosmological constant
• IDEAL characterization of isometry classes of FLRW and inflationary spacetimes
• Initial Conditions for Bubble Universes
• Computing Accurate Age and Distance Factors in Cosmology
• First-order quantum-gravitational correction to Friedmannian cosmology from covariant, holomorphic spinfoam cosmology
• Exploring Cosmological Implications of the Modified Raychaudhuri Equation in Non-Gravitating Vacuum Energy Theory
• Revisiting solving procedure for Ermakov-Pinney equation (with applications in the field of cosmology)
• A simple ghost free and caustic free mimetic scalar field dark matter model
• Evolution of Cosmological Total Energy Density and Transient Periods in Cosmology
• A cyclic cosmological model based on the f(ρ) modified theory of gravity