## Denny Marfatia’s talk on Neutrinos and Dark EnergyMay 22, 2008

Posted by dorigo in astronomy, cosmology, news, physics, science.
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Denny spoke yesterday afternoon at PPC 2008. Below I summarize as well as I can those parts of his talk that were below a certain crypticity threshold (above which I cannot even take meaningful notes, it appears).

He started with a well-prepared joke: “Since at this conference the tendency is to ask questions early, Any questions ?“. This caused the hilarity of the audience, but indeed, as I noted in another post, the setting is relaxed and informal, and the audience interrupts loosely the speaker. Nobody seemed to complain so far…

Denny started by stating some observational facts: the dark energy (DE) density is $2.4 \times 10^{-3} eV^4$, and the neutrino mass difference $\Delta M^2$ is of the same order of magnitude. This coincidence of scale mighti imply that neutrinos coupled to a light scalar might explain why $\Omega_{DE}$ has a similar value to $\Omega_M$, i.e. why we observe a rather similar amount of dark energy and matter in the universe.

But he noted that there is more than just one coincidence problem. In fact DE density and other densities have ratios which are small values. Within a factor of 10 the components are equal.
Why not consider these coincidences to have some fundamental origin ? Perhaps neutrino and DE densities are related. It is easy to play with this hypothesis with neutrinos because we understand them the least!

We can have the neutrino mass made a variable quantity. Imagine a fluid, the scalar, a quintessence scalar, and the potential is $M_\nu n_\nu + V(m_\nu)$. There is a ansatz to be made: the effective potential is stationary with respect to the neutrino mass.

So one makes a decreasing neutrino mass at the minimum of the potential, with a varying potential. Some consequences of this model are given by the expression $w = -1 + m_\nu n_\nu/V_{eff}$. W can thus deviate from -1. It is like quintessence without a light scalar.
Neutrino masses can be made to vary with their number density: if w is close to -1, the effective potential has to scale with the neutrino contribution. Neutrinos are then most massive in empty space, and they are lighter when they cluster.
This could create an intriguing conflict between cosmological and terrestrial probes of neutrino mass. The neutrino masses vary with matter density if the scalar induces couplings to matter. There should be new matter effects in neutrino oscillations. One could also see temporal variations in the fine structure constant.

If neutrinos are light, DE becomes a cosmological constant, w = -1, and we cannot distinguish it from other models. Also, light neutrinos do not cluster, so the local neutrino mass will be the same as the background value; and high redshift data and tritium beta decay will be consistent because neither will show evidence for neutrino mass.

So one can look at the evidence for variations in time of the fine structure constant. The status of measurements of transition frequencies in atomic clocks give the limit $\delta \alpha/\alpha < 5 \times 10^{-15}$.

The abundance ratio of Sm 149 to Sm147 at the natural reactor in Oklo shows no variation in the last 1.7 billion years, with a limit $\delta \alpha/\alpha < 10^{-7}$.
Resonant energy for neutron capture.

Meteoritic data (at a redshift z<0.5) constrain the beta decay rate of Rhenium 187 back to the time of solar system formation (4.6 Gy), $\delta \alpha/ \alpha = 8 \pm 8 \times 10^{-7}$.

Going back to $0.5, transition lines in quasars QSO spectra indicate a value $\delta \alpha/ \alpha = -0.57 \pm 0.10 \times 10^{-5}$. Found to be varying at 5-sigma level! The lines have an actual splitting which is different. Result not confirmed, depends on the magnesium isotopic ratio assumed. People say you are just measuring chemical evolution of magnesium in these objects: the three isotope ratio might be different from what is found in our sun, and this would mess up the measurement.

Then, there is a measurement of CMB (at z=1100) which determines $\delta \alpha/\alpha<0.02$ from the temperature of decoupling, depending on binding energy.
Also primordial abundances from Big-bang nucleosynthesis (at z=10 billion) allow one to find $\delta \alpha/\alpha<0.02$. Bounds on a variation of the fine structure constant at high redshift are thus very loose.

One can therefore hypothesize a phase transition in $\alpha$: it was done by Anchordoqui, Barger, Goldberg, Marfatia recently. The bottomline is to construct the model such that when the neutrino density crosses the critical value as the universe expands, $\alpha$ will change.

The first assumption is the following: M has a unique stationary point. Additional stationary points are possible, but for nonrelativistic neutrinos with subcritical neutrino density, only one minimum, fixed, and no evolution.

For non-relativistic neutrinos, with supercritical density, there is a window of instability.

You expect neutrinos at the critical density at some redshift. The instability can be avoided if the growth-slowing effects provided by cold dark matter dominate over the acceleron-neutrino coupling. Requiring no variation of $\alpha$ up to z=0.5, and then a step in $\delta \alpha$, and enforcing that the signal in quasar spectra is reproduced, one gets results which are consistent with CMB and BBN.