Does Ignoring Small Scale Physics Hurt Cosmology? Probably Not.

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When cosmologists study the universe they usually assume it is homogeneous and isotropic with linear perturbations.  On large scales this turns out to be a very good approximation.  Fortunately, these assumptions greatly simplify the math since:

1. The equations are linear and therefore easily solvable.
2. (Related to #1.)  Fourier modes decouple meaning you can solve for each mode independent of the others.

(If #1 and #2 above don't make sense it's fine.  Just know that the math becomes simple and solvable with the above assumptions.)

Recently, Baumann et al. asked a very interesting question: "Are we sure that small-scale non-linearities do not induce a large backreaction?"  In more lay terms: The physics on small scales is not linear, homogeneous and isotropic.  Are we ignoring important effects that physics on these small scales may place on the physics on large scales when we assume the universe has these nice properties on all scales?  

This isn't a new concept.  In particle physics one faces the same issue.  Physics that happens at high energies (or small scales) may have non-trivial effects on low-energy physics. (or large scales.)  These are often called non-perturbative effects and a good low-energy prediction must to take them into account.  "Integrating out" these small scale effects is at the heart of renormalization in particle physics.

Fortunately for cosmologists, Baumann et al. found that any back-reaction effects are very small.  Second, at most the these effects exert a slight positive pressure on the universe.  Therefore, backreaction effects cannot account for something like dark energy that has non-trivial negative pressure.  Lastly, they found the small scale effects completely decouple from large scales confirming that applying linear theory to large scales is well motivated.

Therefore, doing cosmology with the above simplifying assumptions appears to pass yet another important test.

(Image: Credit: NASA / WMAP Science Team)

Daniel Baumann, Alberto Nicolis, Leonardo Senatore, & Matias Zaldarriaga (2010). Cosmological Non-Linearities as an Effective Fluid eprint arXiv: 1004.2488v1