## A review of yesterday’s afternoon talks: non-thermal gravitino dark matter and non-standard cosmologies May 21, 2008

Posted by dorigo in cosmology, news, physics, science.
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In the afternoon session at PPC2008 yesterday there were several quite interesting talks, although they were not easy for me to follow. I give a transcript of two of the presenations below, for my own record as well as for your convenience. The web site of the conference is however quite quick in putting the talk slides online, so you might want to check it if some of what is written below interests you.

Ryuichiro Kitano talked about “Non-thermal gravitino dark matter“. Please accept my apologies if you find the following transcript confusing: you are not alone. Despite my lack of understanding of some parts of it, I decided to put it online anyway, in the hope that I will have the time one day to read a couple of papers and understand some of the details discussed…

Ryuichiro started by discussing the standard scenario for SUSY dark matter, with a WIMP neutralino. This is a weakly interacting, massive, stable particle. In general, one has a mixing between bino, wino, and the higgsinos, and that is what we call neutralino. In the early universe it follows a Boltzmann distribution, then there is a decoupling phase when the process inverse to production becomes negligible, so at freeze-out the number density of the neutralino goes with T^3. The final abundance is computed by equating two terms at time of decoupling, to get $<\sigma v> = (n^2_\chi -n^2_{eq}$.

In this mechanism there are some assumptions. The neutralino is a LSP: it is stable. The second assumption is that the universe is radiation-dominated at time of decoupling. A third assumption says that there is no entropy production below T=O(100 GeV), otherwise relative abundances would be modified. Are these assumptions reasonable ? Assumption one restricts to gravity mediation. There is almost always a moduli problem. This is inconsistent with assumptions 2 and 3. If you take instead anomaly mediation, wino LSP and it gives too small abundances. We thus need a special circumstance for the standard mechanism to work.

The moduli/gravitino problem: in gravity mediation scenario, there is always a singlet scalar field which obtains a mass throuhg SUSY breaking. S is a singlet under any symmetry, and it gives a mass dump to the gaugino. Its potential cannot be stabilized, and it gets mass only through SUSY breaking. Therefore, there exists a modulus field. We need to include it to consider the cosmological history, because it has implications.

During inflation, the S potential is deformed because S gets mass only from SUSY breaking. So, the initial value of the moduli will be modified. Once S-domination happens it is a cosmological disaster. If the gravitino is not LSP, it decays with a lifetime of the order of one year, and it destroys the standard picture of big bang nucleosynthesis (BBN). if the decay is forbidden, it is S
to have a lifetime of O(1y), still a disaster. Inconsistent with neutralino DM scenario, or better, gravity mediation is inconsistent.

So we need some special inflation model which does not couple to the S field; a very low scale inflation such that deformation of S potential is small; and a lucky initial condition such that S-domination does not happen. Is there a good cosmological scenario that does not require such conditions ?

Non-thermal gravitino DM is a natural and simple solution to the problem. Gauge mediation offers the possibility. SUSY breaking needs to be fixed in the scenario. Most of it has the same effective lagrangian. This implies two parameters in addition to the others: the height of the potential (describing how large is the breaking) and the curvature $m^4/\Lambda^4$. In this framework, the gravitino is the LSP.

In non-thermal gravitino dark matter scenario, the mechanism can produce the DM candidate. After inflation, S oscillation starts. We have a potential for it, there is a quadratic term. Second step is decay. The S coupling to superparticles are proportional to their mass. S-Gravitino coupling is instead suppressed. Gives a smaller branching ratio to gravitino. Good for the gravitino abundance. Also the shorter lifetime as compared to gravity mediation is good news for BBN.

The decay of S to a bino pair must be forbidden to preserve BBN abundances. So $S \to hh$ is the dominant decay mode if it is open. If we calculate the decay temperature, we find good matches with BBN and it is perfect for DM as far as its abundance is concerned.

There are two parameters: height of potentials and curvature. We have to explain the size of gaugino mass and fix one of the parameters. Gravitino abundance is explained if gravitino mass is about 1 GeV. Baryon abundances however have to be produced by other means.

Step three is gravitino cooling. Are they cold ? THey are produced by the decay of 100 GeV particles, relativistic, but their distribution is non thermal. It slows down by redshift. These must be non-relativistic at time of structure formation.

If we think of SUSY cosmology we should be careful about the consistency with the underlying mode, of gravity mediation. Gauge mediation provides viable cosmology with non-thermally
gravitino DM.

Next, Paolo Gondolo gave a thought-provoking talk on “Dark matter and non-standard cosmologies“. Again, I do not claim that the writeup below makes full sense -not to me, but maybe to you it does.

Paolo started by pointing out the motivations for his talk: they come directly from the previous talks, the problem with the gravitino and with the moduli. One might need to modify usual cosmology before nucleosynthesis. Another motivation is more phenomenological. The standard results on neutralino DM are presented in standard parameter space $M_0 – M_{1/2}$, and one gets a very narrow band due to constraints of dark matter from cosmology. These constraints come from primordial nucleosynthesis. They assume that neutralinos were produced thermally, decoupled at a later time and remained with a residual abundances. This might not be true, and if it isn’t, the whole parameter space might still be consistent with cosmological constraints.

[This made me frown: isn’t the SUSY parameter space still large enough ? Do we really need to revitalize parts not belonging to the hypersurface allowed by WMAP and other constraints ?]

The above occurs just by changing the evolution of the universe before nucleosynthesis. By changing $\tan \beta$ you can span a wider chunk of parameters, but that is because you look at a projection. Cosmological constraints give a n-1 hypersurface. One can extend it outside of it. But this comes at the price of more parameters. Don’t we have enough parameters already?

Cosmological density of neutralinos may differ from usual thermal value because of non-thermal production or non-standard cosmologies. J.Barrow, in 1982, wrote of massive particles as a probe of the early universe. So it is an old idea. It continues in 1990, with a paper by Kamionkowski and Turner: Thermal relics: do we know their abundances ?

So let us review the relic density in standard cosmology, and the effect of non-standard ones. In standard cosmology the Friedmann equation governes the evolution of the scale factor a, and the dominant dependence of $\rho$ on a determines the expansion rates. Today we are matter-dominated, and we were radiation-dominated before, because $\rho$ scales with
different powers of the scale factor: now $\rho = a^{-3}$, but before it went $a^{-4}$. Before radiation domination there was reheating, and before, the inflation era. At early times, neutralinos are produced in e+e- production, and mu+mu-. Then production freezes out, and here they say neutralino anihilations ceases, but it really is the production which ceases. Annihilation continues at smaller rates until today so that we can look for it, but it is production that stops. Number of neutralinos per photons is constant at freeze out. The higher the annihilation rate, the lower the final density. There is an inverse proportionality.

The freeze-out occurs during the radiation-dominated epoch, T = 1/20th of the particle mass, so we have much higher temperature than that of a matter-dominated universe. Freeze-out occurs before BBN. We are making an assumption of the evolution of the universe before BBN. What can we do in non-standard scenarios ? We can decrease the density of particles, by producing photons after freeze-out (entropy dilution). Increasing photons you get lower final density. One can also increase the density of particles by creating them non-thermally, from decays. Another way is to make the universe expand faster during freeze-out, for instance in quintessence models.

The second mechanism works because if we change the expansion rate we need a higher density. What if instead we want to keep the standard abundance ? We want to produce WIMPS in a thermal mechanism. We need a standard Hubble expansion rate down to $T=m/23$. down to freeze-out. A plot of $m/T_{max}$ versus $<\sigma v>$ shows that production is aborted at $m/T>23$.

How can we produce entropy to decrease the density of neutralinos after freeze-out ? We add massive particles that decay or annihilate late, for example a next-to-LSP. We end up increasing the photon temperature and entropy, while the neutrino temperature is unaffected.

We can increase the expansion rate at freeze-out by adding energy in the Universe, adding a scalar field, or modify the Friedmann equation by adding an extra dimension. In alternative, produce more particles by decays.

In braneworld scenarios, matter is confined to the brane, and gravitons propagate in the bulk. It gives extra terms in the Friedmann equation, proportional to the square of the density and the Planck mass squared. We can get different densities. For example, in the plane of $m_0$ versus gravitino mass, the Wino is usually not a good candidate for DM but here it is in Randall-Sundrum type II scenarios. We can resuscitate models of SUSY that people think are ruled out by cosmology.

Antiprotons from WIMP annihilation in the galactic halo constrain the RS model II. The 5-dimensional Planck constant M5 has different constraints, antiprotons give bounds >1000 TeV.

Non-thermal production from gravitational acceleration: at the end of inflation acceleration was so high you could create massive particles. They can have density of dM if mass is of order of Hubble parameter. Non-thermal production from particle decays is another non-standard case which is not ruled out.

Then there is the possibility of neutralino production from a decaying scalar field: In string theories, the extra dimensions may be compactified as orbifolds or Calabi-Yau manifolds. The surface shown is a solution of equation such as $z_1^5 + z_2^5=1$, with z complex numbers. The size and shape of the compactified dimensions are parametrized by moduli fields $\phi_1, \phi_2, \phi_3$… The values of the moduli fields fix the coupling constants.

Two new parameters are needed to evade the cosmological constraints to SUSY models: reheating temperature T_rh of the radiation when phi decays. It is >5 MeV from BBN constraints. Other parameter is the number of neutralinos produced per phi decay divided by phi mass, b/m_phi. b depends on the choice of the Kahler potential, superpotential, and gauge kinetic function, so on the high energy theory: the compactification , the fluxes etc. you put in your model. By lowering the reheating temperature you can decrease the density of particles. But the higher b/m, the higher the density you can get. So you can get almost any DM density you want.

Neutralino can be cold dark matter candidates anywhere in MSSM parameter space, provided one allows for these other parameters to vary.

If you work with non-standard cosmology, the constraints are transferred from the low-energy to the high-energy theory. The discovery of neutralino DM which is non thermal may open an experimental window on string theory.

[And it goes without saying that I find this kind of syllogism a wide stretch!].