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?

# 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, December 7, 2016

## 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?

## Wednesday, November 23, 2016

## Wednesday, November 16, 2016

### dissipation time scale

there are many structures visible in Jupiter's atmosphere. can you estimate a dissipation time scale for the turbulent motion?

## Wednesday, November 9, 2016

### motion or not?

can you show that a cosmological fluid in a FLRW-universe it at rest in all freely falling frames, but shows recession motion?

## Tuesday, November 8, 2016

### implications of a confirmed $\Lambda$

this post is in celebration of $2^{16}$ views!

imagine that future experiments have constrained the dark energy eos-parameters to be $w_0=-1$ and $w_a=0$ at high precision: would that imply that we have confirmed that the covariant divergence $\nabla^\mu g_{\mu\nu}$ of the metric $g_{\mu\nu}$ is zero, implying a metric connection, at least under the FLRW-symmetries?

imagine that future experiments have constrained the dark energy eos-parameters to be $w_0=-1$ and $w_a=0$ at high precision: would that imply that we have confirmed that the covariant divergence $\nabla^\mu g_{\mu\nu}$ of the metric $g_{\mu\nu}$ is zero, implying a metric connection, at least under the FLRW-symmetries?

## Wednesday, November 2, 2016

### cosmology works?

a freely-falling observer experiences the metric $g_{\mu\nu}$ of generated by any energy-momentum distribution $T_{\mu\nu}$ as being of Minkowskian shape $\eta_{\mu\nu}$. the observer would conclude that there is no curvature and consequently, no gravitational fields and that the energy-momentum is vanishing.

but isn't that what we're doing in cosmology? as a freely-falling observer we aim to determine the energy-momentum of all cosmological fluids $T_{\mu\nu}$ expressed in terms of their density parameters $\Omega$ and their equations of state $w$. but how can one measure the energy-momentum-tensor of a gravitating matter distribution with a gravitational experiment?

but isn't that what we're doing in cosmology? as a freely-falling observer we aim to determine the energy-momentum of all cosmological fluids $T_{\mu\nu}$ expressed in terms of their density parameters $\Omega$ and their equations of state $w$. but how can one measure the energy-momentum-tensor of a gravitating matter distribution with a gravitational experiment?

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