Summary of "Dark Energy and the Structure of the Coma Cluster of Galaxies" by A. D. Chernin et al.

Soumendra Nath Thakur

04-09-2024

Three Types of Masses:

Matter Mass (Mᴍ): Total mass of both dark matter and baryonic matter within the cluster, contributing to its gravitational binding.

Dark Energy Effective Mass (Mᴅᴇ): Conceptual mass representing dark energy's effect, characterized by negative pressure, which creates a negative mass (Mᴅᴇ < 0) that opposes gravitational attraction.

Gravitating Mass (Mɢ): Net mass causing gravitational attraction, combining the effects of matter mass and dark energy:

Mɢ = Mᴍ + Mᴅᴇ

Matter Density (ρᴍ) in the Cluster:

Definition: Total mass per unit volume, including dark and baryonic matter.

Formula: ρᴍ =Mₜₒₜₐₗ/V

Components:

Dark Matter Density (ρᴅᴍ): Dominant component (~80-90%).

Baryonic Matter Density (ρᴏʀᴅ): Visible matter (~10-20%).

Density Relationships:

Matter Density (ρᴍ): Density of all matter components.

Dark Energy Density (ρᴅᴇ): Constant, uniform density (ρᴅᴇ ≈ 0.71 × 10⁻²⁹ g/cm³).

Gravitating Mass Density (ρɢ): Combined density including matter and dark energy:

ρɢ = ρᴍ + ρᴅᴇ

Matter Density of the Coma Cluster:

The average matter density (ρᴍ) in the core of the Coma Cluster is about ρm ≈ 10⁻²⁶ kg/m³, with dark matter constituting 85-90% of this total.

Uniformity of Average Matter Density (ρᴍ) in the Universe:

The average matter density across the universe is roughly uniform on very large scales, in accordance with the cosmological principle. Local variations exist due to structures, but these average out over larger distances.

Effective Mass and Negative Effective Mass:

Effective Mass: Includes both matter and dark energy effects, representing the net gravitational influence.

Negative Effective Mass: Arises from dark energy's negative pressure, contributing to antigravitational forces.

Comparison with Classical Mechanics:

Classical mechanics equates "mass" and "gravitational mass," assuming gravitational forces are always attractive. The study suggests extending classical mechanics to include dark energy's effects to account for observed antigravitational forces.

Keywords: Dark Energy, Gravitating Mass, Matter Density, Coma Cluster, Antigravitational Force,

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