Subject: An Extended Classical Mechanics (ECM)Interpretation of Big Bang Inflation and Cosmic Evolution

Soumendra Nath Thakur | Tagore’s Electronic Lab, India | June 25, 2025

Overview:

In ECM, the evolution of the universe from the Big Bang is not interpreted as a quantum fluctuation into existence or a purely relativistic event, but rather as a progressive redistribution of mass-energy governed by effective gravitational mass Mɢ, apparent mass Mᵃᵖᵖ, and their transformations through kinetic and potential energy states. This note outlines how the dynamics of early universe inflation, halting of expansion, and subsequent accelerated expansion emerge directly from mass balance equations under ECM.

1. Pre-Matter Era: Dominance of Dark Energy Mass (Mᴅᴇ)

At the Big Bang origin, the universe begins with:

• Mᴍ → 0 (no ordinary or dark matter mass),

• Mᴅᴇ > 0(effective negative mass of dark energy, Mᴅᴇ < 0),

• Therefore, Mɢ = Mᴍ + Mᴅᴇ = 0 + Mᴅᴇ = Mᴅᴇ > 0.

Since Mᴅᴇ < 0 in physical nature, it manifests antigravitational acceleration.

With no matter mass (Mᴍ) to impose inertial resistance, expansion occurs under pure negative pressure—an unbound release of −ΔMᵃᵖᵖ, converting dark energy potential into kinetic energy:

−ΔPEᴅᴇ → +KEᴇᴄᴍ → v > c (superluminal inflation)

This inflationary phase is explained in ECM not by inflation fields, but as the free dominance of negative effective mass-energy unopposed by matter inertia.

2. Matter Formation and Expansion Halt: Mass-Energy Equilibrium

As the universe expands and cools:

• Light nuclei form → Mᴍ increases

• Mass clustering begins → gravitational structures emerge

When:

Mᴍ = |Mᴅᴇ| ⇒ Mɢ = 0

Gravitational binding and antigravity balance out.

At this point, the universe reaches a dynamical equilibrium: no net gravitational effect and expansion halts temporarily. This is the turning point of the universal trajectory—an ECM-specific mass-density balance condition.

3. Decline in Matter Density and Acceleration Re-emerges

With further time:

• Mᴍ density decreases due to volume increase and ΔMᴍ → KE

• Mᴅᴇ remains invariant in density

Eventually, the inequality:

Mᴍ < |Mᴅᴇ| ⇒ Mɢ < 0

leads to a renewed dominance of antigravity.

Expansion restarts, this time gradually accelerating, not explosively, due to retained Mᴍ > 0inertia.

4. Summary of Evolution in ECM Terms

Epoch Dominant Factor ECM Condition Effect

Pre-Matter Inflation −ΔMᵃᵖᵖ, Mᴅᴇ > 0 Mᴍ ≈ 0 Pure antigravity → superluminal v>c

Matter Formation ↑ Mᴍ Mᴍ → Mᴅᴇ Expansion halts (Mɢ = 0)

Post-Balance Expansion Mᴍ < Mᴅᴇ Mɢ < 0 Restart of expansion → acceleration

Conclusion:

The inflationary origin, halt, and accelerated expansion of the universe are, in ECM, direct consequences of shifting relationships among Mᴍ, Mᴅᴇ, and Mᵃᵖᵖ. ECM removes the need for hypothetical inflation fields by grounding cosmic evolution in a physical causality based on dynamic mass-energy redistribution and gravitational balance conditions.

This reaffirms that cosmic behaviour—at all stages—is consistent with extended classical laws, and the universe's trajectory is shaped not by spacetime curvature or singularities, but by evolving mass terms and effective energy transformations.

Clarification on ECM Note: Inflation, Expansion, and Mass-Energy Balance in the Early Universe

In response to questions raised on the ECM Note titled “Inflation, Expansion, and Mass-Energy Balance in the Early Universe,” the following clarifications are provided to elaborate on specific foundational concepts, mechanisms, and observational considerations presented within the ECM framework.

1. Definition of Mᴅᴇ and Its Role as Potential Energy

In ECM, Mᴅᴇrefers to the effective negative mass attributed to dark energy, which contributes negatively to total gravitational mass:

Mɢ = Mᴍ + Mᴅᴇ

In the pre-matter epoch (Big Bang origin), Mᴍ → 0 and Mᴅᴇ < 0, so Mɢ = Mᴅᴇ appears effectively positive in gravitational outcome (i.e., antigravitational acceleration). This yields a repulsive gravitational field unopposed by inertial mass. Such interpretation is consistent with:

Chernin et al. (2013), “Dark energy and the structure of the Coma cluster of galaxies”, A\&A, 553, A101

DOI: https://doi.org/10.1051/0004-6361/201220781

Thus, Mᴅᴇ in ECM is equated with stored negative potential energy, whose transformation follows:

−ΔPEᴅᴇ → +KEᴇᴄᴍ,

leading to superluminal inflation when unconstrained by Mᴍ.

2. Mechanism of "Kinetic Transformation" of Mᴍ

The ECM model describes mass-energy redistribution through:

Mᴍ = (Mᴍ − ΔMᴍ) + ΔMᴍ

Where:

• (Mᴍ − ΔMᴍ) remains as rest/inertial mass,

• ΔMᴍ transforms into kinetic or radiative energy.

This corresponds to:

Eₜₒₜₐₗ = PE + KE = (PEᴇᴄᴍ − ΔPEᴇᴄᴍ) + ΔPEᴇᴄᴍ,

Or:

½ΔMᴍv² + (Mᴍ − ΔMᴍ)gᵉᶠᶠ·h

In the declining mass density epoch, this transformation reduces the gravitational effect of Mᴍ, resulting in effective acceleration (Mᴍ < Mᴅᴇ ⇒ Mɢ < 0).

3. Observational Verification

Appendix 16 asserts qualitative alignment with known cosmic acceleration. This is supported by:

• Supernovae Type Ia distance-redshift relations,

• CMB anisotropy data (e.g., WMAP, Planck),

• Galaxy cluster dynamics (e.g., Coma cluster).

The use of:

Chernin et al., A\&A 2013 (DOI above) provides observational precedent for interpreting antigravitational mass components within ECM. Future work will model ECM’s quantitative fits to observed H(z) curves, Ωᴍ/Ωᴅᴇ ratios, and structure growth rates.

4. Comparison with Conventional Models

ECM diverges from ΛCDM by:

• Rejecting cosmological constant Λ in favour of −ΔMᵃᵖᵖ-based mass evolution,

• Replacing spacetime curvature with causal mass-energy redistribution.

Planned work includes scenario-specific modelling of:

• Expansion rate evolution,

• Matter-radiation-dark energy balances,

• Transition epochs and deceleration-acceleration shifts.

This will highlight predictive divergences and causal clarity where ECM surpasses or realigns conventional expectations.

5. Concept of Apparent Mass (ΔMᵃᵖᵖ and −ΔMᵃᵖᵖ)

Apparent mass, denoted ΔMᵃᵖᵖ, refers to the portion of Mᴍ undergoing energetic transition:

ΔMᵃᵖᵖ = ΔMᴍ,

So that:

Mᴍ = (Mᴍ − ΔMᴍ) + ΔMᴍ

Then,

−ΔMᵃᵖᵖ defines the reduction in gravitational contribution, enabling antigravitational effects.

This dynamic shift redefines gravitational response in ECM—not as curvature but as a product of ongoing mass-energy conversion, consistent with kinetic release and cosmic volume increase.

Conclusion

These clarifications strengthen the causal structure of ECM’s cosmological vision: inflation, equilibrium, and acceleration emerge from mass-energy transitions, not geometric postulates. Future expansions will provide numerical models, empirical comparisons, and deeper formulations of ΔMᵃᵖᵖ-based dynamics.