Classical scalar field as Dark Matter

[fhenryco]

The pressure of a scalar field is: Φ˙2−V(Φ)

so to have zero or negligeable pressure it needs to have equipartition of its energy in potential and kinetic form ==> the potential must be positive. In particular a mass term m2Φ2 ... could be all right: the field should tend to roll down this potential to zero energy if the field is interacting significantly with other fields ... but otherwise would oscillate for ever to maintain the equipartition of the energy on the mean (and thus zero pressure for our scalar field).

So it seems that the zero pressure situation is not only natural for a dust field (as is baryonic matter or Dark matter) but could also be for a fundamental field such as the scalar field above. So even if this field is fundamentally classical, thus has no quanta, hence no detectable particle associated to it and therefore only interacts with gravity in a classical way, it could behave just as cold dark matter : being pressure less it would gravitationnally collapse. Obviously such kind of explanation for CDM must have already been considered but my question is : is there any other argument against it beyond the "shared conviction" that everything in nature must be quantized ?

 

[PeterDonis]

The pressure of a scalar field is: Φ˙2−V(Φ)

Only if the field does not vary at all in space. Which is not possible if you expect it to explain dark matter, since the density of dark matter does vary in space.

being pressure less it would gravitationnally collapse

But dark matter does not gravitationally collapse as much as ordinary matter does. That's why it forms huge halos around galaxies instead of clumping near the centers of galaxies like ordinary matter does.

 

[fhenryco]

What makes you think that the classical scalar fluid would collapse more like baryonic matter than dark matter ?

 

[PeterDonis]

What makes you think that the classical scalar fluid would collapse more like baryonic matter than dark matter ?

What makes you think it wouldn't? You are drawing an analogy based on "zero pressure means gravitational collapse". So a "zero pressure" scalar field should collapse the same as any other "zero pressure" thing, including baryonic matter. So if you think there's a difference between the two, you need to explain why.

 

[PeterDonis]

so to have zero or negligeable pressure it needs to have equipartition of its energy in potential and kinetic form ==> the potential must be positive.

This, btw, is also a lot less likely than you appear to think. It requires the time derivative of the field to be positive, and to be precisely equipartitioned, as you say. Remember that ##\dot{\Phi}## is not the "kinetic energy" of a thing just moving around, even though the term "kinetic energy" is often used to refer to it; it's the time derivative of a field. A positive ##\dot{\Phi}## with no spatial variation (which, as I noted before, is what you need for your formula for the pressure to be valid) would mean the field's value is increasing everywhere. How?

A typical actual model for a scalar field with little or no spatial variation is the scalar field model of inflation; in this model ##\dot{\Phi}## is zero or negative (depending on whether there is a "slow roll") and the pressure is therefore negative, so that ##\rho + 3 p## is negative and the field causes inflationary expansion.

 

[fhenryco]

your last answer does not appear completely ... (?) parts have been cutted apparently

 

[PeterDonis]

your last answer does not appear completely

It looks fine to me. You might need to refresh the page or restart your browser.

 

[fhenryco]

the densities only involve the square of field derivative , which are always positive terms ... so I'm wondering why you are talking about the sign of the field derivative

 

[PeterDonis]

the densities only involve the square of field derivative

Yes, you're right, the square will be positive regardless of the sign of the derivative. However, if ##\dot{\Phi}## is nonzero, you still have to explain why the field is changing. A "slow roll" model will do that, but, as I said, such a model is an inflation model, and will cause exponential expansion, not "gravitational collapse".

 

[fhenryco]

Refering to formula 7 and 8 of
http://hep.itp.tuwien.ac.at/~wrasetm/files/2017S-GRplusScalar.pdf
for the densities and pressure of a scalar field, if the potential term dominates the gradient term, which is certainly true for sufficiently small k (sufficiently large wavelength) , then we essentially have an oscillator exchanging it's energy between the kinetic term (square of time derivatives) and the potential term, at fréquency m, so i would say the equipartition of the energy is realized, not at every time but on the mean.

So on those large enough scales, it's a ~ pressureless fluid (p<<rho) ready to collapse under the effect of gravity, and we just need to ajust the field mass m in such a way that it collapses on the CDM scales and not the baryonic smaller scales at which pressure is again significant ... what's wrong with this reasoning ?

 

[fhenryco]

apparently it's not so wrong because searching for ultralight dark matter (the idea is that the compton wavelength associated to the particle must be huge to prevent collape on baryonic scales ) i have just found this:
https://en.wikipedia.org/wiki/Scalar_field_dark_matter
the only difference with my initial question is that one does not need BEC or superfluid states nor ultralight particles if the scalar field is actually not quantized.
Understood as a classical field it actually even does not need to be scalar nor even bosonic... which i find interesting because the ratio of Dark Matter density and baryonic matter is close to one (~20%). Si there might exist a mechanism according to which 80% of the same field exists in an unquantized form while 20% is quantized ...

 

[Orodruin]

Understood as a classical field it actually even does not need to be scalar nor even bosonic... which i find interesting because the ratio of Dark Matter density and baryonic matter is close to one (~20%). Si there might exist a mechanism according to which 80% of the same field exists in an unquantized form while 20% is quantized ...

Axion dark matter is essentially a coherent state, which is the QFT equivalent of a classical field. This does not mean that you can split the field in "quantised" and "unquantised".

 

[fhenryco]

Orodruin,
I'm completely aware that the idea of a field existing both in a quantized version and a classical version is completely strange and foreign to QFT ... and i have actually no idea how it could work in practice , but i find the direction of thinking interesting since after all nobody knows where quantization comes from (it remains a postulate) and that searching along this way might eventually clarify the origin of the quanta...

 

[PeterDonis]

Refering to formula 7 and 8

These are for a scalar field covering the entire universe. They are assuming the FRW metric. This is irrelevant for modeling dark matter halos around galaxies, since the metric around a galaxy is not FRW; galaxies and their halos are not expanding.

 

[PeterDonis]

I'm completely aware that the idea of a field existing both in a quantized version and a classical version is completely strange and foreign to QFT

In other words, this is personal speculation, which is off limits here at PF. Thread closed.