# Different densities of the universe on different angles?

• I
• KingSnackMan
In summary, the conversation discusses the possibility of determining the density of the universe along a specific line of sight, as well as the variations in density in different directions. It is mentioned that the universe is isotropic, but there may be small deviations from the average density due to large scale structure. There is no known method to measure the density along an entire line of sight, but measurements of the matter power spectrum and the integrated Sachs-Wolfe effect may provide some information on the statistical properties of the matter distribution in the universe.

#### KingSnackMan

Does anybody know of a resource that I could use to determine the density of the universe along a specific line of sight? (right ascension and declination)

I am investigating inertial forces and looking to identify both the most and least dense directions in space and determine by how much they differ.

KingSnackMan said:
Does anybody know of a resource that I could use to determine the density of the universe along a specific line of sight? (right ascension and declination)

I am investigating inertial forces and looking to identify both the most and least dense directions in space and determine by how much they differ.
The universe is isotropic, meaning that its density is the same in all directions.

CMB temperature anisotropies measure density gradients across the sky. Results from WMAP and Planck have determined the variation to be on the order of 1 part in 100,00, meaning the density of the universe is extremely unform in all directions. If the density gradient were larger this would show up as hot and cold spots in the CMB. The angular separation between these hot and cold spots would indicate the size of these various overdense and underdense regions.

Fervent Freyja
It's important to contrast my and Chronos's replies. Chronos refers to the non-uniformity of the temperature of the CMB at the time of decoupling: this means that the temperature of the universe at the places where the CMB photons observed today were emitted did indeed vary. This shows up today as an anisotropy of the temperature of the last scattering sphere. However, along the line of sight from Earth out to the edges of the observable universe, all of these variations should average out in a universe that is homogeneous and isotropic on large scales.

Fervent Freyja
Thank you bapowell and Chronos. I understand that on the universe is very close to isotropic, but because of the Large Scale Structure there must be some directions where there are just slightly more voids, and others where there I slightly more nodes, right? I am looking for very small deviations from the average density of the universe.

You would need to define exactly what you mean. Do you want the average density along a line of sight all the way back to the surface of last scattering, or just out to some distance? And how large a δθ do you want to average over? If δθ is small, then a line of sight that intersects a nearby neutron star will have a much higher average density than one that does not.

KingSnackMan said:
Thank you bapowell and Chronos. I understand that on the universe is very close to isotropic, but because of the Large Scale Structure there must be some directions where there are just slightly more voids, and others where there I slightly more nodes, right? I am looking for very small deviations from the average density of the universe.
Sure, there will be tiny differences in the density as a function of direction since the universe isn't perfectly uniform. But you'd have to add up all the matter along each line of sight (each with some small cross section) between Earth and the edge of the observable universe to determine the anisotropy. This is not possible with today's cosmological observatories.

KingSnackMan said:
Does anybody know of a resource that I could use to determine the density of the universe along a specific line of sight? (right ascension and declination)

I am investigating inertial forces and looking to identify both the most and least dense directions in space and determine by how much they differ.
I'm not aware of any method to measure the density along an entire line of sight. The only observable I can think of that might reflect that would be the lensing of the CMB, but that's a pretty subtle effect to measure, and I think you could only get some very generic statistics of the mass distribution, not the specific density along a particular line of sight.

It's definitely possible to measure the masses of particular structures via gravitational lensing (both strong and weak), but that won't get you the entire density along a line of sight.

I think if you just want to get an idea of the statistical properties of the matter distribution in our universe, look up measurements of the matter power spectrum.

bapowell said:
Sure, there will be tiny differences in the density as a function of direction since the universe isn't perfectly uniform. But you'd have to add up all the matter along each line of sight (each with some small cross section) between Earth and the edge of the observable universe to determine the anisotropy. This is not possible with today's cosmological observatories.
It is also unclear what that value would represent, as you integrate along an arbitrary line in both time and space. The integrated Sachs-Wolfe effect is something not too far away from that concept, and measurable.

bapowell
mfb said:
It is also unclear what that value would represent, as you integrate along an arbitrary line in both time and space. The integrated Sachs-Wolfe effect is something not too far away from that concept, and measurable.
Yes. But the ISW effect doesn't measure the density. It measures the change in gravitational potentials over time. When there's dark energy around, gravitational potentials get shallower over time, which blueshifts CMB photons that pass through large overdense regions. The problem is that the redshift/blueshift which results is indistinguishable from the fluctuations of the CMB itself, meaning that it can only be detected through the fact that it changes the statistical properties of the CMB.

mfb