can you explain why the ratio between the Hubble mass (i.e. the mass inside the Hubble volume today for a critical universe) and the Planck mass is about $10^{60}$? why are stars roughly in the middle (on a logarithmic scale)? or even more puzzling: why's the ratio between Hubble and Planck-mass about equal to the ratio between stellar masses and the masses of nucleons?

# cosmology question of the week

CQW is an educational resource for theoretical physics and astrophysics, field theory, relativity and cosmology. we post a new question every wednesday for students to get and for teachers to stay in shape.

## Wednesday, January 18, 2017

## Wednesday, January 11, 2017

### forces on dust particles

can you compute the ratio between radiation pressure and gravity acting on a dust particle in the solar system? could one relate the two forces to the mass of the Sun and establish a minimal mass from which on there would be no dust and hence no planetary system?

we wish all CQW-readers a successful year 2017 full of cosmological discoveries.

we wish all CQW-readers a successful year 2017 full of cosmological discoveries.

## Wednesday, January 4, 2017

### funny way of writing Maxwell's equations

can you reformulate the Maxwell-equations in terms of the complex-valued field $\vec{X} = \vec{E}+\mathrm{i}\vec{B}$? would there be potentials $\Phi$ and $\vec{A}$ for $\vec{X}$, and can one even find a covariant formulation?

## Wednesday, December 21, 2016

### comets and their tails

why is the tail of a comet curved? and could you estimate how fast the curvature of the tail could change?

with this very christmassy question we wish all followers of CQW a merry x-mas and a happy and successful year 2017. we hope to see you again in january.

with this very christmassy question we wish all followers of CQW a merry x-mas and a happy and successful year 2017. we hope to see you again in january.

## Wednesday, December 14, 2016

### Poynting-flux and magnetic charges

in the derivation of the Poynting-theorem one needs to substitute a term $\vec{B}\mathrm{div}\vec{B}$, which is equal to zero due to the fact that the magnetic field is purely rotational, $\mathrm{div}\vec{B} = 0$. insisting to introduce magnetic charges by requiring $\mathrm{div}\vec{B} = 4\pi\rho_\mathrm{mag}$, would that lead to a violation of energy-momentum conservation? are there other arguments, e.g. from the covariance of electrodynamics, why this is not possible?

## Wednesday, December 7, 2016

### electrodynamics with non-conserved charges

following up on last week's question: could one construct a theory of electrodynamics with non-conserved charges, i.e. where $\partial^\mu\jmath_\mu\neq 0$? what consequences would that have?

## Wednesday, November 30, 2016

### gravitational fields for non-conservative systems

Einstein's field equation links the Einstein-tensor $G_{\mu\nu}$ to the energy-momentum tensor $T_{\mu\nu}$, which is divergence-free, $\nabla^\mu T_{\mu\nu}=0$. energy-momentum conservation is usually established by considering fields whose Lagrange-density $\mathcal{L}$ does not have an explicit dependence on time or position, leading to the definition of $T_{\mu\nu}$ with the corresponding continuity. in what way would fields $\phi$ with $\mathcal{L}(\phi,\nabla^\mu\phi,x^\mu)$ source a gravitational field?

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