5. Nature of Dark Energy in the ECM Framework:

Soumendra Nath Thakur

February 05, 2025

The core of how ECM treats dark energy and its relationship to effective mass contributions outline below:

1. Dark Energy in ECM

In ECM, dark energy is not a conventional field or particle as in some quantum field theories. Instead, ECM treats dark energy as:

• A gravitationally interactive background that influences mass distributions at intergalactic scales.

• A cosmic energy component that affects large-scale gravitational interactions.

• A source of effective mass contribution through its interaction with dark matter.

2. Is Dark Energy a Field?

Unlike classical scalar fields (e.g., quintessence), ECM does not assume dark energy to be a fundamental field with local quantum excitations. Instead, dark energy manifests through its effect on gravitational dynamics, particularly at intergalactic scales.

• It does not contribute within gravitationally bound systems (e.g., galaxies, clusters), meaning it has no local effect on stars or planetary orbits.

• It acts on cosmic scales by modifying the gravitational potential in ways that lead to the observed cosmic acceleration.

Thus, rather than being a conventional field, dark energy in ECM is a background energy effect with gravitational influence.

3. How Does Dark Energy Give Rise to Mᴅᴇ?

In ECM, Mᴅᴇ is a derived effective mass rather than a fundamental physical mass. It arises due to:

(A) Gravitational Interaction Between Dark Matter and Dark Energy

At intergalactic scales, dark matter interacts with the gravitational influence of dark energy. This results in an effective mass contribution, which is represented by Mᴅᴇ.

Mathematically, we express:

Mɢ = Mᴍ + Mᴅᴇ

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where:

• Mɢ is the total gravitationally inferred mass.

• Mᴍ is the matter mass (baryonic + dark matter).

• Mᴅᴇ represents the additional contribution from the interaction of dark matter with dark energy at intergalactic scales.

Thus, Mᴅᴇ is an emergent gravitational effect, not a fundamental mass term.

(B) The Role of Negative Apparent Mass

From ECM’s formulation:

Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ)

where apparent mass Mᵃᵖᵖ emerges due to energy redistribution. Since dark energy affects large-scale gravitational interactions, it indirectly contributes to Mᵃᵖᵖ, leading to an additional inferred mass component, Mᴅᴇ.

Thus, ECM suggests that Mᴅᴇ is not a true inertial mass but a gravitationally inferred contribution from the cosmic-scale effects of dark energy.