- #1
johne1618
- 371
- 0
Present critical density of Universe
rho_crit = 3 H^2 / 8 Pi G
H = Hubble Constant = 2.2E-18 sec^-1
rho_crit = 8.6E-27 kg / m^3
What particle mass does this represent?
The length scale associated with a quantum particle of mass m is
the Compton wavelength lambda where
lambda = h / m c
This translates to the following density:
rho_particle = mass / volume
rho_particle = mass / lambda^3
rho_particle = m / (h / m c)^3
rho_particle = m^4 c^3 / h^3
Let us equate the two densities:
rho_particle = rho_crit
m^4 = h^3 * 8.6E-27 / c^3
m = 1.7E-38 kg
m = 1 meV / c^2
The Cosmic Microwave Background has a photon energy of 1 meV.
Surprising coincidence or not?
I suppose this is not surprising if the mass and radiation energy at
the recombination time were similar.
Or maybe it is surprising as mass density is supposed to scale as R^-3 whereas radiation density scales as R^-4.
rho_crit = 3 H^2 / 8 Pi G
H = Hubble Constant = 2.2E-18 sec^-1
rho_crit = 8.6E-27 kg / m^3
What particle mass does this represent?
The length scale associated with a quantum particle of mass m is
the Compton wavelength lambda where
lambda = h / m c
This translates to the following density:
rho_particle = mass / volume
rho_particle = mass / lambda^3
rho_particle = m / (h / m c)^3
rho_particle = m^4 c^3 / h^3
Let us equate the two densities:
rho_particle = rho_crit
m^4 = h^3 * 8.6E-27 / c^3
m = 1.7E-38 kg
m = 1 meV / c^2
The Cosmic Microwave Background has a photon energy of 1 meV.
Surprising coincidence or not?
I suppose this is not surprising if the mass and radiation energy at
the recombination time were similar.
Or maybe it is surprising as mass density is supposed to scale as R^-3 whereas radiation density scales as R^-4.
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