Yoga for dark matter: Making the Cold Dark Matter model more flexible

This guest post was written by Tanvi Karwal. Tanvi is a grad student at Johns Hopkins studying cosmology. She’s a theorist who likes hunting for evidence of exotic kinds of dark matter and dark energy in the cosmic microwave background. She has also dabbled in cosmic rays. In her free time, she draws puns on the blackboards at work when money is short and scuba dives when it is not.


Title: Structure formation with generalized dark matter

Authors: Wayne Hu

First Author’s Institution: Princeton University

Status: Published by The Astrophysical Journal, open access 


Why should dark matter do yoga?

The \LambdaCDM (\Lambda-Cold Dark Matter) model is the current standard model of cosmology and consists of normal matter, photons, neutrinos, cold dark matter and dark energy occupying a flat universe. The aptly-named Dark Sector can be described very simply: dark energy is a Cosmological Constant (\Lambda) and dark matter is cold (i.e. its particles move slowly compared to the speed of light). Each component of \LambdaCDM can be quantified by a single parameter. Dark energy drives cosmic acceleration, while dark matter clusters and seeds structure formation.

The simple \LambdaCDM model has done exceptionally well in describing the large-scale structure of the universe: it accurately predicts features in phenomena such as baryon acoustic oscillations, the matter power spectrum and the cosmic microwave background (CMB). Even in the local universe, measurements of dark energy do not deviate signi ficantly from \Lambda and CDM has had successes explaining galaxy clusters.

Thankfully, \LambdaCDM might not be the whole picture (or I would be out of a job!). When a \LambdaCDM model is fit to the CMB, the model under-predicts the current rate of expansion of the universe (the infamous Hubble tension). Physically motivating a cosmological-constant-like dark energy has left physicists bending over backwards (even when they’re not doing yoga). Dark matter has not yet been directly detected and models of dark matter remain limited to candidates that are considered to be well-motivated theoretically. Hence, the Dark Sector remains, well, dark – despite some recent progress, our understanding is woefully incomplete.

If \LambdaCDM is not the whole picture, how can we construct a more complete model? One way to assemble the pieces of this cosmological puzzle is to employ a phenomenological approach, rather than deriving the model from first principles. A phenomenological model describes relationships between variables based on experiment and observations, instead of being derived from fundamental theory.


Making dark matter do yoga with a Generalised Dark Matter model

The Generalised Dark Matter (GDM) model, first proposed by Wayne Hu in 1998, is precisely such a phenomenological approach. GDM introduces flexibility into the Dark Sector that is not possible in \LambdaCDM.

GDM postulates that dark matter is really like an imperfect fluid. In this description, dark matter has a non-zero intrinsic pressure, given by w_g times its energy density, where w_g is a dimensionless equation-of-state parameter. Because dark matter has now been imbued with a non-zero pressure, it can have pressure waves with some e ffective sound speed (just like the speed of sound [link to video] in air is 343 m/s). Additionally, it has a non-zero viscosity that damps the pressure waves.

As the GDM model incorporates pressure, unlike its cold counterpart, we can observe some interesting features from this property alone. As the energy density of any species of particle is proportional to the scale factor a_{3(1+w)}, its energy density evolves di fferently relative to CDM. If GDM replaces CDM, the energy density of the dominant matter species can evolve di fferently over time compared to \LambdaCDM. Replacing w_{CDM} with w_g can alter the time at which the universe exhibited matter-radiation equality, the time of the emission of the CMB and therefore changes the features in the CMB itself.

And that’s not all. If GDM has pressure waves, its energy density can oscillate about a mean value. If it is viscous, these oscillations will be damped and decay. GDM therefore changes how matter clusters and hence the shape of the matter power spectrum.

Furthermore, clustered matter forms a gravitational potential well. As GDM continues to oscillate, so does the depth of these wells. CMB photons travelling toward us through the cosmos gain and lose energy to these wells through a mechanism known as the Integrated Sachs-Wolfe (ISW) e ffect. Photons gain energy by being attracted into gravitational potential wells, and lose energy as they try to climb back out of the wells. If the height of the well changes as the photon is travelling through it, it emerges from the well with a little less or more energy. Hence, GDM adds power to the CMB at the scales where oscillation occurs.

Radiation leaking from gravitational potential wells also causes the wells to decay. Hence, increasing (decreasing) w_g decreases (increases) the radiation density of the Universe relative to CDM and therefore decreases (increases) the ISW e ffect due to radiation. This e ffect occurs at scales less than or equal to the size of the Universe, when the energy density of radiation was appreciable. The effects of the GDM model on the CMB can be seen in Figure 1.

Figure 1:  The CMB power spectrum predicted by \LambdaCDM (black dotted line) is compared to that obtained from various GDM scenarios from Kopp et al. Each additional line corresponds to one GDM parameter being varied: (i) the equation of state w (blue), (ii) the effective sound speed c^2_s (green) or (iii) the viscosity parameter c^2_{\mathrm{vis}} (red). The ISW effect is boosted at large scales (l \leq 400) for the green and red lines. At smaller scales (l \geq 30), the effects of changing w are visible.

The additional parameters that we have incorporated into the dark matter model make it more flexible. But, flexibility aside, did making dark matter do yoga make it more powerful?


Why does flexibility matter?

The GDM parametrisation is indeed powerful, not just because it allows us to extend the vanilla CDM model, but also because it can be used to model numerous other particle species. If the GDM parameters are assumed to be constant, we can model a cosmological constant, neutrinos and dark radiation, which is a hypothetical form of radiation that mediates interactions between dark matter particles. If they are allowed to vary over time, GDM can model hot and warm dark matter and scalar fields that describe dark energy. Hence, the GDM model allows dark matter to vary its behaviour across di fferent epochs in cosmic history and can better probe the behaviour of particle species such as neutrinos.

Thus, the flexibility of this model does make it more powerful – a very good reason to make dark matter do yoga!


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1 Comment

  1. In the Generalised Dark Matter (GDM) model, the GDM has pressure waves.

    Dark matter is a supersolid that fills ’empty’ space and is displaced by visible matter.

    The supersolid dark matter ripples when galaxy clusters collide and waves in a double-slit experiment, relating general relativity and quantum mechanics.

    What is referred to geometrically as curved spacetime physically exists in nature as the state of displacement of the dark matter. The state of displacement of the dark matter is gravity.

    There is evidence of supersolid dark matter every time a double-slit experiment is performed, as it is the medium that waves.



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