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5

You are presumably thinking of the FLRW metric for a universe with greater than critical density i.e. a closed universe. We normally use comoving coordinates to describe this, in which case the time coordinate is not curved and at every point along this time coordinate the three spatial coordinates have the topology of a 3-sphere. That is, if we draw a ...


5

Whether the dark energy is constant or not will ultimately be determined by experiment. At the moment there is no evidence that the dark energy is changing, but the experimental errors are still quite large so a change is not ruled out. There are lots of papers on this subject, but as yet no firm conclusions. It is important to be clear that dark energy ...


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Good numbers for this have only been coming out for a decade or so, so its a relatively new topic. There does seem to be a strong tendency for dwarf and satellite galaxies to have much lower mass-to-light ratios, and correspondingly smaller baryon-to-DM ratios. See, for example, Stringer+2009, Strigari+2008. These observations are backed up by simulations ...


4

I wonder of you are overthinking this. Wald says: If the universe had always expanded at its present rate that is, $\dot{a}$ is a constant and independent of time. In that case the value of $a$ at time $t$ after the Big Bang is simply: $$ a = \dot{a} t $$ So if you define $T$ by $T = a/\dot{a}$ then $T$ is necessarily the age of the universe.


4

The answer is the same reason why a glass of water left out at room temperature will evaporate. Even though most of the particles will be below the boiling point, the equilibrium one expects is not entirely in the liquid phase. The occasional particularly energetic water molecule will vaporize, just as the occasional neutral hydrogen atom will be struck by a ...


3

The heat death of the universe is the idea you are describing (this idea is also known as the Big Freeze). The problem with this idea is for it to work the cosmological constant has to be zero...and it isn't zero. It's very tiny, but it isn't zero. The other problem with your idea is the belief that because it all "freezes", so to speak, it'll all collapse ...


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You must not really have looked hard enough. They are the same phenomenon The Big Freeze, which is also known as the Heat Death, is one of the possible scenarios predicted by scientists in which the Universe may end. It is a direct consequence of an ever expanding universe. The most telling evidences, such as those that indicate an increasing rate of ...


3

I would like to answer with the words of L.D. Landau, from his book Statistical Physics (first edition $1958$):


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There are a few problems I can think of with this idea - Gravity has to, at some distance turn from positive, to zero, to negative. It would be interesting to know that distance. Will the repulsion increase, or decrease with increasing distance? Dark energy hypothesis indicates repulsion would go up with increasing distance. Which does not make sense - ...


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The technique is to sight in on known frequencies of sources in the Milky Way and other galaxies. Any signal bearing the multiband set of data is subtracted.


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In the Standard Model coupled to GR as an effective theory, the cosmological constant is predicted to be $m_{Pl}^4$ i.e. $10^{123}$ times the correct value (you mentioned the correct value). SUSY improves this situation by cancellations between superpartners (fermions contribute the same to the C.C. as their bosonic partners but with the opposite sign if ...


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"If inertia is a property of the matter form of mass-energy, and it is a property that allows for the transfer of energy, then why doesn't the energy dissipated in a vacuum, as does applied radiant/free energy" The problem with your logic is that is flawed. It is equivalent to "some fruits are apples; oranges are fruits: why do not oranges taste like ...


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The raisin bread analogy can be used to help in understanding this too: Dough is much more expandable than the raisin material. Raisins will expand a bit due to the heat and the pull from the dough stuck on their surface, but it is the dough that is moving. The forces that are holding the raisin together are much stronger than the force expanding the ...


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I'd put this as a comment, but don't have enough rep...anyway, as this answer and the comments within state, the equation of state isn't necessarily linear. One thing I'd add is that one can define $w$ to be the ratio $\frac{P}{\rho}$ (as it's dimensionless), and since in general both pressure and density depend on time (no $\vec x$ dependence is allowed in ...


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So, there are several possible ways the universe could be baryon symmetric: A region of the universe where antimatter dominates. There is a problem with this theory, though - 30 years' worth of scientific research has calculated just how far away this type of region would have to be, and from these calculations it is considered very unlikely that any part ...


2

The derivation by Pols is correct. Ryden makes the strange decision to plug the relativistic rest energy $\varepsilon = \rho c^2$ into the classical ideal gas law. Surely it makes more sense to define a classical kinetic energy $$ u = \frac{1}{2}\rho\langle v^2\rangle $$ so that $$ P = \frac{2kTu}{\mu\langle v^2\rangle} = \frac{2}{3}u. $$


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No. To make a long story short, if the Higgs field changed its coupling to particles with time then particles in the distant past would have different masses. This would mean atomic spectra of distant galaxies would has differences from spectra now here on Earth. No such change is observed.


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You are right that the universe formed atoms much earlier (at the temperature when photons can no longer ionize the atoms, i.e. at around $T = 150,000 K$ as you point out with your order of magnitude calculation). However, photons could still scatter off these atoms. Indeed this was quite likely considering the high density of matter in the universe. The ...


2

I don't know if negative pressure (but see my added edit below) , more importantly there is a theory of inflation, and some good evidence for it. It was caused by a yet unknown inflation field, with its parameters somewhat matching what the cosmic microwave background (CMB) measurements show. [edit added: The field is a quantum field that rolled from a high ...


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There's not reason to assume nature should treat everything symmetrically. There are many phenomena in nature that we actually know are asymmetric. For example the weak force violates parity symmetry (meaning the weak force has a preference for right or left handedness).


2

Gravity, per general relativity (GR), is normally attractive. Normally means that the sources of the gravity, and thus the sources that determine the geometry and curvature of spacetime, have positive energy density, and obey other positive energy conditions. The pressure and other factors that enter into the stress energy tensor that is the source of the ...


1

I'm not sure if this is exactly what you want, but there's a book called Practical Statistics for Astronomers by J.V. Wall and C.R. Jenkins that might fit the bill. According to the Cambridge University Press website (the book is a part of Cambridge Observing Handbooks for Research Astronomers): Astronomy needs statistical methods to interpret data, but ...


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The key statement is that the $a_{\ell,m}$ are independent Gaussian random variables. For each $\ell$, there are $2\ell+1$ of them. So their sum is, essentially by definition, a chi-squared distribution with $2\ell+1$ degrees of freedom. Now, it is a known fact that the variance of a chi-squared distribution with $k$ degrees of freedom is just $2k$, so ...


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The idea of a "Zero-Energy Universe" is a theory held by a limited number of scientists. There are several stackexchange question that expand on the theory and may help you. Zero energy universe Total energy of the Universe


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Infinity is a mathematical concept, as well as the concept of variables describing dimensions. Physics is about observations, either in the laboratory or of the cosmos, which are fitted with mathematical models. It started with the geocentric system, became the heliocentric system and then the realization that the galaxy is composed out of sun like stars, ...


1

Sticking with the sphere analogy, first remember that in this analogy, the Universe is a shell, i.e. only the points on the surface of the sphere exist in the Universe, not points inside or outside. If the Universe has a spherical geometry, then the centre would be the centre of this sphere, which is not in the Universe anymore (which is why one would say ...


1

You are correct, the recession velocity predicted by the hubble law is negligible at the local group, even if gravity among them could be absent. Their gravitational attraction though, is hard enough to keep them bound together.


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The FLRW energy equation for the motion of test masses in the universe is $$ \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G\rho}{3}. $$ the scale factor for space is $a$ and its time derivative is $\dot a$. I derived this from Newtonian dynamics. The density of mass $\rho$ for the case of a quantum vacuum energy level is constant. I now replace this with ...


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The noboundary condition means there is no boundary that marks the end of space or time. With respect to time one might think of the lines of longitude on a globe as representing the time direction at different point in a spatial manifold modeled as the lines of latitude. As one looks further to the north, which is the big bang that eventually you look north ...


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Under the assumptions that $a > 0$ and that the universe is expanding, we can derive some interesting results about the fate of such a universe. From the Friedmann equations alone, we may derive $$ \frac{d}{d \tau} (\rho a^3) = - P \frac{d}{d \tau} (a^3). $$ For $P = w \rho$, as long as $w \neq -1$, this yields $$ \rho \propto \frac{1}{a^{3(1 + w)}}, $...



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