Cosmic micro-wave background, also cosmic gravitation-wave background?

[Spinnor]

Can one assume in the very early Universe that there was a whole lot of gravitational radiation?

Would such radiation "decouple" like the early photons did that give us our present CMB?

What is the present energy density of this radiation assuming it exists?

Thanks for any help.

 

[evilcman]

Any particle, that decoupled somewhere along the expansion is a background now. You can estimate the background temperature the same way you do with photons. So for the graviton it would go something like this( I use natural units ):
the interaction rate can be estimated as
Gamma ~ Sigma * n ~ G^2 T^5
at the time of decoupling this rate should be the same as the expansion rate
H ~ T^2 / m_Pl
meaning the decouling took place at Planck scale

The temperature can be gotten from the constraint of adiabatic expansion,
if you take into account only ultrarelativistic species:
entropy density = s ~ g*S T^3 ~ constant
where g*S is an effective degeneracy normalized so the T is the photon temperature
s = K (g1 T1^3 + g2 T2^3 + ...)
(for bosons, for fermions there is an additional 7/8) meaning
g_*S = sum for fermions(7/8) (T_f/T)^3 + sum for bosons (T_b/T)^3

now g_*S is known today, but it is not known at the time of graviton the decoupling, since it is really high energy, if we take into account only standard model particles it was 106.75 then and 3.91 today so the temperature would be (3.91 / 106.75)^(1/3) T roughly 0,9K but it could be much smaller actually, because of the possible other particles at high energy(the predictions of unification theories...) to we can conclude that the temperature of the assumed graviton background < 0.9K

Something like that...

 

[evilcman]

sorry, I should correct myself, g*is not necesarrily known today, but it can be computed with the known ultrarelativistic particle species(that is neutrinos and photons)

 

[Spinnor]

Any particle, that decoupled somewhere along the expansion is a background now. You can estimate the background temperature the same way you do with photons. So for the graviton it would go something like this( I use natural units ):
the interaction rate can be estimated as
Gamma ~ Sigma * n ~ G^2 T^5
at the time of decoupling this rate should be the same as the expansion rate
H ~ T^2 / m_Pl
meaning the decouling took place at Planck scale

The temperature can be gotten from the constraint of adiabatic expansion,
if you take into account only ultrarelativistic species:
entropy density = s ~ g*S T^3 ~ constant
where g*S is an effective degeneracy normalized so the T is the photon temperature
s = K (g1 T1^3 + g2 T2^3 + ...)
(for bosons, for fermions there is an additional 7/8) meaning
g_*S = sum for fermions(7/8) (T_f/T)^3 + sum for bosons (T_b/T)^3

now g_*S is known today, but it is not known at the time of graviton the decoupling, since it is really high energy, if we take into account only standard model particles it was 106.75 then and 3.91 today so the temperature would be (3.91 / 106.75)^(1/3) T roughly 0,9K but it could be much smaller actually, because of the possible other particles at high energy(the predictions of unification theories...) to we can conclude that the temperature of the assumed graviton background < 0.9K

Something like that...

Thank you for a detailed reply!

Can I assume these gravitons still interact with each other?

Would they tend to "clump" gravitationally around clusters of galaxies?

Thank you for your knowledge.

 

[evilcman]

Since the gravitons are supposed to be massless themselves(gravity is a long range force...) I see no reason why they would be attracted to massive objects, so they should be quite close to isotropic and homogeneous in density.

 

[Spinnor]

Since the gravitons are supposed to be massless themselves(gravity is a long range force...) I see no reason why they would be attracted to massive objects, so they should be quite close to isotropic and homogeneous in density.

In a sense they are "charged", they have energy and so couple to each other and to mass? Gravitons can scatter by emitting and absorbing virtual gravitons?

Have a good weekend, thanks for your time.

 

[Spinnor]

Any particle, that decoupled somewhere along the expansion is a background now. You can estimate the background temperature the same way you do with photons. So for the graviton it would go something like this( I use natural units ):
the interaction rate can be estimated as
Gamma ~ Sigma * n ~ G^2 T^5
at the time of decoupling this rate should be the same as the expansion rate
H ~ T^2 / m_Pl
meaning the decouling took place at Planck scale

The temperature can be gotten from the constraint of adiabatic expansion,
if you take into account only ultrarelativistic species:
entropy density = s ~ g*S T^3 ~ constant
where g*S is an effective degeneracy normalized so the T is the photon temperature
s = K (g1 T1^3 + g2 T2^3 + ...)
(for bosons, for fermions there is an additional 7/8) meaning
g_*S = sum for fermions(7/8) (T_f/T)^3 + sum for bosons (T_b/T)^3

now g_*S is known today, but it is not known at the time of graviton the decoupling, since it is really high energy, if we take into account only standard model particles it was 106.75 then and 3.91 today so the temperature would be (3.91 / 106.75)^(1/3) T roughly 0,9K but it could be much smaller actually, because of the possible other particles at high energy(the predictions of unification theories...) to we can conclude that the temperature of the assumed graviton background < 0.9K

Something like that...

There may have been, in the first instants of our universe, equal amounts of matter and anti-matter? Latter, matter and anti-matter mostly annihilated leaving a "small" amount of matter, one part matter for 10^? parts initial matter anti-matter.

Would this have any consequences for the above calculation?

Thanks for any thoughts.

 

[evilcman]

There may have been, in the first instants of our universe, equal amounts of matter and anti-matter? Latter, matter and anti-matter mostly annihilated leaving a "small" amount of matter, one part matter for 10^? parts initial matter anti-matter.

Would this have any consequences for the above calculation?

Thanks for any thoughts.

No, the estimate remains to same without regard to the precise mechanism of baryogenesis. The reason is the following: When calculating the entropy density we only take into account ultrarelativistic particles, that is particles with mass << T, if this holds than the entropy density is proportional to T^3 just as I have written, these particles can be created easily by processes like gamma gamma -> e- e+ and such since the thermal energy is high enough to produce particles of such mass. Meaning when we calculate g* we have to take into account the antiparticles also, as degeneracy, so for example for electrons still in thermal equilibrium with photos( Telectron = T ) the contribution of the electrons and positrons to g* would be
(7/8) * 2 * 2
since they are fermions, with 2 degeneracy: e- or e+ * 2 degeneracy(spin up-down)

 

[evilcman]

Also, I was a bit sloppy, what remains contant is not the entropy density s, but s*R^3 where R is the scale factor, but that's just sloppy explanation, the result remains the
same.