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Homogeneity in cosmology means uniformity from point to point, not only in composition or content, but in geometry as well. An empty space with a singularity is still non-homogeneous. Isotropy at every point does imply homogeneity, but we are not in a position to observe the universe from every point. Mathematically, isotropy at any two distinct points ...

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Strictly speaking the FLRW metric doesn't specify that time starts at the Big Bang. It specifies only that the Big Bang is a singular point so it is impossible to analytically continue a geodesic back in time past the Big Bang. If it helps to make things clearer, exactly the same happens with an object falling into a black hole. A geodesic that crosses the ...

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The particle horizon is the distance from which light emitted at the moment of the Big Bang will just now be reaching us. The CMB was emitted 380,000 years after the Big Bang. So the CMB radiation we see has been travelling for less time than the light emitted at the Big Bang, and therefore the CMB radiation has travelled a shorter distance than the ...

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OK, I'll give this a shot, cause . . . why not. The article you quoted covers a lot of ground - perhaps too much ground. And I'm not sure the quote of Matt Strassler is fair because he's answering a very specific question and while the source is given, it's not mentioned that it's a specific question that he's answering. but, lets jump to this part: ...

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Yes, the vacuum energy of a spacetime lattice with finite spacing and periodic boundary conditions within a box of finite size is finite. One would not call this "quantizing", though, rather discretizing because we are not carrying out any "quantization procedure" in the sense of going from a classical to a quantum system. In this approach, the finite size ...

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The size of atoms is determined by the strength of the electromagnetic force, the mass of the electron and some other constants like the value of Planck's constant. If the size of atoms was changing it means that one or more of these constants must be changing. The trouble is that these fundamental constants crop up all over the place in physics, and if ...

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Olbers’ Paradox says that in an infinite universe every line of sight will end on a star. That statement is incomplete. The paradox requires not only an infinite universe, but also one that is both static and infinitely old. Neither of the second two statements are true for our universe. Your question considers the effect of aging. As our position ...

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The ultimate fate of the universe (and here I'm taling about things on cosmic scales not what happens to stars and galaxies etc.) depends on the equation of state of the material within it. In cosmology the equation of state is represented by a dimensionless number that is the ratio of the pressure to the (energy) density. i.e. $$w = \frac{P}{\rho}$$ and ...

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I've heard that some physicists think that the net energy of the universe is zero. Me too. They talk about gravitational energy being negative. But see Einstein talking about gravitataionl field energy here. It's positive. For this to happen, I would assume that the negative gravitational energy of a body ought to cancel out its rest energy. That's what ...

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Using the standard model of cosmology we calculate the Hubble time to obtain an estimate of the age of the universe. Yes, 13.8 billion years. But IMHO there's an issue worth discussing, to do with something John said in another answer: "A distant observer sees falling objects slow as they approach the event horizon and asymptotically approach zero speed at ...

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Let me clear up a few misconceptions. The edge of our observable universe would contain information from the beginning of the universe, since it is a particle horizon. However, the edge of the observable universe is not currently visible to us. What we can currently see only goes as far back as the recombination era, when electrons first joined with nuclei ...

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Let embrace your attitude here. If the atom is 'empty', all that we have is charge and mass. By Newton's third law we have that this 'empty' with charge and mass need to absorb energy and momentum too. Now we have an empty space with charge and mass that absorb momentum and energy. Furthermore, this empty are allowed to move through space, because is ...

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The ratio of dark to baryonic matter is 5.25 in the first diagram and 5 in the second diagram, but I don't think the difference is significant. We don't know the densities with absolute certainty, especially near the Big Bang, and the small difference between the ratios is probably just down to the uncertainties in the densities. We would expect the ratio ...

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You set $\rho$ equal to one for no reason. In detail the expression for $\Gamma$ is: $$\Gamma^1_{01}=\frac{1}{2}\sum_\rho g^{1\rho}\left[\frac{\partial g_{1\rho}}{\partial x^0} + \frac{\partial g_{\rho 0}}{\partial x^1} - \frac{\partial g_{01}}{\partial x^\rho}\right].$$ And since $g_{01}$ equals zero (since your metric is diagonal), all four partial ...

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Here is a short summary inspired by Barbara Ryden: Homogeneity: No preferred location Isotropic: No preferred direction And here are some examples to clarify things: Example of homogeneous but not isotropic: A forest, it looks the same no matter where you are, but trees make the vertical direction distinct. Example of Isotropic but not homogeneous: When ...

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Assuming you found a way and managed to accelerate above light speed without disintegrating, and went to the edge of the universe... I'm confident you can't go faster than light, but when it comes to the edge of the universe, I'm also confident that nobody knows any answers. However people say they do and state categorically that there is no edge. For ...

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Your question isn't quite right - not all closed universes are younger than all flat universes, and all open universes are not older than all flat universes. As a reference Universe, pick your favourite flat Universe - the density may be in several components (matter, radiation, $\Lambda$), but it must be exactly critical. Suppose we want an open universe ...

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In your model, of everything stretching, there would be no way to observe any stretch. We would live in static dimensions as far as we are concerned. It is our observations of the way the stars, galaxies and clusters of galaxies behave that has led to the idea of an expanding universe : Hubble inferred the recession velocity of the objects from their ...

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This part of Lawrence Krauss' brilliant "A Universe from Nothing" lecture describes the fate of an expanding universe quite well. Long story short, because the expansion of the universe is accelerating, in a hundred billion years or so the rate will exceed the speed of light (this doesn't require objects to move through space faster than light, that's ...

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As the comments to the questions state, this is a question on the research state about the generation of the universe, and the first moment is modeled in the Big Bang model. The real beginning point is not yet known even in this model since gravity has not been consistently quantized within the model, only effective theory is used. Nevertheless existing ...

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Given that we can only interact or observe the universe out to a certain distance, it isn't possible to test whether the universe is infinite. Even if it is, the parts of it beyond a certain distance are inaccessible to us through any means, because all information is limited to the speed of light, including the travel of gravitational waves and massless ...

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Ha! Some time ago I read an article where they proposed an experiment where they wanted to test exactly what you're asking. Here is the article and here is the paper. The idea is the following: Place a shielded neutron detector near a neutron reactor and place a thick wall between them. This wall should be thick enough so that they normally don't reach the ...

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The phenomenon you are referring to is Poincaré recurrence. The idea is that if a closed system has only a finite number of possible states then it must eventually return to a state that is has been in before. However the universe is not a closed system with a finite number of states and the recurrence theorem does not apply to it. For example the average ...

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Here's the horizon problem: Look at the sky. Look at one side of the sky. Then look at the other side of the sky. The light from one side has just now reached you, as has the light from the other side. When we look back to the earliest observable moments of the universe, the Cosmic Microwave Background (CMB), we do the same thing. We look at light that was ...

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how the hell does relativity justify that the character can be thrown in black hole and survive ? This is a big question and scientists (physicists) are asking the question that "what will be the fate of an astronaut falling into a black hole?" ,since the concept of general relativistic black holes have arisen. The answer is the astronaut may not ...

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1) What you call $\rho$ should really be called $\epsilon$ (this is the energy density, not the particle density). 2) The thermodynamic variables $\epsilon$ and $P$ are expectation values of certain operators in a thermal ensemble. You should not confuse equations for the operators with equations for thermodynamic quantities. 3) The operator that ...

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