Here we are plotting delta T/T as a function of angle between two

directions. When the angle is approximately 1 degree or in terms

of l values near 200, delta T/T goes through a pronounced maximum.

This is called the acoustic pick. We would like to know why delta T/T

has a maximum at this angle. What is the physics behind it.

It has to do with the size of the particle horizon at the time. Imagine an initial perturbation, a slight overdensity. This initial overdensity is also an initial overpressure. This overpressure tries to equalize itself with the surroundings, and this simply results in an expanding spherical sound wave, in a similar way that all sound waves are formed. The main difference here is that this wave travels at about 0.5c, since the speed of sound is extremely high. The angular distance of these acoustic peaks, gives a measure of how far initial perturbations have propagated. It's possible to use them, in combination with other sources -see the first link below- to estimate Ω

See this page, for an explanation of how it depends on other cosmological parameters http://background.uchicago.edu/~whu/araa/node15.html#sec:sensitivity

Also here a nice explanation is provided "...The distance sound waves could have traveled in the time before recombination is called the sound horizon, rs. The sound horizon is a fixed physical scale at the surface of last scattering. The size of the sound horizon depends on the values of cosmological parameters. The distance to the surface of last scattering, dsls, also depends on cosmological parameters. Together, they determine the angular size of the sound horizon..." from http://ned.ipac.caltech.edu/level5/Sept02/Reid/Reid5_2.html

Stathis Artis,

Thank you very much for your post. I was interested to know how the

fraction of dark matter with respect to total energy+matter affect

shapes and positions of acoustic picks. Specially I was interested

to know why PLANK data is giving 26.8 % dark matter. Previous

estimates of this fraction was slightly lower.

the acoustic spectrum is generated by the coupled baryon+dark matter fluid that is oscillating inside a gravitational potential and generating acoustic (pressure) waves.

The symmetry of the second and third peaks, hinted at by WMAP but really confirmed by Planck provides the first direct evidence for Dark Matter.

Hello G. Bothun and Stathis Artis:

Thanks for replying.

Could you please explain the symmetry between second and third

peak. How is this symmetry is connected with dark matter ?

I can understand the presence of high and low density areas.

Correspondingly there is a small temperature difference, which

should be periodic in the angle variable, between high density

and low density areas. Therefore in the plot of deltaT/T we can

expect a few picks.

Odd numbered peaks are associated with the free fall time of the plasma in a local gravitational potential well (the plasma compresses and heats). These peaks are enhanced by the amount of baryons in the potential.

Even numbered peaks are associated with how far the plasma "rebounds". Baryons serve to suppress that rebound.

Symmetry between the second and third peaks can only occur if baryons are not dominating the local gravitational potential and that dominance is determined by

dark matter.

There is a SHM type equation with an additional term due to

the presence of dark matter. Please see the following quote,

" The effects of dark matter also explain why the temperature

fluctuations in the CMB are of order deltaT/T =10^-5 , instead of 10^-3

as originally expected. Because dark matter does not have pressure, it

could begin to collapse at earlier times, when the collapse of baryons

was still resisted by the pressure of the photons to which they were

coupled."

reference:

http://www.gravity.phys.uwm.edu/~dawn/astron401/lecture34.pdf

Biswajoy,

Please edit your question to change all "pick" to "peak" - I think this would help a lot. You can edit the question by clicking on the 'pencil' icon...

IMO, there may be a false analogy at the heart of the current interpretation of acoustic oscillations. As I understand, it is more correct to consider that it is the fundamental inertial effect of the photon-baryon fluid's mass-energy density that resists its expansion - not any strictly gravitational interaction. Radiation pressure drives the fluid's expansion, producing the oscillating acoustic signal...

I'm referring to http://www.gravity.phys.uwm.edu/~dawn/astron401/lecture34.pdf - and http://background.uchicago.edu/~whu/intermediate/gravity.html - which describes its illustrative animation:

"Likewise we will represent the inertia of the fluid, or loosely speaking its mass (really energy density), as massive balls falling under gravity"...

Also see http://background.uchicago.edu/~whu/intermediate/baryons4.html - which states:

"Although we cannot yet claim that the second peak is as precisely measured as the first, we can say that (assuming it exists!) it is definitely of lower amplitude than the first"...

Also, how would cold dark matter particles have been initially 'heated' (by density/compression?) - then 'cooled', since they do not participate in electromagnetic interactions? If expansion was being driven by radiation pressure, why and how would dark matter have expanded at all - shouldn't it have generally retained its initial density as a result of its inertial mass/gravitational effect? It seems that only direct collisions between (less massive) expanding baryonic particles and dark matter particles could have imparted any momentum to dark matter...

Oh wow James, it is the second time I am doing a global change

from picks to peaks. Thank you very much.

James, Hot and cold dark mater refers to dark matter particles

moving in relativistic and non relativistic velocity. Dark matter

does not interact with photons, therefore photons cannot increase

temperature of the photon-baryon plasma (before decoupling).

Yes photons cannot put expanding pressure on dark matter

particles. I agree with you on this point. Because space-time

itself is expanding, dark matter also expands with it. Dark matter

contributes to matter density as a function of space-time

coordinates.

Biswajoy,

Of course I understand the difference between proposed types of dark matter, as we already discussed in https://www.researchgate.net/post/Can_the_Lambda-CDM_cosmological_model_survive_the_discrepancy_between_galaxy_cluster_observations_and_CMB_projections. As explained above, the baryonic oscillations are exhibited in their expansion due to thermal (photon) pressure that is independent of any effects of spacetime expansion.

The point I'd like to make is - since baryons are in motion as a result of photon pressure and dark matter cannot be pressured by photons - how could baryon and dark matter particles remain coupled in an oscillating fluid? Shouldn't they universally differentiate as a result of their different universal momentum?

Again - since gravitational interactions among particles has never been observed - isn't the opposition to the baryonic momentum that produces its oscillating momentum more likely the product of the inertial effects of their masses than any proper gravitational interaction?

The dark matter is still trapped in the same local gravitational potential as the baryons

G. Bothun,

That seems to require that fundamental particles interact gravitationally - an unobserved phenomenon - correct? Again, particle inertial mass effects might produce the oscillation of momentum rather than proper gravitational interactions among particles.

James, I think gravitational interaction between elementary

particles are extremely small. It is so small that with

present day technology it is an unconfirmed phenomenon.

That does not rule the possibility of gravitational interactions

between elementary particles.

Comparing coupling constants of four fundamental forces we

see that gravity is 10^-37 times weaker than electromagnetic force.

see for example:

http://hyperphysics.phy-astr.gsu.edu/hbase/forces/couple.html

Generally all textbooks with which we have grown up

(say Halzen and Martin) assumes that there are four

fundamental forces acting on an elementary particle.

I think this is an assumption. Do you know of any experimental

group which is trying to measure gravitational interaction of

elementary particles ? Please let me know.

Following paper addresses a related problem.

Effective gravitational interactions of dark matter axions

Toshifumi Noumi (RIKEN (main)), Ken'ichi Saikawa

(Tokyo Inst. Tech.), Ryosuke Sato (KEK, Tsukuba),

Masahide Yamaguchi (Tokyo Inst. Tech.).

Oct 1, 2013. 26 pp.

Published in Phys.Rev. D89 (2014) 065012

I must apologize for not better explaining my taking exception to what are certainly concordance descriptions of physical phenomena within the LCDM. Certainly - in that sense you're correct.

I am questioning though, why primordial events should be attributed to an unobserved gravitational effect - while the well demonstrated inertial effects of particle mass are omitted! This is crucial in terms of potential requirements for primordial dark matter - thought to be necessary to provide gravitational resistance to baronic momentum.

Moreover, I must question drawing definitive conclusions such as "The symmetry of the second and third peaks, hinted at by WMAP but really confirmed by Planck provides the first direct evidence for Dark Matter" especially if, for example, as http://background.uchicago.edu/~whu/intermediate/baryons4.html states:

"Although we cannot yet claim that the second peak is as precisely measured as the first, we can say that (assuming it exists!) it is definitely of lower amplitude than the first"... At any rate, I must challenge the 'directness' of this highly derivative evidence.

That the effective coupling constant used to evaluate local gravitational effects is many orders of magnitude weaker than those of quantum interactions suggest to me that it is _not_ a strictly local interaction among particles - and that GR describes gravitation in terms of dimensional spacetime distortions because the external vacuum is an essential component of physical gravitational processes.

Alternatively, as an emergent interaction, gravitation may not have even _existed_ prior to the recombination epoch! Please see http://www.nature.com/news/superfluid-spacetime-points-to-unification-of-physics-1.15437 - especially my comment extracted below:

---

It may be instructive to consider that the process of ordinary particle accretion in the relative vacuum of spacetime is initiated not as any gravitational interaction among particles but as the attraction of EM charge interactions. ‘Weaker’ gravitational effects soon take precedence over EM particle charge interactions - eventually producing discrete, cohesive, massive objects.

Note that any condensation of matter (mass-energy) - both initially by EM and subsequently by gravitation - necessarily produces an equal and opposite _reaction_: the extraction of mass-energy from the vacuum!

This neglected counter-action may be crucial, as it produces an effective, macro scale, mass-energy 'charge' differential between positive mass material objects and the negatively mass-charged vacuum.

This depleted-mass-energy vacuum state may be described by the contraction of dimensional spacetime coordinates - as in general relativity - that physically induces the relative motions of massive objects within spacetime...

In this way, gravity is not a fundamental force interaction of quantum particles - it may rather be an _emergent_, macro-scale only, mass-charge interaction of the vacuum.

---

Your Noumi et al.,reference can be found at http://arxiv.org/abs/1310.0167. As I understand, it is a highly theoretical analysis based on a quantum basis for gravitational interactions among particles.