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The Hartle-Hawking no-boundary proposal suggests that the universe as we know it was not created from nothing. Rather, its history would be finite, though unbounded. In the words of Stephen Hawking: "The no boundary proposal, predicts that the universe would start at a single point, like the North Pole of the Earth. But this point wouldn't be a ...


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Couchyam's answer is for undeformed de Sitter space - empty if you will. So no orbits in that. What you are asking is if one put an object the mass of the earth in a de Sitter space, could objects the mass of the moon orbit the earth thing? It would seem that the earth like mass would follow a prescribed path, but since its a rule in General Relativity ...


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When talking of cosmology one needs a model, and the standard model for cosmology at present is the Big Bang Model. This developed fitting observations and taking into account General Relativity ( which includes gravitational redshift.) . In this model the universe started from a small spacetime singularity which is not explorable with the physics we know ...


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I'll assume you are asking about geodesics in de Sitter (If the objects contribute to the energy-momentum tensor they perturb the metric and perform orbits). De Sitter space can be thought of as the set of points in 4+1-dimensional Minkowski space that satisfy $$ X_1^2+X_2^2+X_3^2+X_4^2=1+X_0^2. $$ Cross sections of constant $X_0$ are 3-spheres, so you ...


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Correct, the standard Schwarzschild metric is asymptotically flat and indeed the time co-ordinate $t$ is the local time of an observer infinitely removed from the black hole and sitting in this flat space and so there is no pair of points outside the black hole's event horizon which ultimately cannot causally reach or signal each other. The de ...


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Standard cosmology assumes homogeneity (as well as isotropy) of the universe. Though we know that this is only an approximation, we also know that for cosmic scales it is a good one. This can be seen in the cosmic microwave background radiation (CMB). However, the initially small inhomogeneities are responsible for galaxy and star formation through ...


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To get to an expression to use, first note that the "WI" is for "Weakly-Interacting", which tells you that you should expect cross-section similar to those for neutrinos. That means small, so you can treat a WIMP gas as dilute almost without worrying about it's actual density. So, taking the RMS velocity of on of the particles to be $v_{RMS} = ...


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For velocity-averaged cross-section $\sigma v$ and number density $n$: $dn/dt = -n^2 (\sigma v)$ Replace $\rho=m_\chi$ $d\rho / dt=-\frac{\rho^2 \sigma v}{m_\chi}$


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My guess, and I hope you get a better answer, is that gravity is the only force involved, and that does not have complicated laws, unless it's a many body problem, which I don't think you are referring to here, as you want to treat cosmological objects as distinct, and far away from each other. Moreover, does it even make sense to talk about a speed ...


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Actually its perfectly possible within standard GR to do so! The question then becomes at what point does GR break down, and if it formed a mass at that point would it have time to decay via hawking radiation down to a Planck remnant? Many types of matter exhibit what is called type II critical collapse where if you carefully tune initial data, you can ...


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It is the Dark Energy constant (AKA Cosmological Constant). It's 138 * 10^-121 in reduced Planck units. Thanks to Hritik Narayan for actually finding the video I was referring to (number appears at 5:28). https://www.youtube.com/watch?v=bf7BXwVeyWw The video is of Brian Greene talking about why out universe seems fine-tuned for life. He describes the ...


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If I understand correctly, you are just asking about the relation between energy and distances in both radiation and matter (and cosmological constant) dominated eras of the expansion of the universe. Consider the Einstein equation $$ G_{\mu\nu} = 8\pi G T_{\mu\nu} \ ,$$ where $G$ is Newton's constant. In a FLRW unverse $G_{\mu\nu}$ is diagonal and using ...


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The constant that has those last three digits as its most significant digits would be the Boltzmann constant $k_B = 1.38 \times 10^{-23} \, \mathrm{[J / K]}$, or 0.0000000000000000000000138, which relates the energy of the individual particles to temperature. No commonly-encountered fundamental constant has that impressive number of zeroes, unless you're ...


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Simply put, it is: how many aliens could we meet? More specifically: The Drake Equation is a way of predicting how many intelligent species there might be in the universe and the likelihood of them contacting us. There are a lot of things that can change the number of aliens we can expect to find. So we use what we know about the universe so far and ...


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I don't think I can explain all the technical stuff, but first things first. Primordial means "at the creation", so if it was created today it wouldn't be primordial. Now "Primordial size" black hole, is probably what you mean and even that is a bit vague as estimates vary on the possible sizes of Primordial black holes, (and there's some uncertainty as ...


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If people brought all the trash in the galaxy to a single place and dumped it, a black hole could eventually form from the ever-increasing density without ever forming a star. Hypothetically, a bunch of heavier elements (incapable of starting a fusion/fission process to hold the gravitational collapse at bay) could happen to end up in the same region of ...


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Cosmic rays have a de Broglie wavelength. The de Broglie wavelength is redshifted by the expansion of space in the same way that the wavelength of light is redshifted. Another way of saying this is that their peculiar momenta with respect to a co-moving local volume decrease as the inverse of the scale factor. This means that the energies of any cosmic rays ...


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If a particle either "is" or "isn't", then its count is either 1 or 0. Even in quantum mechanics it's not possible that half a particle exists. It is possible to detect it with 50% probability, but if you set about counting all the particles one at a time, you necessarily end up with an integer answer.


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You can't tell directly. But you can look at a bunch of it and notice that it is at the same temperature here there and everywhere in all directions in every single place where your view isn't blocked by some moon planet star or galaxy. And that temperature is quite cold it is hard to get something that cold. And either there are many things with the same ...


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Distance is equivalent to time. The time at which the cosmic microwave background was emittied was the time when the universe made a phase transition from being a plasma to being atomic matter. During this time, the universe finally became transparent. Before this time, the universe was so hot that all matter was opaque. The CMB is the wall that ...


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Could we be on the inside of a concave hollow universe? Nope. Nor are we on the inside of a hollow Earth. Recently I was discussing this theory again (a little drunk, I admit) and then tried to find answers, but couldn't find anything satisfying. That's because it's bunk. There is a theory (or several theories) that we could be living on the ...


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For any transformed shape of the Universe, one may always easily define the theory in such a way that its results will be absolutely indistinguishable from the original theory. For example, one may describe the Earth and its vicinity by the polar coordinates $$ R, \theta, \phi $$ so that $R\gt R_E$, the Earth's radius, corresponds to the space outside the ...


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So, can an area of space a few feet across (externally) be a light-year wide (internally) (TARDIS sort of thing)? Yes. It can and that's normal. If you made a region with less space inside than the surface area indicated that would require exotic matter. And with exotic matter you can make time machines. So ... Ironically you need something smaller on ...


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The typical extinction for a line of sight out of our Galaxy (but avoiding the Galactic plane) is of order a few tenths of a magnitude at visible wavelengths (it is a factor of 10 less in the infrared and factors of a few more in the UV). This means that the typical attenutation of a signal arriving at the HST from outside the Galaxy is around say ...


2

You are approaching the question from the wrong end. The expansion of the universe is described by a particular solution to Einstein's equation called the FLRW metric. To derive this metric we have to make some assumptions, and the key assumptions are that the universe is isotropic and homogeneous i.e. that it is the same everywhere. So the universe being ...


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Photons have two degrees of freedom, the helicity. But they are not an ideal gas with equation of state $$PV = NkT,$$ so the usual derivation of the adiabatic exponent does not apply. You need to use the equation of state $$U = PV$$ which is valid for any ultra-relativistic gas. You can derive it in the same way as the ideal gas law -- by considering ...


0

Expansion of space is allowed by General Relativity. Which has made quite specific predictions that passed. So it seems valid to have solutions with an expanding space on the table (and leave it to observation to exclude them or to favor them). And there are two different situations where it comes up. A cosmological context where the expansion is the ...


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This is a good question because sometimes people argue there is evidence that the universe is infinite. Basically when you assume space is isotropic and homogeneous then you are left with three options, a space that is flat and two other types. The two other types can easily be finite and I don't see much argument about it. The flat one seems pretty easily ...


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Yes. You can make a model where you have coordinates $t, x,y,z$ where for any $x,y,z$ the universe looks the same. The metric ends up looking e.g. like $$ds^2=dt^2-(a(t))^2(dx^2+dy^2+dz^2)$$ and you can move your $x,y,z$ to have any value and everything looks the same (those things do loom different for different cues of $t$). You end up with the densities ...


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You are not travelling faster than light in the sense that if you send some light to your destination it gets there before you do. It can be faster than light in the sense that if space is isotropically and homogeneously distributed with energy and such then there is an obvious global frame and distance in the global frame between two points can decrease ...


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My understanding is that Hubble said the farther our we look into the Universe, the higher the redshift, therefore the faster things are moving. Pretty much. If you were some raisin in a rising cake, you'd say the same of the other raisins. But my question is, why is this surprising? It isn't. What was surprising is that the expansion rate is ...


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The first thing is to change your cartoon picture of Big Bang (an exploding egg of matter and energy). Big bang was not an explosion it was the start to expansion and the big bang theory tells the aftermath of this i.e. How the Universe evolved with time.What Hubble did observe was that the farther the galaxy or the source of light was faster it seemed to ...


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good strategy! Hubble Constant = Ho = [d/s]/[d/1] in basic variables, thus it reduces to 1/s which is time inversed, that is, the inverse of the age of the universe at whatever Ho constant value used and further adjustments from the Standard Model equations. The big adjustment is U. acceleration [ and significant deceleration during first 2 billion years]. ...


0

One astrophysical constraint is that dark matter particles must not be produced in too large numbers in stars. Suppose that the reaction $\gamma + Ze^+ \to \gamma + Ze^+ + D$ or something similar, is allowed where $D$ is a dark matter particle. Since a star is opaque to photons, that energy stays in the star, but the dark matter particle escapes, like ...


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Good question! I agree with the two restrictions on dark matter (DM) that you mentioned. In total I would mention four main restrictions: It must be non-luminous: In practice this means no coupling (or extremely weak) to $U(1)_{em}$ and no coupling to $SU(3)_c$. We know it cannot interact with the strong force because e.g. radiation of gluons would ...


2

To address the question of whether the age estimates are in years on Earth or years for a comoving observer in deep space, I could tell you the same thing John Rennie said. But that would make this redundant, unproductive, and redundant. Instead, let me show you that it doesn't really matter. The equation for time dilation due to gravity is as follows: ...


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The geometry of the expanding universe is (approximately) described by the FLRW metric, and to express this there is a natural space/time split called comoving coordinates. The comoving time coordinate is roughly speaking the time measured by an observer who is at rest with respect to the cosmic microwave background. Since most galaxies have peculiar ...


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First, let us suppose you have the energy to travel at any speed you like. The only restriction you have is that you cannot travel at the speed of light, because you would need infinite energy, and even though you have infinite energy, you cannot apply infinite energy if you don't have infinite time to apply it. So you accelerate in a ship let us say at ...


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I have heard three theories for how space-time is shaped, flat, sphere-like, or saddle-like. Flat is the most likely, as all our measurements implies that space time has curvature close to 0. Inflation makes it so that a sphere like or saddle like spacetime evolves into a sphere like or saddle like spacetime that has a curvature very very close to zero. ...


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Is it plausible for spacetime to be shaped something like a torus? I can't give a factual answer, so I will give an opinion. People have proposed that space or spacetime has a toroidal topology. This goes back to the old asteroids game, and there's plenty of papers on the arXiv. But there's nothing actually plausible about these proposals. There's no ...


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Heavy elements couldn't form right after the Big Bang because there aren't any stable nuclei with 5 or 8 nucleons. Source: Wikipedia (user Pamputt) In the Big Bang nucleosynthesis, the main product was $^4He$, because it is the most stable light isotope: 20 minutes after the Big Bang, helium-4 represented about 25% of the mass of the Universe, and the ...


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In the case of a supernova explosion it is possible to create heavy elements through fusion. Supernovae have a tremendous amount of energy in a very small volume but not as much energy per volume as there was in our early universe. So, what is the major difference? Why didn't the Big Bang create heavy elements? I just want to point out, too much ...


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This question is answered in detail by the so-called "Big Bang Nucleosynthesis", the theory about the creation of the nuclei in the early Universe. Almost out of nothing, it allows one to determine that 75% of the nuclear mass was coming in hydrogen, 25% in helium, and some small traces of lithium appeared, too. Even though Gamow used to think that all ...


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This new paper addresses exactly this question, albeit with simulations. Here's a partial breakdown of the distribution of matter in the Universe, summarized from the above paper: Dark matter makes up about 26% of the critical energy density budget of the Universe, while "baryonic matter" (which is jargon for "visible matter" and includes all baryons as ...


0

Can you compare curvatures in space, spacetime Yes, you can compare spatial curvature with spacetime curvature. Have a look at this Baez article: "Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial". ...


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We don't know what caused inflation, and we don't know what dark matter is. You'll appreciate that this makes a definitive answer to your question somewhat elusive. However it's generally believed that the matter we see around us today was created at the end of inflation by the decay of the inflaton field. This included both baryonic and dark matter, though ...


2

There are 4 general contributors to the mass density of our co-moving patch of what may be a larger universe: (1) Visible baryonic matter (including clouds of baryonic matter which may be visible only as shadows blocking galaxies). NASA estimates 4.6% of all matter is baryonic (http://map.gsfc.nasa.gov/universe/uni_matter.html). (2) Dark matter (not ...



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