Measuring Neutrinos with the distribution of galaxies in the Universe

In this blog post, I will summarise the paper Baumann et al. (2018) which my collaborators and I just published. The paper reports a measurement of the phase shift in the Baryon Acoustic Oscillation signal due to free streaming particles (neutrinos) in the early universe. So what does that mean?

1. What is the Baryon Acoustic Oscillation (BAO) scale? The BAO scale is a special scale in the distribution of galaxies. If you look at the separation of galaxies in the Universe, you will find that at around 150 Megaparsecs (500 000 000 light years) there is a sudden increase in the number of galaxy pairs. This special scale in the distribution of galaxies was imprinted when the Universe was just 300 000 years old at the so-called decoupling era. If you measure the correlation function of a galaxy distribution, meaning you count the number of galaxy pairs as a function of scale, the BAO signal will show up as a peak at 150 Megaparsecs. If you look at the Fourier transform of the correlation function, the power spectrum, it will show up as an oscillation signal. This signal is what we use in this analysis.

2. What is the decoupling era? In the early Universe photons and baryons were coupled together due to the high pressure. 300 000 years after the Big Bang the temperature and pressure dropped enough so that photons and baryons decoupled. From that point forward most of the photons in the Universe just traveled through the Universe without any interactions with anything. For that reason, we can look at these Cosmic Microwave Background (CMB) photons and basically see a snapshot of the Universe as it was 300 000 years after the Big Bang.

3. What is the effective number of relativistic species? This number describes all particles which had a relativistic velocity at the decoupling era. Currently, this number is assumed to be three, given the three known species of neutrinos ($\nu_{e}$, $\nu_{\mu}$ and $\nu_{\tau}$). We know that these particles must have been produced during the Big Bang and since they are very light, they should have had relativistic velocities at decoupling.

Figure 1 shows the impact of the effective number of free-streaming relativistic species ($N_{\rm eff}$) on the BAO signal and you can see that it leads to a shift in the phase.

Figure 1: This figure shows the impact of the effective number of relativistic species ($N_{\rm eff}$)
on the Baryon Acoustic Oscillation (BAO) scale in the matter power spectrum. It is the shift in the
phase of the BAO which we measured for the first time in this analysis (reference: This plot is from
Baumann et al. 2017).

This phase shift is very small, but we now managed to constrain the BAO scale to 1% using the Baryon Oscillation Spectroscopic Survey (BOSS), which makes us sensitive to such small effects.

So why are we interested in this effect?

Well, it could be that there are additional particles which propagated in the early Universe, but which we have not seen yet in particle accelerators. In this sense, we are using the Big Bang as the ultimate high energy collider and test whether the remains of the Big Bang show any evidence for new particles.

Besides that, the neutrinos generated by the Big Bang are also a very interesting probe of the early Universe. As mentioned before we can use the Cosmic Microwave Background (CMB) to get a snapshot of the Universe when it was only 300 000 years old. But we cannot actually look any closer to the Big Bang. If we could see the distribution of neutrinos produced by the Big Bang, we would actually see the Universe when it was only 1 second old, because neutrinos stopped interacting with other components of the Universe much earlier than photons, 1 second after the Big Bang.

So if we want to investigate the Universe at its very early age, the neutrino background produced by the Big Bang would be one way to do that. Another would be the gravitational wave background produced by the Big Bang. However, right now we do not have experiments sensitive enough to detect the neutrino or gravitational wave background. The detection of the phase shift in the BAO is an indirect detection of the neutrino background.

The shift in the BAO signal is not quite scale independent, hence the first step is we have to create a template for the shift, which we include in the standard BAO fitting pipeline, which I developed for the BOSS analysis back in 2017 (Beutler et al. 2017). The template for the phase shift is shown in Figure 2.

Figure 2: Template describing the shift in the BAO phase as a function of wavenumber. We
include this template in our analysis, but put a free parameter as its amplitude. 

The figure shows that the shift caused by neutrinos $f(k)$ is larger at larger wavenumber $k$.

The amplitude of this template is a free parameter in the fit, which we call $\beta$. We then use the BOSS dataset to constrain this parameter.

Figure 3: Constraints on the amplitude of the phase shift ($\beta$) obtained from the BOSS dataset
in two redshift bins ($z_1$ and $z_3$).

Figure 3 shows the constraints on the amplitude of the template ($\beta$) obtained from the BOSS dataset. In BOSS we have two redshift bins, $z_1$ ($0.2 < z < 0.5$) and $z_3$ ($0.5 < z < 0.75$). We use both redshift bins for our constraint, which yields $\beta = 1.2\pm 1.8$. This constraint can then be converted into a constraint on the effective number of relativistic species. $\beta = 0$ would correspond to $N_{\rm eff} = 0$, while $\beta = 2.45$ would correspond to $N_{\rm eff} = \infty$.

You can see that our constraint just from the BOSS data can't really constrain $N_{\rm eff}$. However, Figure 3 also shows that there is a strong degeneracy between the parameter $\beta$ and the BAO scale parameter $\alpha$. If we fix the cosmological model, we can get strong priors on the $\alpha$ parameters from the Cosmic Microwave Background. The constraints including these priors are also included in Figure 3 (red and orange contours on the left and red solid line on the right) resulting in $\beta = 2.05\pm0.81$. This excludes $\beta=0$ (corresponding to $N_{\rm eff} = 0$) with more than $2\sigma$. Note that the expected value of $\beta$ in a standard cosmological model with $N_{\rm eff} = 3.046$ is $\beta = 1$, while our data seem to prefer larger values. However, $\beta = 1$ is well within our likelihood distribution (red line in Figure 3, right) and hence we do not see any significant deviation from the standard model. 

A similar measurement of the phase shift in the photon distribution (CMB) using the Planck data has been reported in Follin et al. 2015. They measured $N_{\rm eff} = 2.3^{+1.1}_{-0.4}$, which is consistent with our measurement.

In summary, we, for the first time, measured the phase shift in the BAO signal in the galaxy power spectrum, representing an (indirect) detection of the cosmic neutrino background produced by the Big Bang. Our measurement confirms the current standard model with three neutrino species. While the detection significant of our measurement is fairly low, future galaxy surveys like DESI and Euclid will improve these measurements significantly.

Our paper about this measurement was published in Nature (see https://www.nature.com/articles/s41567-019-0435-6)

Let me know if you have any comments or questions below.

best

Florian