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How can the Cosmic Neutrino Background (CνB) have a temperature? How can any neutrino have a 'temperature'?

Loosely speaking, any system where the degrees of freedom can exchange energy with each other and is in equilibrium has a temperature. A "system" here is a collection of particles, fields, ...
IronWidget's user avatar
3 votes

Why is nonzero net charge density incompatible with the cosmological principle?

I don't agree with the assumption that the electric and gravitational fields must be proportional to ${\bf r} - {\bf r}_0$ for some central point ${\bf r}_0$. As discussed at Gauss's law in a ...
tparker's user avatar
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8 votes

Why is nonzero net charge density incompatible with the cosmological principle?

The relevant difference between gravitational and electrostatic forces is that a gravitational field accelerates everything equally, whereas an electric field produces different accelerations on ...
Sten's user avatar
  • 5,877
4 votes

Why is the universe charge-neutral?

Charge conservation says that a universe which began charge-neutral would have remained charge-neutral. But why assume that it started out charge-neutral? A better way to ask the question is to ...
rob's user avatar
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1 vote

Can Bose-Einstein condensates and Fermionic condensates survive for long periods of time in space?

It wouldn't survive for long as you need a trapping potential to keep the gas together.
Jesse's user avatar
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6 votes

Why is the universe charge-neutral?

A nonzero net charge density is incompatible with the cosmological principle. Homogeneity implies a constant electromagnetic field, which implies via Gauss's law that the contained charge is zero. The ...
benrg's user avatar
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0 votes
Accepted

Why is the universe charge-neutral?

There is as of yet insufficient data to produce a meaningful answer. I would certainly love to tell you that the universe is charge-neutral, because that would imply I know enough about the Universe ...
controlgroup's user avatar
2 votes

Is it possible to learn about an event that occurred outside of your observable universe?

I know it's an old question, but maybe someone could still find it useful. First of all, let's consider a general scale factor $a(t) \sim q^t$, with $q \in \mathbb{R}$. We can work out the comoving ...
Robrecht Keijzer's user avatar
0 votes

Please help me with this paradox

This is because of general relativity. GR says that spacetime is not fixed, but can "curve" and change depending on what's living on it. The universe is expanding and this means that the ...
AccidentalTaylorExpansion's user avatar
2 votes

Change of variables from FRW metric to Newtonian gauge

I'll show how you can do this with Mathematica very quickly. If you don't have access to Mathematica through your institution I believe WolframCloud is free. We're starting with the FRW metric $$ds^2 =...
delon's user avatar
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4 votes

Please help me with this paradox

The recession rates you are talking about are not relative velocities, so it's not meaningful to compare them to the speed of light, and it's incorrect to use them to calculate relativistic effects. ...
Sten's user avatar
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10 votes
Accepted

Age of a dark energy dominated universe

In non-dark-energy-dominated phases, $a\propto (t-t_1)^\gamma$ for some $\gamma>0$ and some reference time $t_1$. This means that $a=0$ when $t=t_1$, so that time $t_1$ is the beginning of the ...
Sten's user avatar
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0 votes

Kolb and Turner's expresion for number density Eqn. (3.46) and pressure in Eqn. (3.48)

I think relation (2) can be derived the following way. Consider an element of surface $\delta S$ with its unit vector $\vec n$. The particles that will collide with it during a time ${\rm d} t$ lie in ...
Nebul's user avatar
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4 votes
Accepted

Negative Horizon distance

The integral $$\int_0^t\frac{\mathrm{d}t^\prime}{a(t^\prime)}\propto \int_0^t\frac{\mathrm{d}t^\prime}{t^{\prime \frac{2}{3+3w}}}$$ diverges if $w\leq-1/3$. It doesn't give a negative result (nor ...
Sten's user avatar
  • 5,877
1 vote
Accepted

Net particle number density for relativistic particles at finite chemical potential (tricky integral)

Your question is purely mathematical. I will set $\mu=1$ with no loss of generality in the following. If you think in terms of fugacity: $$ z = e^\beta $$ you can use polylogarithms: $$ \text{Li}_s(x) ...
LPZ's user avatar
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0 votes

Horizon problem: Angular size of the causality patches on the CMB surface

I tried the same calculation, using radiation domination instead of matter domination before $t=t_{\rm CMB}$ and then matter domination after. For $t>t_{\rm CMB}$, one must have $a=\left(\frac{t}{...
QuantonPhysics's user avatar
1 vote

Change of variables from FRW metric to Newtonian gauge

$\def \b {\mathbf}$ from $$ ds^2=-dt_c^2+a(t)\,dx_c^2 $$ $$ds^2=\underbrace{\begin{bmatrix} dt_c & dx_c \\ \end{bmatrix}}_{\mathbf q_p^T} \underbrace{\begin{bmatrix} -1 & 0 \\ 0 & a(...
Eli's user avatar
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0 votes
Accepted

Age of universe vs Hubble time in Milne universe

At $t = t_0, \, a(t_0) =1$. Thus, $t_0$ is the time when the scale factor is unity. If you want to assume that the scale factor is one right now, then $t_0$ is today. To measure expansion rate, I ...
S.G's user avatar
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6 votes
Accepted

Change of variables from FRW metric to Newtonian gauge

Firstly as you suggested, $$ d t_{c} = \frac{\partial t_{c}}{\partial t} d t+\frac{\partial t_{c}}{\partial \vec{x}} d \vec{x}$$ $$d t_{c} = d t-\frac{1}{2} \dot{H}(t) \vec{x}^{2} d t-H(t) \vec{x} \,d ...
S.G's user avatar
  • 2,515
0 votes

According to Hubble's Law, how can the expansion of the Universe be accelerating?

So it tells you what the recession velocity of a galaxy is right now, not what it was in the past. Measurment is NOW and event ("acceleration") is in the PAST.
Simon's user avatar
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1 vote
Accepted

How to find critical density?

The Friedmann eqn is: $$H^2+\frac{k}{a^2}=\frac{\rho}{3M_p^2}$$ where $M_p^2=1/8\pi G$ is the Planck mass. In this eqn we take cosmology constant as dark energy, which becomes a part of $\rho$ above. (...
Albert Zhao's user avatar
0 votes
Accepted

How to understand critical density?

1: The critical density is the required density for a flat universe, so it requires only $\Omega_{\rm K}$ to be $0$, but not $\Omega_{\Lambda}$, so it also holds with dark energy if you include its ...
Yukterez's user avatar
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1 vote

Why are spherical shapes so common in the universe?

In a wider sense: The sphere is the smallest surface that encloses a given volume. The sphere is the solution to one of the most general optimization problems in three-dimensional geometry. This makes ...
Peter - Reinstate Monica's user avatar
4 votes
Accepted

Why can photon be treated like gas?

So, usually, any group of particles which have very weak interaction between them can be compared to an ideal gas. If the interaction is slightly more, then it is compared to a liquid and if the inter ...
SchrodingersCat's user avatar
0 votes

Why can photon be treated like gas?

Symmetries, said the space must be homogenous and isotropic, on large scales determine the form of their energy-momentum tensors. By Cosmos principle, $T_{00}$, $T_{0i}$ and $T_{ij}$ are maximally ...
Albert Zhao's user avatar
1 vote

Are modified theories of gravity credible?

Although the existing answers aren't wrong, I feel like this part has not been emphasized enough. NB: I'm interpreting your question as "are modified gravity theories that eliminate the need for ...
Allure's user avatar
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1 vote
Accepted

Why is the First Law of Thermodynamic related to Fluid Equation?

The laws of thermodynamics are universal. If the number of particles in the system is huge (such as our universe) then it obeys the laws of thermodynamics regardless of its contituents.
Thomas Bastos's user avatar
4 votes

Why are spherical shapes so common in the universe?

The surface to volume ratio is the least for a spherical object. This means that a sphere for attractive forces will have the highest binding energy. All objects tend to a state of lowest potential ...
SAKhan's user avatar
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2 votes

Why are spherical shapes so common in the universe?

I kept reading and reading and couldn't believe I wasn't finding anything about hydrostatic equilibrium.... Until I did. In space, when an object has enough mass, it will ALWAYS take the shape of a ...
JP Anthony's user avatar
0 votes
Accepted

R-W Metric and null geodesic path of photon

In any metrics in general relativity, the photon geodesic is light-type by definition. Consequently, the scalar product of an elementary displacement of the photon $ \overrightarrow{ds}.\...
Cornelius Fyla's user avatar
2 votes

Why are spherical shapes so common in the universe?

Although Torus/Donut Shapes are among the most common shapes in the transparent, invisible universe, like the Magnetospheres of various planets and galaxies, what humans can easily discern are dense ...
Tristian's user avatar
  • 121
12 votes

Why are spherical shapes so common in the universe?

A planetary body would always want to achieve hydrostatic equilibrium: In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at ...
Nilay Ghosh's user avatar
  • 1,257
6 votes

Accelerating Expansion of Universe - Why Not Caused by Radiation?

Here's an article illustrating the relative magnitudes of radiation pressure vs. gravitational attraction of the Earth and the Sun. So, if we want to know how hard the Sun pushes on the Earth, we ...
Allure's user avatar
  • 21.3k
4 votes

Accelerating Expansion of Universe - Why Not Caused by Radiation?

Radiation pressure forces are relevant in cosmology, but only at the level of studying localized perturbations in the density. This is because you only get a net force if there is a gradient in the ...
Sten's user avatar
  • 5,877
6 votes

Why are spherical shapes so common in the universe?

Equilibrium states in time-varying processes are local minima of exergy which preserve conserved quantities. Those things are (or can be reliably predicted to be) roughly sphere-like for which ...
g s's user avatar
  • 13.9k
12 votes

Accelerating Expansion of Universe - Why Not Caused by Radiation?

Positive pressure like that of radiation has attractive gravity, not repulsive. If the universe was radiation dominated the Hubble parameter would go like $$\rm H(a)=\frac{H_0}{a^2} \to H(t)=\frac{1}{...
Yukterez's user avatar
  • 12.2k
15 votes

Accelerating Expansion of Universe - Why Not Caused by Radiation?

Radiation pressure, both from the cosmic microwave background and all the stars of all the galaxies is so far, far, FAR smaller than the gravitational pull of the galaxies that it can completely, ...
Alfred's user avatar
  • 4,386
17 votes

Why are spherical shapes so common in the universe?

On a astronomical scale spherical shape is due to gravity and the more massive the body the bigger gravity. Let's start with the stars: Stars form by collapsing cloud of gas in so called "pre-...
Graphenjoyer's user avatar
10 votes

Why are spherical shapes so common in the universe?

A classical philosopher like Aristotle would say this is because "sphere is a perfect solid and the heavens are a region of perfection". A more modern version of the essentially same answer ...
John's user avatar
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47 votes
Accepted

Why are spherical shapes so common in the universe?

Spherical shapes in the universe are common because the dominant long range forces like gravity and electromagnetism are central (in that they only depend on the distance between objects). Our planet, ...
CStarAlgebra's user avatar
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0 votes

Why does Hubble's Law indicate motion?

So far, since almost a century, the only possible explanation for the cosmological redshift is a Doppler shift. All other explanations have failed. See https://en.wikipedia.org/wiki/Tired_light.
my2cts's user avatar
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0 votes

If dark matter is axion particles, how did such light particles slow down?

Thermally produced light axions could not be cold dark matter for the reasons you identify. The CDM axions are hypothesised to be produced by (Peccei-Quinn) symmetry breaking around the epoch of ...
ProfRob's user avatar
  • 132k
0 votes

Why does Hubble's Law indicate motion?

I have been trying to understand ... why Hubble's Law needs to implicate any sort of relative motion between galaxies. First we have to clearly define what we mean by "relative motion". Let'...
KDP's user avatar
  • 5,211
1 vote

Why does Hubble's Law indicate motion?

In the standard cosmological model (ΛCDM), the expansion of the universe is just the relative motion of the objects in the universe. The redshift is a Doppler shift due to the relative motion, and the ...
benrg's user avatar
  • 27.4k
2 votes

Why does Hubble's Law indicate motion?

Why can't this just be a property of how light experiences the expansion of space for example? Because if light experiences it, we definitely do. The way the Universe's expansion is most usually ...
controlgroup's user avatar
0 votes

Does the fact that we are able to see CMBR implies that universe expanded faster than light?

Although another answer accurate points out that we don't see radiation from arbitrarily early times, we could in principle without violating relativity. For example, the possibility has been ...
Sten's user avatar
  • 5,877
1 vote

Does the fact that we are able to see CMBR implies that universe expanded faster than light?

No, the fact that we see the CMB simply means that the radius of the observervable universe is at least 13 billion light years. If you imagine the early universe as a 3D infinite sea of bright orange ...
RC_23's user avatar
  • 9,291
2 votes

Does the fact that we are able to see CMBR implies that universe expanded faster than light?

We do not detect any CMBR from the inflationary epoch. The CMBR originated about 370000 years later, at recombination. Before that time the universe was opaque, like a star or substantially hotter. ...
Dale's user avatar
  • 102k
3 votes

Could Space and Time Be Decoupled Pre- Big Bang?

As pointed by gandalf61, all we can do here is mostly speculation. We are far from getting answers to these questions, both from theory and observation. I don't know any theoretical framework which ...
Léo Vacher's user avatar
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3 votes
Accepted

Could Space and Time Be Decoupled Pre- Big Bang?

We really don't know anything about space or time before the Big Bang - or even if the phrase "before the Big Bang" is at all meaningful. This is because General Relativity predicts a ...
gandalf61's user avatar
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