# Recent content by BillSaltLake

1. ### Integrating Friedmann Equation of Multi-component universe respect to a and t

Try substituting x = 1/a and then use a table of integrals.
2. ### Mediaeval wormholes

This proves conclusively that wormholes exist.
3. ### Is the speed of light constant for a co-moving observer?

If you're talking about a "global" comoving frame, then the 1 lyr ruler, which is rigid, will be shrinking by just over 1 mile/day. The photon will always take a year to travel the length of the ruler, even though the ruler will have "shrunk" ~430 miles WRT the global comoving frame during that...
4. ### Just how dark is Pluto from orbit? How about Saturn?

The OP asked about the relative surface brightness of Earth vs. Saturn vs. Pluto when viewed close. Obviously an object will reduce in brightness if viewed from far away (specifically if the angular size is < 1 minute of arc, it cannot be resolved by the eye, so the farther away it is brought...
5. ### Problem interpreting Mpc/h in maps of DM

Note that h (\propto H) and a have different time evolution. Therefore a parameter that scales with h does not scale with a, and comoving distance scales with a. I think that the scale in the image should read "44/(1+z) Mpc", noting that 1/(1+z) \propto a.
6. ### Problem interpreting Mpc/h in maps of DM

Problem interpreting Mpc/h in "maps" of DM In charts of ρ distribution, such as the z = 0 image http://www.mpa-garching.mpg.de/galform/virgo/millennium/seqF_063a_half.jpg (taken from http://www.mpa-garching.mpg.de/galform/virgo/millennium/ ), the distance scale is usually expressed in...
7. ### Just how dark is Pluto from orbit? How about Saturn?

100 W bulb puts out about 5 lightwatts; zenith sun at earth is about 300 lightwatts/m².
8. ### Just how dark is Pluto from orbit? How about Saturn?

Pluto direct sun illumination would look like average residential indoor lighting at night, or a typical 100 W tungsten light at 8 feet.
9. ### Energy in co-moving co-ordinates?

As with most things, one must be careful of definitions. I assume your coordinate system defines v=0 locally as 'at rest with respect to CMB'. However, there are two different ways that lengths (and time intervals) can then be defined. The "normal" way (such as CGS or MKS, for example)...
10. ### Energy in co-moving co-ordinates?

h has units of (mass)(length2)(time-1). If the time measurement unit is changing, then h must become variable, whether you let l units change in ratio with t units or keep l units constant. Similarly, E has units of ml2t-2, so if you keep c constant by letting l and t units vary in ratio, then E...
11. ### Energy in co-moving co-ordinates?

No. If you impose a time-dependent time (and/or length) scale, then h is also changing, as is the relative meaning of E.
12. ### Cosmological constant from first principles

There's a possible problem here: he's saying (I think) that λLF2 is ~1/nμ where n is the # of phase space cells within the Hubble radius (and μ turns out to be ~1.2). However, during the matter era, n \propto ρ-3/4 \propto t3/2, which would make λ variable. This is not allowed in GR. (When I say...
13. ### Co-moving density should be constant?

In co-moving length units, Planck's constant h would be decreasing, so the photon energy will be decreasing.
14. ### Understanding expansion

The shrinkage atoms and gravitational orbits, with associated increase in atomic and orbital frequencies (to keep c constant) is a different but usable way to think of expansion. Note that if atoms and gravitational orbits were shrinking (at the same rate), we would not see the shrinking because...
15. ### Number of Voids in the (observable) Universe

What might be informative here is a plot of observations (or a plot derived from the millennium simulation) which shows the distribution of energy density. The x axis would be space volume, with the least dense on the left ("x"=0) and the most dense on the right ("x"=1 or 100%-- this is a...