Energy-Mass and the Emergent Universe: A Thermodynamic and Mathematical Framework

1. Introduction

The standard cosmological model describes an accelerating universe [1,2], yet the mechanisms remain debated. This paper builds upon a foundational framework first proposed by the author [12], redefining $E=m{c}^2$ as $E/m=d^2/t^2$, and introducing Energy-Mass where spacetime and quantum physics emerge with $E>0$. Unlike static WIMPs probed by XENON1T with null results ($\sigma <{10}^{-47}{\mathrm{cm}}^2$[11]), this model posits dynamic injections detectable via cosmic microwave background (CMB) anomalies, bypassing underground constraints. A feedback loop accelerates expansion as cold-mass absorbs energy near an infinite state $G_p$, detectable via CMB anomalies [4], offering alternatives to dark energy and dark matter. This framework integrates thermodynamics and quantum mechanics, extending prior concepts with new evidence and derivations.

2. Energy-Mass Framework

Einstein’s $E=m{c}^2$ is reframed as:

$$E/m=d^2/t^2=c^2,$$

(1)

defining Energy-Mass ($E/m$) and Space-Time ($d^2/t^2$). When $E=0$, $d^2/t^2=0$; when $E>0$, spacetime exists, forming an expanding state.

3. The Infinite Universe

Since $m\ne 0$ ($E/0$ undefined) and $E=0$ is viable ($0/m$, $m>0$), Energy-Mass indestructible ensures an infinite universe across forms.

4. Pre-Expansion Infinity: The Golden Point

Hubble’s expansion and infinity before expansion implies an origin at $0/\infty$$(E=0,m=\infty )$, denoted the Golden Point $G_p$, where $d^2/t^2=0$ and momentum is absent. Cold-mass $(E=0;m>0;m<\infty )$ transitions to $E>0$, yet $G_p$ remains immutable:

$$\infty -m=\infty ,\mathrm{for}\mathrm{finite}m.$$

(2)

5. System Definition

Three states define the universe’s evolution:

5.1. State 1: Pre-Spacetime State

• Energy: $E_1=0$
• Mass: $m_1=\infty$ (latent, pre-physical)
• Specific energy: $E_1/m_1=0$
• Temperature: $T_1=0\mathrm{K}$
• Spacetime: Absent ($V_1=0$, no metric)
• Entropy: $S_1=0$ (single ordered state)

State 1, the Golden Point $G_p$, exists pre-spacetime, with no volume or dynamics, rendering density (${\rho }_1=E_1/V_1$) undefined; p=0 negates Pauli exclusion; Heisenberg’s $\Delta x$ is undefined without spacetime.

5.2. State 2: Cold-Mass

• Energy: $E_2=0$ (pre-injection)
• Mass: $m_2=1.78\times {10}^{-25}\mathrm{kg}$ (single WIMP)
• Specific energy: $E_2/m_2=0$ (pre-injection)
• Temperature: $T_2=0\mathrm{K}$
• Spacetime: Absent (pre-transition)
• Entropy: $S_2=0$ (single WIMP, pure state)

State 2 represents cold-mass as WIMPs translocating from $G_p$ before energy absorption.

5.3. State 3: Expanded CMB-like State

The universe evolves within an FLRW metric [3]:

• Energy: $E_3>0,E_3<\infty$
• Mass: $m_3>0,m_3<\infty$
• Specific energy: $E_3/m_3>0$
• Temperature: $T_3=2.725\mathrm{K}$ [4]
• Volume: $V_3>0$, expanding
• Entropy: $S_3\sim {10}^{56}\mathrm{J}{\mathrm{K}}^{-1}$ (high, photon disorder)

$$d{s}^2=-c^{2}d{t}^2+a{\left(t\right)}^2(d{x}^2+d{y}^2+d{z}^2),$$

(3)

$$H^2={\left({\displaystyle \frac{\dot{a}}{a}}\right)}^2={\displaystyle \frac{8\pi G}{3}}\rho .$$

(4)

6. Thermodynamic Evolution and Feedback Loop

Energy ($E_3>0$) near $G_p$ triggers WIMP injections from State 2 into State 3:

• WIMPs ($m_2\approx 1.78\times {10}^{-25}\mathrm{kg},100\mathrm{GeV}/c^2$[10]) tunnel from $G_p$ at $\sim {10}^8{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$, based on CMB photon density ($4.1\times {10}^8{\mathrm{m}}^{-3}$) and a hypothetical cross-section ($\sim {10}^{-44}{\mathrm{m}}^2$) [10], absorbing CMB energy ($E_3$, ${\rho }_3=4.17\times {10}^{-14}\mathrm{J}{\mathrm{m}}^{-3}$) near $G_p$, creating spacetime ($d^2/t^2>0$) and forming cold spots (Figure 1, $\Delta T\sim -70\mu \mathrm{K}$, $m_3\sim {10}^{39}\mathrm{kg}$, $\sim 5.62\times {10}^{63}$ WIMPs) detectable as CMB anomalies. Tunneling may reflect quantum barrier penetration near a pre-spacetime boundary, a topic for future study.
• WIMP annihilation releases energy near $G_p$, forming hot spots (Figure 2, $\Delta T\sim +170\mu \mathrm{K}$, $m_3\sim {10}^{36}\mathrm{kg}$, $\sim 6.5\times {10}^{60}$ WIMPs), with CMB energy dominating over stellar contributions ($\sim {10}^{-12}\mathrm{J}{\mathrm{m}}^{-3}$).
• This increases $V_3$, accelerating expansion over time.

Equilibrium ($E=0$) looms as $a\left(t\right)$ grows.

Theorem 1

(Emergent Properties). When $E>0$, spacetime and quantum properties emerge as derived from Maxwell’s equations, based on a framework first proposed by the author [12].

Proof. 

Begin with Maxwell’s relation for the speed of light:

$$c={\displaystyle \frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}},$$

where c is the speed of light, ${\mu }_0$ is the permeability, and ${\epsilon }_0$ is the permittivity of free space. Squaring yields:

$$c^2={\displaystyle \frac{1}{{\mu }_0{\epsilon }_0}}.$$

In the Energy-Mass framework, $E/m=c^2$, so:

$${\displaystyle \frac{E}{m}}={\displaystyle \frac{1}{{\mu }_0{\epsilon }_0}}.$$

Multiply by m:

$$E={\displaystyle \frac{m}{{\mu }_0{\epsilon }_0}}.$$

Spacetime emerges as:

$$t^2\propto {\mu }_0{\epsilon }_0,d^2\propto {\displaystyle \frac{E{\mu }_0{\epsilon }_0}{m}},(E>0).$$

Now, consider wave properties where $c=\lambda f$ (wavelength $\lambda$, frequency f):

$$c^2={\lambda }^2{f}^2.$$

Substitute into the framework:

$${\displaystyle \frac{E}{m}}={\lambda }^2{f}^2.$$

Equate with Maxwell’s result:

$${\lambda }^2{f}^2={\displaystyle \frac{1}{{\mu }_0{\epsilon }_0}}.$$

Multiply by E:

$$E{\lambda }^2{f}^2={\displaystyle \frac{E}{{\mu }_0{\epsilon }_0}}.$$

Since $E=m{\lambda }^2{f}^2$:

$${\displaystyle \frac{E}{{\mu }_0{\epsilon }_0}}=m{\lambda }^2{f}^2.$$

Multiply through by ${\mu }_0^2{\epsilon }_0^2$:

$$E{\mu }_0^2{\epsilon }_0^2=m{\lambda }^2{f}^2.$$

For quantum mechanics, use Planck’s relation $E=hf$ (where $h=6.62607015\times {10}^{-34}\mathrm{J}\mathrm{s}$):

$$\left(hf\right){\mu }_0^2{\epsilon }_0^2=m{\lambda }^2{f}^2.$$

Divide by f ($f\ne 0$):

$$h{\mu }_0^2{\epsilon }_0^2=m{\lambda }^{2}f.$$

Since $\lambda =c/f$:

$$h{\mu }_0^2{\epsilon }_0^2=m{\left({\displaystyle \frac{c}{f}}\right)}^{2}f=m{\displaystyle \frac{c^2}{f}}.$$

With $c^2=1/\left({\mu }_0{\epsilon }_0\right)$:

$$h{\mu }_0^2{\epsilon }_0^2=m{\displaystyle \frac{1}{{\mu }_0{\epsilon }_{0}f}}.$$

Multiply by ${\mu }_0{\epsilon }_{0}f$:

$$h{\mu }_0^3{\epsilon }_0^{3}f=m.$$

This relates mass to frequency, implying quantum properties (e.g., wave-particle duality) emerge when $E>0$. If $E=0$, $f=0$, suggesting $m=0$ within spacetime. However, conservation of energy holds as $m>0$ persists outside spacetime (e.g., pre-injection cold-mass), transitioning to $E>0$ upon entry, preserving total energy. □

7. Results and Discussion

The feedback loop drives expansion via WIMP injections, detectable as CMB anomalies (cold spots, $m_3\sim {10}^{39}\mathrm{kg}$, $\sim 1\%$ of CMB sky [9], Figure 1; hot spots, $m_3\sim {10}^{36}\mathrm{kg}$, $\sim 0.5\%$, Figure 2) or redshift trends [6]. CMB $\delta \rho /\rho \sim {10}^{-5}$ supports cold spot scale [4,8], while hot spots reflect annihilation energy near $G_p$, contrasting static dark matter halos [10]. These scales align with WMAP’s $\sim {10}^5$ anomalies across 41,253 deg²[8]. Unlike traditional WIMPs forming halos post-recombination, these dynamically inject from $G_p$, offering a testable alternative to dark energy [7].

8. Conclusions

Energy-Mass ($E>0$) drives expansion via a WIMP-based feedback loop, detectable via CMB anomalies, approaching $E=0$ equilibrium, contrasting dark matter theories.