The density of "dark energy": assiociated to the cosmological constant

is constant. The fraction of dark energy in an expanding universe increases because the other components (matter, radiation) decrease as the inverse cube of the scale factor.

Gerard Smadja

Thank you for your participation.

The ECM is based on the principles of classical mechanics, which includes the broarder principles of Planckian quantum mechanics, and is also based on observational cosmology. Relativity is excluded.

However, a simple answer is that the accelerating expansion means that dark energy is becoming dominant, and so the mass density of matter is decreasing. Therefore the effective gravitational mass of dark energy is increasing.

- Soumendra

Vivek Mishra,

Your response neither addresses nor counters the points raised in the discussion. Instead, it introduces external terms that are not relevant to the topic at hand.

You have questioned "increasing mass," attributed unrelated properties to spacetime, and suggested the application of the cosmological constant—none of which are pertinent to this discussion.

If you wish to contribute constructively, please ensure that your response directly addresses or challenges the content within the scope of the post.

Your framework treats dark energy as an effective negative mass term (Mᵉᶠᶠ < 0) whose relative contribution grows as the universe expands. From this perspective, “dark energy is increasing” does not require an intrinsic growth of energy itself, but rather reflects the dynamic shift in balance: positive effective mass density (matter) dilutes with expansion, while the negative effective mass density remains dominant. The acceleration can then be understood as a manifestation of this asymmetry between decreasing positive Mᵉᶠᶠ and the comparatively stable negative Mᵉᶠᶠ.

Vivek Mishra,

It is not my responsibility to teach you the fundamentals of cosmological physics before addressing the inconsistencies in your statements.

Here is my nuanced explanation:

Please refer to the leading observational research titled “Dark energy and the structure of the Coma cluster of galaxies” by A. D. Chernin et al. ( DOI: https://doi.org/10.1051/0004-6361/201220781 ), where the negative effective mass of dark energy is expressed as:

Mɢ = Mᴍ + Mᴅᴇ,

with Mᴅᴇ, the effective mass of dark energy, being negative (Mᴅᴇ < 0).

Now refer to the ResearchGate discussion:

https://www.researchgate.net/post/Growing_Influence_of_Dark_Energy_Over_Matter_Mass_An_ECM_Perspective

This relationship applies only at the intergalactic, cosmological scale. In contrast, Extended Classical Mechanics (ECM) defines effective mass as:

Mᵉᶠᶠ = Mɢ = Mᴍ − Mᵃᵖᵖ,

which is applicable at both local and cosmological scales. These two expressions align as:

Mᴍ + Mᴅᴇ = Mᴍ − Mᵃᵖᵖ,

implying that:

Mᴅᴇ = − Mᵃᵖᵖ,

which explains why Mᴅᴇ < 0. ECM’s broader framework allows for a detailed description of cosmic expansion similar to Mɢ = Mᴍ + Mᴅᴇ.

A closer examination of both expressions shows that as the dominance of − Mᵃᵖᵖ or Mᴅᴇ < 0 increases, the matter mass MᴍMᴍ decreases accordingly. When matter mass equals the negative apparent mass, or the negative effective mass of dark energy, it is expressed as:

Mᴍ = − Mᵃᵖᵖ or, Mᴍ = Mᴅᴇ < 0,

leading to the gravitating or effective mass becoming zero:

Mᵉᶠᶠ = Mɢ = 0,

since Mᴍ = − Mᵃᵖᵖ = 0 or Mᴍ = Mᴅᴇ = 0.

Further increases in − Mᵃᵖᵖ or Mᴅᴇ result in Mɢ < 0, implying a negative gravitating mass and thus an anti-gravitational effect. As anti-gravitational forces cause acceleration, this demonstrates that the influence of dark energy is increasing, refuting the assumption that dark energy is constant.

Please note that, in ECM, mass (Mᴍ) is a frequency-dependent, energy-related property of matter that varies with interactions and oscillations rather than being an absolute, unchanging quantity.