How to determine the total energy in the universe

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SUMMARY

The total energy in the universe is estimated to be approximately 9.419 x 1071 joules, derived from the Lambda-CDM model parameters and observational data from the Hubble Space Telescope and WMAP. This calculation considers the observable universe's mass-energy equivalence, factoring in that matter constitutes about 25% of the universe, with dark energy making up the remaining 75%. The Hubble constant is noted as 72 km/s/Mpc, and the observable universe is approximately 46 billion light-years in radius. The energy density and volume calculations lead to a total mass of about 1.048 x 1055 kg for the observable universe.

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  • Understanding of the Lambda-CDM model
  • Familiarity with the Hubble constant and its implications
  • Knowledge of mass-energy equivalence (E=mc2)
  • Basic grasp of cosmological parameters and their significance
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Tipi
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How to determine the total energy of matter in the universe

Hi all,

while looking at a table of order of magnitudes of energies in nature, I just realize that I really don't know how to determine the total energy contained in the universe (near 10 to the 69).

Can someone get this number with a simple argument?

Thanks a lot,

TP
 
Last edited:
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It's not known. Many physicist believe (Feynman was one of them) that the total energy content of the universe is exactly zero, with the positive energy of the matter in the universe being exactly canceled by the negative energy of the gravitational field.
 


phyzguy said:
It's not known. Many physicist believe (Feynman was one of them) that the total energy content of the universe is exactly zero, with the positive energy of the matter in the universe being exactly canceled by the negative energy of the gravitational field.

Ok. That was not the answer I was looking for but it's interesting.

So, how could we determine the positive energy of matter, for instance?

Thanks,

TP

[edit] Enhanced title...
 
Well, we don't know the extent of the universe, or even whether it is finite or infinite. You could calculate the energy content of the matter in the observable universe by adding up all of the mass and multiplying by c^2. The observable universe has been estimated (http://en.wikipedia.org/wiki/Observable_universe) to contain about 10^80 baryons, so, since a proton has an energy content of about 2 GeV, you could estimate a baryon energy content of ~10^89 eV. Then there is the dark matter...
 
The total energy in the universe is a vague concept that might not have a well-defined answer. So let's simplify your question to "what is the total rest energy of all the matter in the observable universe?". This is easier to answer now.

Some assumptions (ask if you need elaboration on any of them): The universe is at the critical density, and matter makes up 25% of the universe. The Hubble constant today is 72km/s/Mpc. The observable universe is 46 billion light years in radius.

We can then get the total energy, as we've defined it, as
E = \frac{1}{4}\rho\,c^2\,V
E = \frac{1}{4}\frac{3H_0^2c^2}{8\pi\,G}\frac{4\pi}{3}R^3

If we put in the numbers, we get about 10^71 joules.
 
nicksauce said:
The total energy in the universe is a vague concept that might not have a well-defined answer. So let's simplify your question to "what is the total rest energy of all the matter in the observable universe?". This is easier to answer now.

Some assumptions (ask if you need elaboration on any of them): The universe is at the critical density, and matter makes up 25% of the universe. The Hubble constant today is 72km/s/Mpc. The observable universe is 46 billion light years in radius.

We can then get the total energy, as we've defined it, as
E = \frac{1}{4}\rho\,c^2\,V
E = \frac{1}{4}\frac{3H_0^2c^2}{8\pi\,G}\frac{4\pi}{3}R^3

If we put in the numbers, we get about 10^71 joules.

Thanks for your answer. Could you explain a little were the first equation come from and how you go to the second?

Thanks,

TP

[edit] OK. I get the first one, I didnt saw its evidence on first look. And for the second one, you used H_\text{crit} =30\sqrt (\rho (m_p/m^3))?
 
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Energy = (1/4 of energy is matter) * energy density * volume

I used 1/4 of energy is matter because the universe is thought to be roughly 75% dark energy, and 25% matter, where the 25% matter can be further decomposed into dark matter and dark energy.

Then I used that
\rho_{crit} = \frac{3H_0^2}{8\pi\,G}
 
I think nicksauce meant the 25% of matter can be further classified by two groups, dark matter and Intergalactic Dust/Stars, just a clarification.
 
Agreed, dark energy is part of the 'missing' ~75% energy component. This makes perfect sense for reasons involving a lot of weird math.
 
  • #10
Kevin_Axion said:
I think nicksauce meant the 25% of matter can be further classified by two groups, dark matter and Intergalactic Dust/Stars, just a clarification.

Errr yes. Of course.
 
  • #11
Total amount of energy in the Universe...

Tipi said:
while looking at a table of order of magnitudes of energies in nature, I just realize that I really don't know how to determine the total energy contained in the universe (near 10 to the 69).

Can someone get this number with a simple argument?

Affirmative.

These are my equations for the total Universe_mass-energy equivalence based upon the Lambda-CDM model parameters and the Hubble Space Telescope (HST) and WMAP observational parameters and the Hubble radius in Systeme International units.

H_0 = 2.3298 \cdot 10^{- 18} \; \text{s}^{- 1} - Hubble parameter (WMAP)
\Omega_s = 0.005 - Lambda-CDM stellar Baryon density parameter
dN_s = 10^{22} - Hubble Space Telescope observable stellar number
dV_s = 3.3871 \cdot 10^{78} \; \text{m}^3 \; \; \; (4 \cdot 10^{30} \; \text{ly}^3) - Hubble Space Telescope observable stellar volume
M_{\odot} = 1.9891 \cdot 10^{30} \; \text{kg} - solar mass

Hubble Space Telescope observable stellar density:
\rho_s = M_{\odot} \left( \frac{dN_s}{dV_s} \right)

Hubble radius:
R_0 = \frac{c}{H_0}

Hubble sphere volume:
V_0 = \frac{4 \pi R_0^3}{3} = \frac{4 \pi}{3} \left( \frac{c}{H_0} \right)^3

Observable Universe_mass-energy equivalence total mass integration by substitution:
M_t = \frac{\rho_s V_0}{\Omega_s} = \frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3 = 1.048 \cdot 10^{55} \; \text{kg}

Observable Universe_mass-energy equivalence total mass
\boxed{M_t = \frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}

\boxed{M_t = 1.048 \cdot 10^{55} \; \text{kg}}

However, only a fraction of this total mass exists in the form of mass in the Universe, which is composed of 22.8% cold dark matter and 4.56% ordinary baryonic matter.

\Omega_m = \Omega_{c} + \Omega_b = 0.2736 - Lambda-CDM total matter density

Universe total matter mass integration by substitution:
M_u = \Omega_m M_t = \frac{4 \pi M_{\odot}}{3} \left( \frac{\Omega_m}{\Omega_s} \right) \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3 = 2.867 \cdot 10^{54} \; \text{kg}

Universe total matter mass:
\boxed{M_u = \frac{4 \pi M_{\odot}}{3} \left( \frac{\Omega_m}{\Omega_s} \right) \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}

Universe total matter mass:
\boxed{M_u = 2.867 \cdot 10^{54} \; \text{kg}}

Universe_mass-energy equivalence integration by substitution:
E_t = M_t c^2 = \left[ \frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3 \right] c^2 = \frac{4 \pi c^5 M_{\odot}}{3 \Omega_s H_0^3} \left( \frac{dN_s}{dV_s} \right) = 9.419 \cdot 10^{71} \; \text{j}

Universe_mass-energy equivalence total energy:
\boxed{E_t = \frac{4 \pi c^5 M_{\odot}}{3 \Omega_s H_0^3} \left( \frac{dN_s}{dV_s} \right)}

Total amount of energy in the Universe:
\boxed{E_t = 9.419 \cdot 10^{71} \; \text{j}}

However, only a fraction of this total energy exists in the form of energy in the Universe, which is composed of dark energy at 72.6%.

\Omega_{\Lambda} = 0.726 - Lambda-CDM dark energy density

Total amount of dark energy in the Universe integration by substitution::
E_{\Lambda} = \Omega_{\Lambda} E_t = \frac{4 \pi c^5 M_{\odot}}{3 H_0^3} \left( \frac{\Omega_{\Lambda}}{\Omega_s} \right) \left( \frac{dN_s}{dV_s} \right) = 6.838 \cdot 10^{71} \; \text{j}

Universe dark energy total energy:
\boxed{E_{\Lambda} = \frac{4 \pi c^5 M_{\odot}}{3 H_0^3} \left( \frac{\Omega_{\Lambda}}{\Omega_s} \right) \left( \frac{dN_s}{dV_s} \right)}

Total amount of dark energy in the Universe:
\boxed{E_{\Lambda} = 6.838 \cdot 10^{71} \; \text{j}}
[/Color]
Reference:
http://en.wikipedia.org/wiki/Hubble%27s_law"
http://en.wikipedia.org/wiki/Lambda-CDM_model"
http://en.wikipedia.org/wiki/Universe"
http://en.wikipedia.org/wiki/Observable_universe"
http://en.wikipedia.org/wiki/Hubble's_law#Interpretation"
http://en.wikipedia.org/wiki/Hubble_volume"
http://en.wikipedia.org/wiki/Dark_matter"
http://en.wikipedia.org/wiki/Dark_energy"
 
Last edited by a moderator:
  • #12
Excellent, response.
 
  • #13
Total amount of energy in the Universe...


800px-2MASS_LSS_chart-NEW_Nasa.jpg

The distribution of galaxies beyond the Milky Way.

Hubble radius:
R_0 = \frac{c}{H_0}

\boxed{R_0 = 1.286 \cdot 10^{26} \; \text{m}}

However, the present observable Universe radius exceeds the Hubble radius due to cosmic inflation:
\boxed{R_u \geq R_0}

R_u = 3.419 \cdot R_0 = \frac{3.419 c}{H_0} = 4.399 \cdot 10^{26} \; \text{m} \; \; \; (46.5 \cdot 10^9 \; \text{ly})

Universe observable radius:
\boxed{R_u = 4.399 \cdot 10^{26} \; \text{m}}

Hubble critical density:
\rho_c = \frac{3 H_0^2}{8 \pi G}

Universe sphere volume:
V_u = \frac{4 \pi R_u^3}{3}

For the post #5 equation for the Universe total energy integration by substitution:
E_t = \rho_c c^2 V_u = \frac{4 \pi c^2}{3} \left( \frac{3 H_0^2}{8 \pi G} \right) R_u^3 = \frac{H_0^2 c^2 R_u^3}{2 G} = 3.112 \cdot 10^{71} \; \text{j}

\boxed{E_t = \frac{H_0^2 c^2 R_u^3}{2 G}}

\boxed{E_t = 3.112 \cdot 10^{71} \; \text{j}}

These are my equations for the total Universe_mass-energy equivalence based upon the Lambda-CDM model parameters and the Hubble Space Telescope (HST) and WMAP observational parameters and the observable Universe radius in Systeme International units.

R_u = 4.399 \cdot 10^{26} \; \text{m} - observable Universe radius
H_0 = 2.3298 \cdot 10^{- 18} \; \text{s}^{- 1} - Hubble parameter (WMAP)
\Omega_s = 0.005 - Lambda-CDM stellar Baryon density parameter
dN_s = 10^{22} - Hubble Space Telescope observable stellar number
dV_s = 3.3871 \cdot 10^{78} \; \text{m}^3 \; \; \; (4 \cdot 10^{30} \; \text{ly}^3) - Hubble Space Telescope observable stellar volume
M_{\odot} = 1.9891 \cdot 10^{30} \; \text{kg} - solar mass

Hubble Space Telescope observable stellar density:
\rho_s = M_{\odot} \left( \frac{dN_s}{dV_s} \right)

Universe observable radius:
\boxed{R_u = 4.399 \cdot 10^{26} \; \text{m}}

Universe sphere volume:
V_u = \frac{4 \pi R_u^3}{3}

Observable Universe_mass-energy equivalence total mass integration by substitution:
M_t = \frac{\rho_s V_u}{\Omega_s} = \frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) R_u^3 = 4.188 \cdot 10^{56} \; \text{kg}

Observable Universe_mass-energy equivalence total mass
\boxed{M_t = \frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) R_u^3}

\boxed{M_t = 4.188 \cdot 10^{56} \; \text{kg}}

However, only a fraction of this total mass exists in the form of mass in the Universe, which is composed of 22.8% cold dark matter and 4.56% ordinary baryonic matter.

\Omega_m = \Omega_{c} + \Omega_b = 0.2736 - Lambda-CDM total matter density

Universe total matter mass integration by substitution:
M_u = \Omega_m M_t = \frac{4 \pi M_{\odot}}{3} \left( \frac{\Omega_m}{\Omega_s} \right) \left( \frac{dN_s}{dV_s} \right) R_u^3 = 1.146 \cdot 10^{56} \; \text{kg}

Universe total matter mass:
\boxed{M_u = \frac{4 \pi M_{\odot}}{3} \left( \frac{\Omega_m}{\Omega_s} \right) \left( \frac{dN_s}{dV_s} \right) R_u^3}

Universe total matter mass:
\boxed{M_u = 1.146 \cdot 10^{56} \; \text{kg}}

Universe_mass-energy equivalence integration by substitution:
E_t = M_t c^2 = \left[ \frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) R_u^3 \right] c^2 = \frac{4 \pi c^2 M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) R_u^3 = 3.764 \cdot 10^{73} \; \text{j}

Universe_mass-energy equivalence total energy:
\boxed{E_t = \frac{4 \pi c^2 M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) R_u^3}

Total amount of energy in the Universe:
\boxed{E_t = 3.764 \cdot 10^{73} \; \text{j}}

However, only a fraction of this total energy exists in the form of energy in the Universe, which is composed of dark energy at 72.6%.

\Omega_{\Lambda} = 0.726 - Lambda-CDM dark energy density

Total amount of dark energy in the Universe integration by substitution::
E_{\Lambda} = \Omega_{\Lambda} E_t = \frac{4 \pi c^2 M_{\odot}}{3} \left( \frac{\Omega_{\Lambda}}{\Omega_s} \right) \left( \frac{dN_s}{dV_s} \right) R_u^3 = 2.733 \cdot 10^{73} \; \text{j}

Universe dark energy total energy:
\boxed{E_{\Lambda} = \frac{4 \pi c^2 M_{\odot}}{3} \left( \frac{\Omega_{\Lambda}}{\Omega_s} \right) \left( \frac{dN_s}{dV_s} \right) R_u^3}

Total amount of dark energy in the Universe:
\boxed{E_{\Lambda} = 2.733 \cdot 10^{73} \; \text{j}}
[/Color]
Reference:
http://en.wikipedia.org/wiki/Hubble%27s_law"
http://en.wikipedia.org/wiki/Lambda-CDM_model"
http://en.wikipedia.org/wiki/Universe"
http://en.wikipedia.org/wiki/Observable_universe"
http://en.wikipedia.org/wiki/Dark_matter"
http://en.wikipedia.org/wiki/Dark_energy"
http://en.wikipedia.org/wiki/Hubble's_law#Interpretation"
http://en.wikipedia.org/wiki/Hubble_volume"
http://en.wikipedia.org/wiki/Friedmann_equations#Density_parameter"
 
Last edited by a moderator:

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