Dark Energy and E = MC2

[petrushka.googol]

Does dark energy obey Einsteins mass-energy equation E = mc^2,, I was just curious to know ?

 

If it does then how ?

 

Thanks in advance.

[Mordred]

Well we don't know what causes the cosmological constant, so the m term is simply an energy Mass equivalent.

 

However the Einstein field equations relate to the cosmological constant aka dark energy(one possible contributor)

 

via the stress energy tensor.

 

[latex]T_{\mu\nu}=\frac{\Lambda c^4}{8\pi G}G_{\mu\nu}[/latex]

 

http://en.m.wikipedia.org/wiki/Einstein_field_equations

 

http://en.m.wikipedia.org/wiki/Stress%E2%80%93energy_tensor

 

take a good look at the stress energy tensor matrix on the second link

 

This correlates the energy density to pressure relations of the cosmological constant. In the FLRW metric it is determined by its equation of state

 

http://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology)

 

[latex]w=\frac{\rho}{p}[/latex]

 

For the cosmological constant w= -1

 

This article provides some further detail

 

http://cosmology101.wikidot.com/universe-geometry

Page 2 FLRW distance measures

 

 

http://cosmology101.wikidot.com/geometry-flrw-metric/

In short we can relate its energy density to pressure influence. As energy and mass has an equivalence we can also calculate its estimated mass density via the critical density formula.

http://en.m.wikipedia.org/wiki/Critical_density_(cosmology)#Density_parameter

 

The calculations give

1.89*10-27 grams/cm^3

Edited February 6, 2015 by Mordred

[xyzt]

Does dark energy obey Einsteins mass-energy equation E = mc^2,, I was just curious to know ?

 

If it does then how ?

 

Thanks in advance.

The correct formulation is either:

 

1. The total energy E contained by a proper mass [math]m_0[/math] is [math]E=\gamma m_0c^2[/math]

 

2. The variation of total energy [math]\Delta E[/math] released by a variation of proper mass [math]\Delta m_0[/math] is [math]\Delta E=c^2 \Delta m_0[/math]

 

3. In the rest frame co-moving with the mass [math]m_0[/math] the total energy is equal to the rest energy [math]E_0=m_0c^2[/math] because [math]\gamma=1[/math]

 

[math]E=mc^2[/math] is a (bad) shorthand for either 1,2 or 3.

 

Now, there is no mass associated with dark energy, so your question cannot be answered.

Edited February 6, 2015 by xyzt