New answers tagged cosmology
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Looking for a paper on evaluating integral over Haar ensemble
A good discussion of what you are looking for (how to evaluate such integrals) is in my experience provided in a chapter ("Group integration") of a book by M Creutz on lattice gauge theory, ...
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Rigorous definition of the matter power spectrum
$\delta(\vec{x})$ is a random field. It is not a real number. The sample space from which $\delta(x)$ comes from is real-valued functions from $\mathbb{R}^3$ to $\mathbb{R}$. Meaning, if you were to ...
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Correctly determine additional distance covered due to universe expansion
You know the velocity of the photon $c$, the initial distance $X$, and the Hubble parameter $H$ measured in meters per second of apparent recession per meter of distance.
Actually integrating the real ...
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Existence of tachyons
It is one of the fundamental principles in cosmology that the universe is (on average) the same everywhere. The edge of the universe is not actually an edge - it's just the farthest distance we can ...
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Existence of tachyons
Magnetic monopoles are another particle that has been searched for without success. It might or might not exist. All we know is they weren't found,
It might be like looking outside and not finding ...
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Were we all intuitively misled into thinking that the universe has a 'speed' of expansion?
Even in the earliest models of an expanding universe the speed at which a particular galaxy was moving away was proportional to its distance, so there never was a single "speed" of expansion....
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Wien's displacement law
Stars are not perfect blackbodies. They have elements in their atmosphere that absorb and emit light at particular wavelengths. So the general blackbody pattern is slightly modified with lines of ...
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Why is $h_{\mu\nu}$ not a tensor in the perturbed Universe in cosmological perturbation theory?
The equality
$$g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}$$
only exists upto first order in $h_{\mu\nu}$ and we ignore higher order terms $\mathcal{O}(h^2)$, therefore it becomes clear that the ...
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How total mass of universe is calculated?
If the universe is flat (which our universe seems to be within the margins of error) or hyperbolic the total mass is infinite, since finite density times infinite volume equals infinite mass.
If the ...
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How total mass of universe is calculated?
This is a cute observation, but is essentially just dimensional analysis. It follows from doing a rough order of magnitude estimate where you only keep track of the Hubble constant plus fundamental ...
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Max distance in 2d and 3d positively curved space
You are confusing the concepts of path length and shortest distance. It does not help that the unqualified term distance may refer to either concept, depending on context.
If (for a given metric) you ...
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Max distance in 2d and 3d positively curved space
How do we show that the maximum distance along ( r ) is finite?
In a 2-sphere, when you move along $r$, you will eventually return to your starting point after traveling a distance of $2\pi R$. You ...
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How to demonstrate the form of the FLRW metric from homogeneity and isotropy?
Rotational Symmetry and Isotropy
Isotropy means that the universe looks the same in all directions from any given point. Mathematically, this implies that the metric should be invariant under ...
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Does Heisenberg's Uncertainty principle Imply the universe is finite/periodic?
If you are confined to a finite interval of space where your wave function must be $0$ outside the interval, then there are discrete solutions to the Schrodinger equation. For the simple case of a ...
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Does Heisenberg's Uncertainty principle Imply the universe is finite/periodic?
That is to say, if there's a limit of the form "you can't have infinite velocity" then there are are only a finite number of harmonics implying a finite/periodic universe.
Relativity says ...
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Can stardust give rise to new stars?
The sun is a bit less than 2% elements heavier than helium, mostly carbon, oxygen, neon, and iron. While the hydrogen and helium contents are largely primordial, the heavier elements (known as "...
Buzz♦
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Why can we see all the way back to 600 million years after the Big Bang?
Not to take away from the excellent answer by Andrew, I wanted to put together something appropriate for someone who hasn’t studied physics. Not knowing their level of knowledge of the subject I’ve ...
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Can there be decoherence of quantum fluctuations in Minkowski spacetime?
The outcome of an experiment on a quantum system in general depends on what happens to all of its possible states because of interference, see Section 2 of this paper for an example:
https://arxiv.org/...
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What type of atomic structure, if any, would we expect immediately after the Big Bang?
The difficulty is that the conditions in the very early universe were too extreme for even light nuclei to be stable, let alone nuclei of heavy elements. There was a short window of time in which the ...
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Can the age of the universe actually be calculated through Hubble's constant?
There is a vital assumption hidden in this calculation, and that assumption is:
Every point in space has always moved away from us at the exact same velocity.
That is, if a galaxy is moving away ...
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Accepted
Two questions about the expansion of the universe and matter?
1. The self-gravitation of the CνB is nonzero, but it's smaller than that of the CMB, and both are far below the threshold to form bound structures of neutrinos/photons. Even the much larger ...
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How can the ions in intergalactic and interstellar gas held together?
If you have a cloud of completely ionised, net-neutral gas and then you try to remove some of the charged constituents - say the electrons have a higher velocity dispersion - then all that will happen ...
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Why didn't inflation happen right after creation and it had to wait $10^{-36}$ seconds to occur?
One idea - although I think this is some way being a consensus - is that the energy density of the early universe had to first fall below the grand unification energy, allowing the strong force to ...
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How can the ions in intergalactic and interstellar gas held together?
If electrons were to attempt to separate, protons, being oppositely charged, would be naturally drawn to follow them due to the fundamental electromagnetic attraction. However, proton decay, while ...
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Assuming that proton decay occurs, will all types of particles be dispersed without exception?
Yes. You don't even need other rapid expansion scenarios with big $a$. Given very large time scales matter will annihilate and dilute and no significant gravitational clusters could form. The same is ...
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Why is the red shift resulting from the relativistic Doppler effect and a galaxy's velocity of recession, greater than the galaxy's actual red shift?
Hubble's law relates the scale factor to the rate of change of scale factor. Both of those quantities are defined at the same cosmic epoch and neither are directly measurable (except approximately for ...
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Accepted
Why is it necessary the inflaton field?
Inflation is not simply a stage when $\rho$ was very large. To understand what is needed, you should consider the causal structure of spacetime.
Let us take the flat FRLW metric,
\begin{equation*}
ds^...
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Why is the red shift resulting from the relativistic Doppler effect and a galaxy's velocity of recession, greater than the galaxy's actual red shift?
When evaluating Dopper shifts in a curved spacetime, you need to be careful because relative velocities are not uniquely defined in curved spacetimes.
Relative velocities are angles in spacetime. If ...
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Do more distant galaxies move faster with respect to the cosmic background radiation rest frame?
Inside an expanding system, particles that are freely moving will tend to sort themselves, such that particles with similar velocities arrive at nearby positions. This is because any particle that is ...
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Why is the red shift resulting from the relativistic Doppler effect and a galaxy's velocity of recession, greater than the galaxy's actual red shift?
I think I know the answer to this question but it will be very controversial.
If there is any large scale curvature to the universe, velocities of recession will not give rise to any Doppler effect.
...
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Can the age of the universe actually be calculated through Hubble's constant?
I think defining velocity as $D/t$ assumes that velocity is a constant with respect to time. If the present size of the universe is $D_f$, points on its opposite edges move apart with velocity $HD_f$. ...
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Understanding expansion of the Universe as things flying apart
NOTE: I have made a significant revision to this answer and the conclusions are different to the previous version.
Or is the space actually something that wants to expand everywhere and
unless the ...
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Why is the red shift resulting from the relativistic Doppler effect and a galaxy's velocity of recession, greater than the galaxy's actual red shift?
Measure the red shift of a galaxy at 1. Use a standard candle
measurement and you will determine the distance of the galaxy from us
at around 10 billion light years.
I get the predicted luminosity ...
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Accepted
Could thermal or quantum fluctuations in the far future ionize matter?
Yes, this is a consequence of the Herzfeld "paradox", first noted in 1912. The partition function for a sole hydrogen atom is not well behaved, diverging when one takes the infinite number ...
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Do more distant galaxies move faster with respect to the cosmic background radiation rest frame?
If you were to go back in time and examine the CMB from the perspective of our own galaxy, the CMB would be hotter but, to first order, we would be moving at a similar speed with respect to the CMB ...
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Accepted
Can there be a progressive and slow vacuum transition event instead of a sudden one?
What you are essentially looking for is an adiabatic field evolution from one vacuum to another vacuum.
If the potential is constant in time, this is hard to imagine. The field will naturally sit in ...
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A study on the speed of gravity
It is well known that General Relativity predicts that gravitational waves exist [1] and that they travel at the speed of light. But, until the construction of LIGO, these were not experimental facts. ...
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A study on the speed of gravity
The paper introduces a scalar parameter $\alpha_0$ that measures the difference between the speed of light and the speed of gravitational waves
$$\alpha_0 = 2\frac{v_{GW}-c}{c}, $$
and it states that $...
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