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As far as I have understood from this paper, they have given some observational limits to the value of $\Omega_{k,0}$, but this article concludes asserting that "there is no evidence from Planck for any departure from a spatially flat geometry". Taking $\Omega_{k,0}=0$ and the value for $\Omega_{r,0}$ given at this post, one can compute the above integral ...


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I like this video by MinutePhysics on this topic. It can clarify things as a primer. When you state that the universe expanded at a speed higher than the speed of light, you have to stop and ask what is actually meant by such a statement. What is moving with respect to what? In standard cosmology, we describe the universe expansion by the Hubble rate ...


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Most of it would've become radiation- mostly photons and some neutrinos. Some of that can be seen in the cosmic microwave background. The rest would've gone into the kinetic energy of remaining matter particles (i.e., heat). We don't actually know what dark matter is made of, but we do know what the reaction products of matter/anti-matter annihilation are ...


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The word energy tends to be used in a rather vague way, and typically to mean something exotic. In the context of particle reactions energy either means photons or the kinetic energy of the particles leaving the reaction. For example an electron and anti-electron annihilate to produce two photons. By contrast the annihilation of a proton and anti-proton is ...


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When the universe expands, it is important to understand that how its energy content evolves depends on the form of energy involved. If all that energy is locked up in the form of mass energy, then the density of that matter will decrease proportionally to the relative increase of any arbitrary volume of the universe (i.e. if expansion doubles the size of ...


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Temperature means energy. The heat energy is still here. It's just that the "object" (the Universe) grown bigger so this energy had to spread through it. The more energy in a single point, the hotter it is. That's why they say it got cooler. It's like the expanding gas from your spray deodorant is cold when it leaves the can, but it was at room temperature ...


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Let's start by setting the scene. We've got a hyperdense (understatement) singularity containing everything at $t = 0$. This is the beginning of time. Right now, we have no reason to assume that anything existed before then. Asking what happened before the Big-Bang ( depending on which model you use ) is not something that one can ask since we assume nothing ...


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The CMB was emitted at an energy of $E_{em}=13.6\text{ eV}$, which is the binding energy of hydrogen. This corresponds to a wavelength of $$ \lambda_{em} = \frac{hc}{E_{em}} \approx 9.12\times 10^{-8}\text{ m}$$ Redshift can be calculated by $$ 1+z = \frac{\lambda_{obs}}{\lambda_{em}} $$ If we observe blue light at 400 nm, we get a corresponding redshift ...


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Actually the "last scattering surface" of the CMB corresponds to the transition of the interstellar/intergalactic medium from an ionized plasma to cooler neutral atoms, about 300 000 years after the big bang. Most atoms have excitation and ionization energies in the visible, so the CMB was probably visible when it formed. We can be a little more precise ...


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From a distance, black holes are no different from any other matter. Their gravitational attraction is the same as that of any other body with the same mass. If you were to suddenly convert a star into a black hole of the same mass, any planets around that star will keep moving in exactly the same orbits as before. Observers on the planets would not notice ...


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The universe is finite but doesn't have a center. It is also 2 dimensional, like riding the skin of a balloon. It doesn't have a shape. Space is curved due to gravity. There isn't any space that isn't curved. There isn't any edge to the universe. One cannot view the universe from the outside because an outside doesn't exist. Anywhere in the universe can be ...


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The amount of 'randomness' is not the only definition of entropy. Entropy is also known as the amount of unusable energy that's present in a system. So if you have a lot of heat energy in a system, since all of that heat energy can be used up, its entropy would be low. If you have less heat in a system, only a small amount of heat in that system can be used ...


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I would like to think about the universe as a balloon's surface. Imagine yourself as a 2D person living on this balloon, can never get out of it. If the balloon expand, you will just see everything is going far away from you, and vice versa. So if you think of Big Bang as a sudden great expansion of the balloon, you - the 2D person on the balloon - will ...


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The Big Bang didn't occur at a special isolated place in the Universe. It occurred in the whole Universe and every place of it. Every point was an equal player in the Big Bang. Lots of light at various frequencies was produced during the epochs of or after the Big Bang. But it's wrong to imagine that they were coming from a particular distant place. ...


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You cannot place anything "outside" to observe the big bang because there was no space that thing could have existed in (as you rightly said in your first sentence). So any observer is necessarily right in the middle of the bang happening. The popular science illustrations showing a ball of light expanding are essentially wrong. There is nothing the ball ...


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You asked a lot of questions there, many of them not fully formed. I've seen another question of yours asking if dark energy has gravity and asserting Hawking Radiation doesn't exist. Dark energy seems to be your thing. You're tempted to use it as a magic bullet to disprove a lot of cosmological theory without understanding it. Let's talk about Dark ...



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