Cosmic Horizons

[BJC]

There are methods for calculating the horizon size of the cosmic microwave background. Are there similar methods for calculating the horizon size of the cosmic neutrino, gravity wave backgrounds. I suppose a simple percentage addition of (first light)/(universe age) (300,000/13,400,000,000) works if you assume that neutrino, gravity speeds are at the speed of radiation ??

 

Also i have heard that the limits of vacuum energy is 1000 times that of the radiation or CMB horizon. Wouldn't the gravity waves from vacuum energy expansion affect the cosmic gravity wave horizon?

[MigL]

The cosmic microwave background radiation arises from the 'decoupling' of radiation from matter. It is the point in time ( approx 300000 yrs after big bang ) when the temperature of the universe had dropped enough for stable atoms to form, ie electrons captive to atoms of hydrogen, helium and lithium. Previous to this, electrons were free of the ionic plasma which composed the universe because as soon as an electron tried to attach to an ion, it would be knocked lose by an energetic photon, much like the interior of the sun, and so the universe was opaque.

Neutrinos decoupled a lot earlier and since neutrinos are extremely difficult to detect, the red shifted neutrinos from the decoupling era would be impossible to detect.

Gravitons would have decoupled at 10^-34 sec after the big bang, the end of quantum gravity, and we haven't even detected normal gravitons yet, never mind low energy ones from such an early time.

[BJC]

Basically i wanted a theoretical equation for estimating the size of the neutrino and gravity horizons.

 

If you assume the neutrino is mass-less the the neutrino horizon would be ~(300,000 + expansion) light years greater than the CMB horizon. But the neutrino has a small mass (<< 1eV) and as such should slow down and stop as it loses energy.

 

With gravity being a source of gravity plus gravity waves from vacuum energy should make the "cosmological gravity wave horizon" almost impossible to define, even theoretically.

[MigL]

The horizon is the same for any kind of energy as it all travels at c, and the universe is expanding, ie at acertain distance all energies are red-shifted to infinite wavelength and zero energy. This makes the observable universe a finite size no matter which energy wavelength you use to 'observe'.

The CMB permeates all of the universe, it doesn't exist only at the horizon. If you could measure the CMB right beside you, it would be 2.7 deg., not just at extreme extragalctic distances. I hope I'm not misunderstanding your original query. If I'm not you haven't grasped the significance and explanation for the CMB.

[BJC]

The distances i am interested in are calculated by a formula similar to this:

[latex]\int_{t0}^{t1} c \frac{dt}{a(t)}[/latex]

 

which, eventually, arrives at a figure of ~ 93 B. Light-years.

 

1) This is not the precise formula and i would need an estimate of the expansion function a(t) to calculate the integral;

 

2) i could use this formula and just assume that neutrinos must travel at light speed --- but neutrinos do have a small mass and as such should come to rest when they lose energy;

 

3) with gravity: the gravity wave horizon would be affected by (a)the gravity wave itself and (b)gravity waves from vacuum energy expansion.

 

Given these problems i do not see how the CMB or Hubble Volume equation could be used to calculate the other horizon sizes - so what is used?