Abstract

This paper provides some insight into Cosmological Constants and how they come from the well-known Wave Equation.

Keywords: Wave Equation; Gravity Waves; Density; Period

Introduction

The Wave equation has been around since the 18th Century when d ʼAlembert discovered it. In this paper, I work through a few simple calculations for the universe as described by Astrotheology Math (AT Math) [1-2].

The Wave Equation:

∂²u/∂t²=c² ∂u²/∂x²
a=k s”
s=|E|t|sin θ
sʼ=(dE/dt)(dt/dt) cos θ
s”=d²E/dt² (dt²/dt² (-sin θ)
But G=d²E/dt² from the Clairnaut D.E.
s”=G(1)(cos θ)
And,
∂²u/²dt²=a=v =sin 45°=cos 45°=1/√2
1/√2=(-0.4233)(2/3) cos θ
cos θ=2.993(6.67)=2
θ=114388
ln θ=π
Or,
G=cos θ/c
G=cos θ/ [k a]
where k=π-e
a=v=sin 45 =cos 45
∂²u/∂t²=c² ∂²u/∂x²
a=c s”
Let E=t=1
a=1/√2
c=2.99792
s=|E||t| sin θ
s=(1)(1) sin θ
sʼ=cos θ
s”=-sin θ
1/√2=2.99792² (-sin θ)
csc θ=127.3=ρ (Density)
Or 1/ρ=-sin θ
∂²u/∂t²=c² ∂²u/∂x²
∫∂²u/∂t²=c² ∫∂²u/∂x²
a=1/√2=v
v=∫a
c=2.99792
1/[√2× 2.9979²]=∂²u/∂x²
∫∂²u/∂x²=cos θ
cos θ=0.7856
θ=0.667=G
1/G=1.5=Mass Gap
The Laplacian
∇²u=∂²u/∂x²+∂²u/∂y²+∂²u/∂z²
∂²u/∂t²=c² ∇²u
1/√2=0.4233² ∇²u
∇²u=394~396 =1/Period T
Wave Equation:
∂²E/∂t²=c² ∇² E
Rearrange to the Clairaut Differential Equation:
c²∇²E- ∂²E/²t=0
But we know:
∂²E/²t=G
So,
c²∇²E- G=0
E=Mc²
=(-1)c²
=-c²
c²∇²E- G=0
Aside:
∇=∂/∂x+∂/∂dy+∂/∂z
=3(∂/∂x²)
=3 x (dM/dt)ʼ
=3 ℂ
c²∇²E- G=0
c² ∇² E
=c²(-c²) ∇²
Let ℂ=3
=-c⁴ C
=-80.7 (3ℂ)
302 C
=8.9875
=2.99792²
=Speed of light.

Conclusion

The wave equation shows where the mass gap, the frequency and the density as well as the gravity equation wave equation come from.

Acknowledgements

None.

Conflict of interest

The author declares that there is no conflict of interest.

References

1. Cusack P. Astro-Theology, Cusacks Universe. J. Phys. Math. 2016; 7(2): 8.   
2. Steward I. In Pursuit of the Unknown. NY 2012.