# Baryogenesis only at the Planck scale, or none at all?

I can think of three general ways of explaining why the universe contains more matter than antimatter:

(1) Near the Planck time, the universe had zero baryon asymmetry, but at some later time, determined by some GUT energy scale, the Sakharov conditions were satisfied, and the baryon asymmetry became nonzero.

(2) Nonconservation of baryon number occurs only at Planckian energies. Near the Planck time, the baryon asymmetry evolved from zero to some nonzero value.

(3) The Sakharov conditions have never been satisfied. The baryon asymmetry has always been nonzero, and has simply scaled as expected. (Apparently one expects $\Delta n=n_B-n_\bar{B}\propto s$, where $n$ is number density and $s$ is entropy density).

It seems like most theorists are interested in #1, but is there any reason why 2 and 3 aren't possible?

2 seems pretty reasonable, since for the reasons given in this answer, we have good reasons to think that baryon number is not conserved under Planckian conditions.

3 also seems reasonable to me, since even if baryon number is nonconserved at Planckian energies, that's only one of the three Sakharov conditions. I don't see any obvious fine-tuning objections to #3, since the scaling of baryon asymmetry with cosmological expansion isn't particularly drastic (not an exponential decay or anything). Is there something unphysical about maintaining $\Delta n\propto s$ all the way back to the Planckian era?

Some people might object to #3 on aesthetic grounds, since we "expect" the initial conditions of the universe to be symmetric, but that seems weak to me. After all, we don't object aesthetically to the fact that homogeneity was an imperfect symmetry of the early universe, and we even accept that the early universe was in a thermodynamically unlikely state.

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Funny term. Etymologically baryogenesis should mean the genesis (creation) of baryons.. I just found out the term has been preempted to mean baryon asymmetry at genesis. – anna v Jul 25 '13 at 4:51

## 1 Answer

Good question!

Regarding (2) baryon number is certainly violated at Planckian energies. If you can make a black hole, you can eat up baryons. Luboš Motl's argument that you linked to is correct in this regard. Whether you can make a believable scenario of quantum gravity driven baryogenesis at the Planck time is up in the air as far as I know. It's the old problem of what predictions quantum gravity makes for cosmology again. But even if you did come up with a net baryon number you still have the problem of washout (see below)...

Regarding (3) there are two problems. First: despite what you may have heard baryon number is not conserved in the standard model. There are non-perturbative "sphaleron" processes that are in thermal equilibrium above the electro-weak symmetry breaking phase transition. These arise because the baryon and lepton currents are anomalous: $\partial_\mu j_B^\mu = \partial_\mu j_L^\mu \neq 0$. Sphalerons eat three units of baryon number and produce three units of lepton number (and other processes related by crossing). Below the phase transition $T \lesssim 100\ \mathrm{GeV}$ these processes are thermally suppressed to the point that you never see them.

Only the difference $B-L$ is exactly conserved in the standard model, and indeed there are standard model extensions where $B-L$ is coupled to a $U(1)_{B-L}$ gauge symmetry. So it happens that any baryon asymmetry produced sufficiently early (this includes initial conditions) in the orthogonal channel $B+L$ gets washed out exponentially by sphalerons. Only the $B-L$ charge survives and the sphaleron processes divvy out the asymmetry between leptons and baryons. If there are further $L$ violating processes beyond the standard model (such as majorana neutrino masses), you can easily wipe out all of the baryon number before the electroweak phase transition. Alternatively, you can count on $L$ violation producing enough of an $L$ excess that sphalerons convert the excess to $B$ and gives you the baryon number that you need. This describes a leptogenesis scenario.

Second problem: inflation! Inflation happens (if it happens at all) below the Planck scale, so it exponentially dilutes any charges. So to get the right baryon number from a Planck scale initial condition you need a huge initial asymmetry so that after inflation and washout you get a tiny contribution of just the right size to give you the measured baryon asymmetry. This is a very delicate situation. It is much easier to believe that whatever initial asymmetry that may be present is small enough to be wiped out by sixty e-folds of inflation, and there is some dynamical mechanism related to reasonably small violations of $B$, $C$ and $CP$ somewhere between the GUT scale and electroweak scale which is responsible for creating the small observed asymmetry $(n_B - n_\bar{B})/n_\gamma \sim 10^{-10}$.

You are right though: technically it is theoretical prejudice (and the inability to do concrete calculations) that rules out options 2 and 3, not any direct logical or experimental evidence.

## References

The original article on sphalerons:

• Klinkhamer, F., & Manton, N. (1984). A saddle-point solution in the Weinberg-Salam theory. Physical Review D, 30(10), 2212–2220. doi:10.1103/PhysRevD.30.2212

Early calculation of the sphaleron rate (modern calculations use Monte Carlo):

• Arnold, P., & McLerran, L. (1987). Sphalerons, small fluctuations, and baryon-number violation in electroweak theory. Physical Review D, 36(2), 581–595. doi:10.1103/PhysRevD.36.581

Nice pedagogical treatments of sphalerons and electroweak symmetry breaking:

Nice reviews or baryogenesis and leptogenesis (by year):

• Fong, C. S., Nardi, E., & Riotto, A. (2012). Leptogenesis in the Universe. Advances in High Energy Physics, 2012, 1–59. doi:10.1155/2012/158303

• Shaposhnikov, M. (2009). Baryogenesis. Journal of Physics: Conference Series, 171. doi:10.1088/1742-6596/171/1/012005

• Davidson, S., Nardi, E., & Nir, Y. (2008). Leptogenesis. Physics Reports, 466(4-5), 105–177. doi:10.1016/j.physrep.2008.06.002

• Cline, J. M. (2006). Baryogenesis. Retrieved from http://arxiv.org/abs/hep-ph/0609145

• Buchmüller, W., Di Bari, P., & Plümacher, M. (2005). Leptogenesis for pedestrians. Annals of Physics, 315(2), 305–351. doi:10.1016/j.aop.2004.02.003

• Trodden, M. (2004). Baryogenesis and Leptogenesis. Retrieved from http://arxiv.org/abs/hep-ph/0411301

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