What is the average rate of passage of time in the observable universe relative to the passage of time on earth? Main Question: If you were to average out the rate of the passage of time in the observable universe relative to earth, what would it be?
Alternative Precise Question: What is the rate of passage of time at the halfway point between Andromeda and The Milky Way relative to earth? I imagine it must be very fast.
Assume 1 time unit = 1 earth time unit.

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I think it would be interesting to find out that earth experiences time vastly different from the rest of the universe.
 A: Gravitational time dilation in a gravity well is equal to the relativistic time dilation due to the speed required to escape that gravity well (see this Wikipedia article for more information). Escape velocity from the Earth is about 11.2 km/s. Solar escape velocity from Earth's orbit is about 42.1 km/s. Escape velocity from the Milky Way is about 550 km/s. So total escape velocity from Earth to a point halfway between Andromeda and the Milky Way is somewhere in the vicinity of 600 km/s, which produces a time dilation factor of about 1.00000200277612; that is, for each second that passes on Earth around 1.00000200277612 seconds pass at your hypothetical distant point.
(This calculation assumes the observers are at rest relative to one another. If the distant observer is at rest relative to the cosmic microwave background, then there's another factor of about 600 km/s to account for due to the Earth's movement relative to the CMB.)
A: To calculate time dilation with respect to a point midway between the Milky Way and Andromeda you need to account for motion of the Earth relative to that point and for the difference in gravitational potential between the surface of the Earth and that point.
Because both these effects are small they can be treated as additive (in the same way that sometimes people talk about a SR correction and a GR correction to the clocks on the GPS satellites).
Roughly speaking, Andromeda is approaching the Milky Way at $\sim 110$ km/s. The tangential component of the relative velocity is much smaller than that. In addition, the Sun orbits the galactic centre at something like 220 km/s and these two velocities combine to give a speed of about 250 km/s or a Lorentz factor of $\gamma -1 = 3.5\times 10^{-7}$, assuming that the midpoint is co-moving with Andromeda.
If we assume that the point midway between the Milky Way and Andromeda is at zero potential, then if the Milky Way has a mass of $\sim 10^{11} M_{\odot}$ interior to the Sun's galactic radius, then the potential is of order $\Phi \sim -5\times 10^{10}$ J/kg and an associated dilation factor of $$1 - \Phi/c^2 = 1 + 5\times 10^{-7}\ .$$ Note that we don't need to include the gravitational potential due to the Earth itself or due to the Sun because these potentials are about 2 orders of magnitude smaller.
i.e. The two effects are small and of similar size. The total time dilation is $\sim 10^{-6}$. i.e. $1 + 10^{-6}$ seconds pass on Earth for every 1 second on a clock midway between the Milky Way and Andromeda.
To do the calculation between the Earth and an average bit of the universe then I think you would have to go with working out a time relative to the co-moving rest frame. The Sun moves at 370 km/s with respect to the Cosmic Microwave Background (which defines the comoving rest frame). The motion of the Earth around the Sun is much smaller and can be neglected. This yields a time-dilation factor of $\gamma -1 \simeq 7.6\times 10^{-7}$.
For the potential we need to think about not just the Milky Way but the Local Group of galaxies. However, it turns out that the mass of the local group is only a few times that of the Milky Way and is of course spread over a much larger volume. So the additional gravitational potential due to all the other local galaxies is rather small compared to that contributed to mass interior to the Sun's galactic radius. Therefore the time dilation number for the gravitational potential will only be marginally bigger than that to the midpoint between Andromeda and the Milky Way.
Thus my answer for the time dilation factor with respect to the co-moving frame is about $1.3\times 10^{-6}$.
A: Time at the midpoint between Andromeda and the Milky Way (assuming that no gravity is present) passes barely faster than time on Earth, contrary to what you imagine. I'll give a technical derivation.
The spacetime surrounding the Earth is the Schwarzschild metric:
$$
ds^2=\left(1-\frac{r_s}{r}\right)dt^2-\left(1-\frac{r_s}{r}\right)^{-1}dr^2-r^2d\Omega^2,
$$
Here $r$ is the radial distance from the center of the Earth and $r_s$ the Schwarzschild of the Earth (which we can set to be $8,7(mm)$). The only part of the metric we have to take into consideration is the $dt^2$ part, as $r$ and $\Omega$ (representing the angles in the radial coordinates) stay constant. From this, we can see that passage of time is $r$-dependent. Now, let's say that:
-time passage at a point between Andromeda and the Milky Way: 1
-time passage at the surface of the Earth (where $r=6000 000$): $\sqrt{\left(1-\frac{r_s}{r}\right)}=\sqrt{\left(1-\frac{0,0087}{6000000}\right)}$
As you can see clearly, the rate at which time on Earth flows is practically the same as the rate at which it flows at the midpoint between Andromeda and the Milky Way (so time doesn't flow much faster at the midpoint). If a black hole were present at the midpoint, then time on Earth would flow much faster compared to the time passage around the hole. If the Eart revolved around a black hole, then time on Earth could indeed flow considerably slower than at the midpoint (so time at the midpoint would indeed flow much faster than on Earth, though it of course depends what you call much).
What about the flow of time on Earth when compared to the average flow of the whole universe? Considering the fact that space is flat almost everywhere, we can safely say that the average rate of time of the whole universe will be no different from the rate of time at the midpoint between Andromeda and the Milky Way. So time on Earth flows at the same rate wrt to the flow of the whole universe as it does wrt to the midpoint. That is, barely slower. Note that I don't take the gravitational influence of the sun and the Milky Way into consideration. But these contributions don't make time on Earth go substantially slower, so even when you take them into consideration this would not change the conclusion.
