Dark Energy and the Structure of the Coma Cluster: Key Findings from Intercontinental Research

February 21, 2025

The intercontinental research study titled "Dark Energy and the Structure of the Coma Cluster of Galaxies," observed and authored by A. D. Chernin et al present ground breaking conclusions on the role of dark energy in cosmic structures. The key findings are as follows:

1. Significant Antigravity Influence at Large Radii

   • Dark energy’s antigravity effect strongly influences the structure of the Coma cluster at large radii (R ≳ 14 Mpc).
   • This effect must be considered when deriving the cluster's total mass.

2. Dark Energy as the Driver of Cosmic Acceleration

   • The background dark energy produces an antigravity effect stronger than matter’s gravitational pull on a universal scale.
   • This leads to the accelerated cosmic expansion, as discovered by Riess et al. (1998) and Perlmutter et al. (1999).

3. Local Antigravity Effects on Megaparsec Scales

   • Antigravity can exceed gravitational attraction not just globally but also locally on scales of ~1–10 Mpc.
   • This has been demonstrated through studies (Chernin et al. 2000, 2006; Chernin 2001; Byrd et al. 2007, 2012) and confirmed using HST observations by Karachentsev’s team (e.g., Chernin et al. 2010, 2012a).

4. Negative Effective Gravitating Density and Einstein’s Law of Universal Antigravity

   • The effective gravitating density is negative, producing antigravity.
   • According to Einstein’s law, a mass M in uniform dark energy generates an acceleration a(r), which includes both the Newtonian attraction term aN(r) = −GM/r² and the antigravity effect of dark energy.

5. Gravitational Boundaries and Zero-Gravity Sphere

   • Gravity dominates at distances R < RZG, whereas antigravity prevails at R > RZG.
   • A gravitationally bound system with mass Mᴍ can only exist within its zero-gravity sphere, defined by radius RZG.

6. Dark Energy’s Negligible Effect at Small Radii

   • At small radii (R ≪ 14 Mpc), dark energy effects are minimal (|MDE| ≪ Mᴍ), and the gravitating mass Mᴳ is practically equal to the matter mass Mᴍ.
   • At larger radii (R ≥ 14 Mpc), antigravity effects become dominant (|MDE| ≥ Mᴳ), significantly altering the cluster's dynamics.

These findings emphasize the profound role of dark energy in shaping cosmic structures and redefining our understanding of gravitationally bound systems on both local and universal scales.

ECM and the Coma Cluster: Aligning Extended Classical Mechanics with Dark Energy’s Role

February 21, 2025

The findings from A. D. Chernin’s study on dark energy and the Coma Cluster strongly resonate with the principles of Extended Classical Mechanics (ECM). ECM, with its refined gravitational framework, provides a natural and physically consistent interpretation of the observed large-scale effects of dark energy. Here’s how ECM aligns with and extends these conclusions:

1. ECM and the Antigravity Influence at Large Radii

• Chernin’s research confirms that dark energy’s antigravity effect dominates beyond R ≳ 14 Mpc, significantly altering the Coma cluster’s structure.
• ECM explains this by differentiating between matter mass (Mᴍ) and its effective gravitational mass (Mᵉᶠᶠ), which includes counteracting dark energy effects.
• When Mᵉᶠᶠ approaches negative values at large scales, it mirrors the observed transition from gravitational dominance to antigravity effects.

2. Cosmic Expansion and Dark Energy in ECM

• Chernin links the dominance of dark energy to the accelerated expansion of the universe (Riess et al. 1998; Perlmutter et al. 1999).
• ECM provides an alternative to the standard dark energy model by recognizing that as gravitational interactions induce mass, antigravitational interactions counteract or even reverse it.
• This naturally explains why, at intergalactic distances, effective gravitational mass (Mᵉᶠᶠ) becomes negative, leading to accelerated cosmic expansion without requiring exotic vacuum energy interpretations.

3. Local Antigravity Effects: ECM’s View on Negative Effective Mass

• Chernin et al. (2000, 2006) and Byrd et al. (2007, 2012) demonstrate that antigravity is not just a global effect but also acts on local scales of 1–10 Mpc.
• ECM provides a robust explanation:
  • At these scales, Mᵉᶠᶠ can transition between positive and negative values depending on the distribution of mass-energy and the local gravitational potential.
  • This means antigravity effects are not uniform but emerge dynamically in regions where effective mass density becomes negative, aligning with observational data.

4. Einstein’s “Law of Universal Antigravity” in ECM Terms

• Chernin’s interpretation of Einstein’s law states that a mass M in a uniform dark energy field generates an acceleration:
  $$a(r) = -\frac{GM}{r^2} + \Lambda r$$
  • Here, the Newtonian gravity term is opposed by dark energy’s repulsive force.
• ECM expands on this by deriving antigravitational effects naturally from mass-energy interactions, rather than treating them as an imposed cosmological constant (Λ).
• This aligns with ECM’s self-consistent framework, where antigravity emerges from the properties of mass-energy systems without invoking hypothetical vacuum energy densities.

5. The Zero-Gravity Sphere and ECM’s Mass-Induced Boundaries

• Chernin defines a zero-gravity radius (Rᴢɢ), beyond which antigravity dominates over gravity, limiting the region where a bound system can exist.
• ECM inherently predicts this behavior by recognizing that:
  • The gravitationally bound state of a system is determined by the balance of matter mass (Mᴍ) and its effective gravitational counterpart (Mᵉᶠᶠ).
  • At distances beyond Rᴢɢ, where Mᵉᶠᶠ becomes sufficiently negative, the system ceases to be gravitationally bound and is repelled outward, a behaviour consistent with Chernin’s observations.

6. ECM and the Transition from Matter-Dominated to Dark Energy-Dominated Regions

• At small radii (R ≪ 14 Mpc), Chernin notes that dark energy is negligible, and the gravitating mass Mᴳ ≈ Mᴍ.
• ECM supports this by showing that mass-induced gravity dominates in high-density environments where matter effects overshadow large-scale antigravity forces.
• However, at larger radii (R ≥ 14 Mpc), the ECM framework predicts a transition where antigravitational effects exceed traditional gravitational attraction, leading to the observed dynamics of the Coma cluster and similar cosmic structures.

Conclusion: ECM as a Natural Framework for Understanding Large-Scale Cosmic Dynamics

The findings from the study on the Coma Cluster align well with ECM’s perspective, removing the need for ad hoc dark energy models while maintaining consistency with observational data. By correctly distinguishing between matter mass (Mᴍ) and effective gravitational mass (Mᵉᶠᶠ), ECM provides a more physically grounded explanation for:

• Why gravitationally bound systems have finite limits (Rᴢɢ)
• How antigravity emerges naturally at intergalactic scales
• Why cosmic acceleration occurs without requiring exotic energy components

Thus, with ECM’s approach, we clarify the underlying mechanics of cosmic structures like the Coma Cluster and reinforce a deeper, empirically grounded understanding of dark energy’s role in the universe.

Antigravitational Motion and the Gravitational Potential of the Universe:

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

 

February 20, 2025

 

Abstract

Antigravitational motion, driven by negative effective mass, occurs counter to the gravitational potential of massive bodies within a system. However, more fundamentally, it represents a counter-motion to the gravitational potential of the universe, owing to the universal dominance of dark energy. In modern astrophysics, dark energy's negative effective mass (Mᴅᴇ<0) governs large-scale cosmic motion, expressed as Mɢ = Mᴍ + Mᴅᴇ.

 

The Extended Classical Mechanics (ECM) framework refines this understanding by introducing negative apparent mass (-Mᵃᵖᵖ), which dominates interactions involving massive bodies (Mᴍ), leading to a negative effective mass (Mᵉᶠᶠ < 0). This relationship is formulated as Mɢ = Mᵉᶠᶠ where Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ). The resulting antigravitational effects propel sufficiently massive bodies, particularly black holes, against the gravitational potential of the universe.

 

Beyond dark energy’s role, ECM suggests that black holes significantly contribute to galactic recession, reinforcing large-scale cosmic expansion. These insights provide a deeper explanation of antigravitational motion, demonstrating that it not only opposes local gravitational potentials but also fundamentally counteracts the gravitational influence of the universe itself.

 

Keywords: Antigravitational Motion, Negative Effective Mass, Extended Classical Mechanics (ECM), Dark Energy Influence, Galactic Recession,

 

Mathematical Presentation

Motion driven by antigravitational effects occurs counter to the gravitational potential of the interacting massive bodies with matter mass (Mᴍ) in the system. However, more fundamentally, this motion is a counter-motion to the gravitational potential of the universe, as the dominance of dark energy is universal.

 

In modern astronomy and astrophysics, dark energy’s negative effective mass (Mᴅᴇ < 0) governs large-scale motion, driving massive bodies against the universe’s gravitational potential. This relationship is expressed as:

 

Mɢ = Mᴍ + Mᴅᴇ

 

In the Extended Classical Mechanics (ECM) framework, the dominance of negative apparent mass (-Mᵃᵖᵖ) over interacting massive bodies (Mᴍ) results in a negative effective mass (Mᵉᶠᶠ < 0). This negative effective mass not only causes local antigravitational motion but also fundamentally opposes the universe’s gravitational potential. In alignment with modern astrophysical expressions, this relationship is formulated as:

 

Mɢ = Mᵉᶠᶠ where Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ)

 

Here, the negative apparent mass (-Mᵃᵖᵖ) induces antigravitational effects through the resulting negative effective mass (Mᵉᶠᶠ < 0). According to ECM principles, sufficiently massive bodies undergoing gravitational collapse develop extreme antigravitational properties, propelling them counter to the universe’s gravitational potential.

 

Beyond the role of dark energy, black holes within galaxies contribute to galactic recession, reinforcing the observed large-scale expansion. These insights establish that while antigravitational motion counters the gravitational potential of massive bodies in a system, it is, more fundamentally, a counter-motion to the gravitational potential of the universe itself, since dark energy's influence is universal.

 

Mathematical Consistency with ECM and Modern Astrophysics

Mathematically, my presentation is logically aligned with ECM's application and the interpretation of modern astronomy and astrophysics regarding the influence of dark energy on motion. However, let me carefully analyse the relationship Mɢ = Mᴍ + Mᴅᴇ and how ECM refines it.

 

A. D. Chernin et al. describe how dark energy contributes to the dynamics of galaxy clusters, effectively behaving as a negative mass component in the system. This is expressed in the form:

 

Mɢ = Mᴍ + Mᴅᴇ

 

Where: Mᴍ represents the total matter mass (baryonic + dark matter). Mᴅᴇ represents the contribution of dark energy, which has a negative effective mass (Mᴅᴇ < 0).

 

This formulation reflects the competition between the attractive gravitational force of Mᴍ and the repulsive effect of dark energy Mᴅᴇ, which acts as an antigravitational force at cosmic scales.

 

ECM’s Refinement of This Relationship

ECM builds upon this concept by introducing negative apparent mass (-Mᵃᵖᵖ), which emerges due to extreme gravitational collapse, such as in black holes. According to ECM principles, the effective mass of a system is modified by this additional term:

 

Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ)

 

Where: -Mᵃᵖᵖ represents the apparent negative mass effect induced by gravitational collapse.

 

Thus, in ECM, the effective gravitational mass that determines motion follows:

 

Mɢ= Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ)

 

Which remains consistent with the modern astrophysical formulation Mɢ = Mᴍ + Mᴅᴇ because in ECM, the dominant antigravitational term, -Mᵃᵖᵖ, captures both the effects of dark energy and additional influences from black holes.

 

Implications on Motion and Gravitational Potential

Since Mᴅᴇ < 0, its presence in astrophysical systems drives motion counter to the gravitational potential of the universe, leading to cosmic expansion.

 

In ECM, the dominance of -Mᵃᵖᵖ ensures that not only dark energy but also collapsed massive bodies contribute to this counter-motion, reinforcing large-scale recession effects.

 

The logical step in ECM is that a sufficiently large system, dominated by negative apparent mass effects (-Mᵃᵖᵖ), would exhibit a net negative effective mass (Mᵉᶠᶠ < 0), which aligns with the observed acceleration of cosmic structures.

 

Conclusion

My presentation remains mathematically logical within ECM’s framework because it retains the modern astrophysical relation Mɢ = Mᴍ + Mᴅᴇ while extending it with the ECM refinement Mɢ = Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ).

 

The dominant role of -Mᵃᵖᵖ explains how motion is not only counter to local gravitational potentials but also fundamentally counter to the gravitational potential of the universe.

 

This interpretation strengthens the explanation of galactic recession and black hole-driven contributions, offering an ECM-consistent extension to Chernin et al.'s findings.

 

References

[1] Dark energy and the structure of the Coma cluster of galaxies. A. D.  Chernin, G. S.  Bisnovatyi-Kogan, P.  Teerikorpi, M. J.  Valtonen, G. G.  Byrd, M.  Merafina. Astronomy and Astrophysics. Vol. 553, Art. no. A101, 2013. https://doi.org/10.1051/0004-6361/201220781

[2] A Nuanced Perspective on Dark Energy: Extended Classical Mechanics. Thakur.  S. N. http://doi.org/10.20944/preprints202411.2325.v1

[3] Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Thakur, S. N. https://doi.org/10.20944/preprints202409.1190.v3

[4] Classical Mechanics: Systems of Particles and Hamiltonian Dynamics by H. Goldstein, C. Poole, and J. Safko

[5] Dark Matter and the Dinosaurs: The Astounding Interconnectedness of the Universe" by Lisa Randall   

Negative Apparent Mass:

February 20, 2025

Extended Classical Mechanics (ECM) is also based on this idea of ​​introducing negative apparent mass (-Mᵃᵖᵖ), which arises due to extreme gravitational collapse, such as in black holes.

Mass Concepts in Classical, Relativistic, and Extended Classical Mechanics (ECM):

February 19, 2025

The book Concepts of Mass in Classical and Modern Physics by Max Jammer presents traditional mass concepts, primarily defining mass as either inertial mass or rest mass. However, these descriptions do not account for dynamic effective mass or apparent mass.

Extended Classical Mechanics (ECM) expands upon these conventional definitions by introducing negative apparent mass and negative effective mass, extending the concept of mass beyond ordinary matter to include the effects of dark matter. This distinction is crucial in understanding mass interactions at different cosmic scales.

Mass Equivalence in Different Frameworks

In classical mechanics, inertial mass is equivalent to gravitational mass: 

m = m𝑔 

​In relativistic mechanics, rest mass (invariant mass) is also equated to gravitational mass: 

m = m𝑔

​In Extended Classical Mechanics (ECM), gravitating mass (Mɢ) is equivalent to effective mass (Mᵉᶠᶠ), which includes both matter mass (Mᴍ) and negative apparent mass (−Mᵃᵖᵖ):

Mɢ = Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

where matter mass (Mᴍ) is the combined mass of ordinary matter (Mᴏʀᴅ) and dark matter mass (Mᴅᴍ):

Mᴍ = Mᴏʀᴅ + Mᴅᴍ 

Effective Mass at Celestial and Galactic Scales

At celestial or planetary scales within a galaxy, effective mass (Mᵉᶠᶠ) can be either positive or negative, depending on the balance between matter mass and negative apparent mass:

If matter mass dominates (Mᴍ > Mᵃᵖᵖ), then effective mass is positive:

Mᵉᶠᶠ > 0

If negative apparent mass dominates (Mᵃᵖᵖ > Mᴍ ), then effective mass becomes negative:

Mᵉᶠᶠ < 0

The ECM expression for gravitating mass can also be rewritten as:

Mɢ = Mᴍ + (−Mᵃᵖᵖ)

This formulation aligns conceptually with the expression discussed by A. D. Chernin et al. in Dark Energy and the Structure of the Coma Cluster of Galaxies:

Mɢ = Mᴍ + Mᴅᴇ, 

where Mᴅᴇ represents the effective mass of dark energy, which is always negative:

Mᴅᴇ < 0

While ECM extends this concept by incorporating negative apparent mass alongside dark energy effects, both frameworks recognize the role of negative mass contributions in gravitational dynamics.

This framework provides a more comprehensive approach to understanding mass interactions in the universe, bridging the gap between classical mechanics and modern astrophysical observations.

Author:

Soumendra Nath Thakur