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There are many 'distance measures' used in cosmology, it gets very complicated. A good review is here 'Distance Measures in Cosmology', by D.Hogg

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The main thing here is that expansion of universe is not the same thing as the speed which is limited by $c$. The expansion itself has no limit in principle (see other answers for more information). A related fact is that even without cosmic expansion, it is possible to find examples of distances which change at $2c$. If two things approach you from opposite ...

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You ignored the $k$ term, but it's crucial here. $k$ is the curvature not of spacetime but of constant-$t$ spatial slices, so it depends not only on spacetime curvature (represented by $ρ$ and $Λ$) but also on the extrinsic curvature of the spatial slice in the spacetime (represented by $\dot a/a$). You can think of this equation as showing the relationship ...

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A non physicist with an imagination is more valuable to our understanding of the universe than an army of physicists still locked in to current theories. The scientists that dared to theorize and challenge our understanding of the universe are incredible, and they got us where we are now. Nearly all of them were never under the delusion that they were ...

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Yes, the black body radiation follows the apparent temperature change in both shape and magnitude. In a hollow black body, the radiant power density per unit wavelength and per unit area given by Planck's Law ${(2hc^2/\lambda^5)/(e^{hc/{\lambda kT}}-1)}$ The shape of the curve is determined by the denominator and is the same for any $\lambda T$ product. So ...

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Measurements of accelerating expansion are done by generally comparing velocity of distant galaxies by their redshift up against measurement of distances using Type 1A Supernovae. Not a collection of measured distances between two objects over time. As would have related to Special Relativity.

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Let me start by saying that it's not quite correct to say space compresses around an accelerating observer and expands around a decelerating observer. But I do see what you mean and, since I'm not a mathematician, I'm willing to accept your wording and work within that framework to explain the answer to your question. Point the first: We are not decelerating....

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Solving the differential equation for the scale factor $a$ in this case we have explicitly $$\frac{da}{a} =H_0 \cdot dt\qquad \Longrightarrow\qquad a(t) \propto e^{H_0 t},$$ assumming $H_0$ is constant through time. From the expression above you can conclude for this model there is no point in time where the scale factor was exactly zero. You might then ...

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during this time space-time expanded with a speed faster than the speed of light This statement actually is the problem here. The expansion of the universe is not measured in units of speed, so it cannot really be compared to c in the first place. Saying that it is faster than the speed of light is “comparing apples and oranges”. The expansion of the ...

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Please note that the model of the universe corresponding to ΩR=ΩNR=Ωk=0, ΩΛ=1 has no matter and no radiation and no curvature. This is an empty Euclidean universe with no expansion. Therefore Ho and a are and both constants. Since da/dt = 0, then Ho = 0. If a was a variable rather than a constant, then the integral of da/a is ln a, which is infinity. For da =...

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To your first question, you are right : the answer is just that the universe is really really empty. To your second one : Did the expansion of the universe somehow 'outrun' the photon? the answer is more complicated. In some sense, the photons are catching up. Consider a very small volume, 13 billions years ago, and all the photons is that volume. When time ...

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The crystal is a lump of matter of fixed size, and the expansion of the universe simply means that other lumps of matter are moving away from it on average over very large scales. There is no force or other effect due to the expansion that acts on the crystal, that would cause it to gain or lose energy. If the cosmological constant $Λ$ is nonzero then there ...

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It is not necessarily adding energy (in fact, I must admit yours is the first example I've ever heard of energy gain), but yes, the Universe's expansion does change the energy of matter in it. A way of thinking about is the fact that the stress-energy-momentum tensor in general depends on the metric tensor. Let me provide a different example, that also shows ...

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Here are two general observations which might help. First, the big bang "fireball" trapped light inside it not because gravity was so powerful, but instead because the temperature was so high that the photons of light could not travel very far before colliding with something that had an electric charge (electron-positron pairs were all over the ...

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Your intuition that $\rho$ ought to slow the expansion is correct, but that intuition concerns $\ddot{a}$ not $\dot{a}$ (and indeed in the other Friedman equation you do see a minus sign). The $(\dot{a})^2$ term comes from the expression for the curvature when the metric is of FLRW form. The Einstein field equation says there has to be a relationship between ...

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$\dot a$ is the rate of change of the scale factor i.e. it tells us how fast the universe is expanding. Shortly after the Big Bang the universe was very dense and expanding very rapidly so both $\rho$ and $\dot a$ were high. Then as time went by the universe became less dense as the matter was diluted by the expansion, and at the same time the expansion ...

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In the context of general relativity, Weyl's postulate is that a privileged reference frame of spacetime can be defined and have a physical meaning. The most common notion to implement this notion is that of comoving coordinates*, where the spatial reference frame is attached to the average (spatial) positions of galaxies (or any large piece of matter that ...

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If what you want a gut-feeling of what these equations mean, I can share mine. Equation (2) is a consequence of the two others. Take the time-derivative of (3), remembering that K and $\lambda$ are constants and $H=\dot a/a$, combine this derivative with (1) and (3) and you get (2). So no gut-feeling for that one, just trivial algebra. Now gut-feeling of (1)...

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