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0

The web site you link is using the expression: $$ \rho_c = \frac{3}{8\pi G \theta^2} $$ where $\theta$ is the Hubble time and is equal to $1/H$. So your second equation should be: $$ \rho_c = \frac{3}{8\pi G \theta^2} = \frac{3}{8\pi G \left(1/H\right)^2} = \frac{3H^2}{8\pi G} $$


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The evidence for dark matter is extremely compelling provided that Einstein's theory of relativity is assumed. To get out of dark matter means dropping that assumption (or that we've SERIOUSLY botched some observations). Some people study alternate theories of gravity. The two alternate theories (or classes of theories? keywords?) I hear most about are f(R) ...


2

So over the last 48 hours I've been doing a small amount of research on my own question of why being able to detect or even image relic neutrinos would be important. Perhaps the most succinct summary can be found in these slides http://cosmo2014.uchicago.edu/depot/talk-long-andrew.pdf These suggest that there are 3 types of answer: The cosmologist's - ...


-1

Your cousin is right. The Universe is a 4D sphere W = r + Ix + Jy + Kz = [f, V] The universe is defined by energy W = -vh/2pir + cP where -vh/2pir = -vp = -mv^2, a real number potential energy. Newton found this in his theory of Gravity W=-mGM/r = -vh/2pir = -vp = - mv^2. Newton's energy is a real number or scalar 1 dimensional energy. Newton ...


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You're right that determining gravitational boundedness at large distances is difficult. Quick recap of the information on hand regarding the positions and velocities: Angular separation between any two galaxies Redshift Which is really not a whole lot to work with. You can't get a handle on the (projected) physical separation without knowing the ...


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Issue 1: The Expansion Misconception Forget everything you thought you visualized about the Big Bang. Let's start from scratch. First, picture a sheet of rubber with a grid marked on it. This sheet represents space. It is not curved, nor will it ever curve in this example. It might stretch, but that's not particularly important here either. Attach a light ...


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Addressing part of your question: Neutrinos were not emitted prior to (or at the start of) the big bang. "Before the big bang" is a phrase that drives the philosophers nuts, but because the big bang was the beginning of space and time, it is thought that there was no "before". Also, neutrinos of any sort could not have formed until a few fractions of a ...


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$3.36 = 2 + 3[2 Ă— (7/8)(4/11)^{4/3}]$. This is explained in this paper : bottom of page $15$, top of page $16$ + beginning of the discussion chapter $5$, page $14$


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Background neutrinos can't be detected, but neutrino observatories have detected neutrinos into the high TeV range. See e.g. Icecube http://icecube.wisc.edu/ for a high energy neutrino observatory.


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I will answer this since @rob, who provided the link that gives a summary of the proposed methods and technical difficulties, is not doing it (comments are not guaranteed to be invariant to time on this site). It is true that measuring the Cosmic Microwave Background radiation has been extremely important in the development of the model of the beginning of ...


1

In many standard theories, Neutrinos are assumed as the be most common particle in the Universe (known as cosmic neutrino background (CNB) a relic of the Big Bang). Many experiments are being carried out to detect them from different sources. Those from the CNB have been only indirectly detected, but many, originated in violent event across the universe ...


2

This is actually more subtle than you would think it would be. First, remember that a fourier transform is defined, for some time-dependent signal $F(t)$, as${}^{1}$: $$F(\omega) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty} dt\, e^{i\omega\,t} F(t)$$ Well, this is great in special relativity, but in general relativity, what time do we actually use? ...


1

You ask: Is it that space is not expanding within the smaller structures or is space expanding through these structures? where I've highlighted what I think is the key issue. The phrase space is expanding is a convenient metaphor to describe the expansion of the universe, but it is only a metaphor and taking it too literally can lead to confusion. It ...


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Space is expanding. However, nearby atoms (e.g. those in a metre stick) are not moving away from each other because the inter-atomic forces restore them to their original positions. Similarly, as the space between the earth and the sun increases (at an insignificant rate), the gravitational force restores the earth and sun back to their equilibrium ...


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Too long to be a comment, this is an extension to Chris's answer. Suppose a macroscopic object, a thermometer, for example, was placed in that hot intracluster medium (ICM) Chris mentioned in his answer. Even though that thermometer is surrounded by this hot gas, the thermometer will not get hot. It will instead cool to a tiny bit above the cosmic microwave ...


34

To avoid more complex definitions of temperature (which do not require matter), you could say instead that "an object in interstellar space would be in thermal equilibrium with its environment when it is at a temperature near $3K$." The matter nearby is too diffuse to affect the temperature much. Instead, it is thermal equilibrium mostly due to radiation. ...


29

Temperature in a gas is the average kinetic energy per particle. As an intrinsic property its value is entirely decoupled from how much stuff has the property. Whether there are 100 particles per cubic centimeter or only 1 particle per cubic meter, the temperature can be anything. The coldest parts of the ISM are about 3 K, and getting colder than this is ...


3

The universe about halfway through recombination (it was a long process but at the halfway point, it's flips to being mostly clear), much like the universe today, has a temperature. Today the temperature of the universe is about 2.7K, but at recombination it was around 4000K. This temperature corresponds to the blackbody radiation profile of the universe. ...


2

did the sky suddenly become dark, or was the amount of radiation basically same after as before? What would the distribution and timescale have been like? Recombination of hydrogen did not suddenly happen. Instead, to go from 90% of hydrogen being ionized to 10% of hydrogen being ionized, took about 100,000 years, from about 260,000 years after the ...


3

Your 12-year-old cousin might be correct; it isn't yet known for sure. However, some existing experiments are pointing in the direction of your cousin being wrong. What you're calling a "4D sphere" and a "3D sphere", a mathematician would call a "3-sphere" or a "2-sphere", respectively, because mathematically an "$n$-sphere" means something that's ...


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The simple answer is that your cousin could be correct. If his theory is that: the scale of the sphere is far larger than the observable universe there's no way to detect the 4th (spatial) dimension then no experiment we can do could prove him wrong. But then there's no experiment that we can do that could prove him right either, so as theories go it ...


1

There's an old theory called "tired light" where the momentum is lost due to waves hands some other reason, but as far as I'm aware this has been pretty much discounted these days. The background behind the current-best-theory is this: When you look at light from a star it's not a smooth spectrum, it has a series of dark lines in it, an "emission ...


0

As far as I understand, it has something to do with Hubble's Law. Essentially, based on looking back at energy density of a distant star at one point, and then looking at it again, and determining that it has diminished, or something along those lines. I assume it's a far fancier version of looking at a light you just passed as you drive down the road. If ...


0

thanks for your helps! I figure out that what is the meaning of the field becomes tachyonic. when it is where the phase transition occurs and the symmetry breaks. we take the current density proportional to critical density and so we have the above approximation. thak you Holographer and Hindsight.


0

What is the meaning of a field becomes tachyonic? It means that it has a negative coefficient at the $\phi^2$ term in action. The propagator of such field oscillates on the space-like region and decreases exponentially on the time-like region, so it's particles (tachyons) travel faster than the speed of light. It doesn't contradict SR since the ...


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Dark energy is an unknown or unattributed form of energy that is separate and distinct from the other forms of energy. It is not anti-engery. It is dark energy. Anti-energy (were such a thing to exist) would annihilate any form of energy. Dark energy is called "dark" because we aren't exactly sure what it really is or what causes it. The most abundant forms ...


0

The interconversion of matter and energy is described by quantum field theory. If you're interested the question What keeps mass from turning into energy? is on this subject. The particular quantum field theory that describes our universe is called the Standard Model, and there are three important symmetries that apply to the standard model - charge ...


0

Creating only matter without antimatter would violate several conservation laws. Mainly the electric charge conservation and color charge conservation. If you create a lot of electrons without antielectrons (positrons), you create a lot of negative electric charge out of nothing. That is not allowed by the conservation laws. Similarly, you cannot create a ...


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The answer is yes. The de Broglie wavelengths of freely propagating particles (i.e. forget the influence of interactions and gravity perturbations, just consider the Universe as a whole) are redshifted by the expansion of the universe. Another way of saying this is that their peculiar momenta with respect to a co-moving local volume decrease as the inverse ...


-1

We are continually told that the Universe will eventually be a void and everything will have burned up, no stars, no nothing. In my school days we were told that energy can neither be created or destroyed. So, if the universe does become "nothing" what has happened to the energy?


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On your first question the answer should be here http://en.m.wikipedia.org/wiki/Metric_expansion_of_space, after the big bang only the distance between space is expanding but you should be able to understand on the link i have included, yes the speed of light remains constant but the expansion is causing it to have longer time than expected to arrive it is ...


2

Space is indeed expanding everywhere, and not only between galaxies. The reason we don't grow with it, is that the attraction between the electrons and the protons is strong enough to keep them bounded. You can look at it as if they always re-adjust their position to counter the expansion of space. This also applies to our solar system, our galaxy, and even ...


1

I think this question is primarily opinion based. Different people keep different systems, but I'll share my system. To start, version control is absolutely essential. I recommend git. Here are some nice resources: Git for Scientists - an overview aimed at scientists Atlassian Git tutorials - a nice overview and discussion of different strategies for ...


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There are (at least) two things going on. Perhaps the easiest place to start is with the temperature as estimated from the radiation in the universe - possibly what you are referring to when you say the temperature is approaching 0K? The radiation in the universe takes the form of thermal blackbody radiation. It is emitted by material in thermal equilibrium ...


-2

I believe that you are safe in assuming it is cooler because it is spread out more. Wikipedia, on the subject


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If you are using Python then I would recommend Sphinx and git. Check your code into git so you have a history of your work and use Sphinx to generate the documentation off your code. This is a common combination and should meet most of your documentation needs.


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The Big Bang was originally defined as the zero time limit of the FLRW metric, so it's a mathematical construct and not primarily something physical. We have chosen to apply it to the zero time limit of the universe because we thought the FLRW metric was a good description of the universe, but then inflation gatecrashed the party and spoiled the fun. So if ...


1

In my opinion it all hinges on whether one includes quantization of gravity or not. The classical Big Bang just uses General Relativity and solutions of its equations. A singularity has a well defined meaning in the classical approach. As physicists are convinced that the underlying framework of nature is quantum mechanical it is expected that gravity ...


2

The argument is sound given a few oft-omitted (but not too unreasonable) assumptions. Here is one way it can be formulated. Consider a volume $V$. Suppose it has a (possibly infinite) set of possible configurations; call this set of states $S$. Suppose we are interested in a particular configuration, $c \in S$, to within a certain tolerance. Let $C ...


1

The argument rests on the assumed validity of Ergodic theory (see http://en.wikipedia.org/wiki/Ergodic_theory). Quoting it "A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The first result in this direction is the Poincaré recurrence theorem, which claims that almost all points in any ...


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This is a statement about a congruence of null geodesics. We are looking for a conjugate point, which is just a place where the null geodesics cross each other. The theorem is putting a bound on how far you can advance the affine parameter $\nu$ along the geodesics before the conjugate point occurs (this is what is meant by affine parameter distance). ...


3

How a unit is chosen to be defined depends in large part on how precisely the unit can be reproduced based on that definition. Two different atomic clocks built using the best currently possible methods will produce almost exactly the same answer for how long a second is, to within about 1 part in $10^{14}$. The second is defined in terms of a property of ...


0

In General Relativity, energy momentum flows from one region of spacetime to another. But there isn't necessarily a natural "total energy of the universe." It might help to contrast General Relativity with other theories. In Newtonian mechanics, a particle might gain kinetic energy while a corresponding gravitational potential energy decreases, thus you ...


1

In Newtonian mechanics, a particle might gain kinetic energy while a corresponding gravitational potential energy decreases, thus you get that kind of conservation of energy. The total energy is the same before and after any event. However, the amount of energy depends on who's looking. In Special Relativity a transfer of energy has to happen at an event ...


2

Galaxies would appear stretched along the line of sight, not jumbled. Let's say a galaxy is ten million light years away and, as you proposed, is 100,000 light years across and we see it nearly edge on. The front of the galaxy will appear to us as it did ten million years ago and the back of the galaxy as it did 10,100,000 years ago. Thus, if the galaxy ...


1

I think the very short answer is: galaxies are very small, indeed tiny, compared to how far away they are, and secondly, compared to the size of the universe. The answer to the spirit of your question, is that simple! "Galaxies are tiny." You're used to hearing "galaxies are 100,000 light years across!" but that's a piffle compared to either the size of ...


0

I suspect that the nice rotational formations of galaxies we see come from galaxies that are oriented in parallel with our solar plane so that the light arrives almost synchronously. Considering we are talking of gravitational forces the "almost" could cover a large window, the distortions not being too great to lose track of the shape. A galaxy whose ...


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Galaxy rotation happens at a very slow rate (compared to the speed of light). Let's suppose you are observing a galaxy edge-on that the delay from the farthest point is $\Delta t = d/c$, where $d$ is the galaxy diameter. If we take the lag from one extreme point to the other as D: $D = vt = \frac{v}{c}t$ (where $v$ is the rotational speed). You can see ...


1

For a stationary massive object like Earth or the Sun, the gravity well does not change from the expansion of space. The gravity well at one time is the same as the gravity well at future times for the same mass. Any minute force imposed by the expansion of space does not constitute a change in the gravity well itself. The well is not stretched or ...


1

If we assume that general relativity is the correct theory for this case, and there are currently no indications, that I am aware of, that it isn't, then the expansion of the universe adds a small modifying term to gravity wells. I doubt that it is measurable at the scale of the solar system. The current best estimate for the Hubble constant is ...



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