Structure formation and backreaction in growing neutrino quintessence

A dependence of the neutrino masses on the dark energy scalar field could provide a solution to the why now problem of dark energy. The dynamics of the resulting cosmological model—growing neutrino quintessence—include an attractive force between neutrinos substantially stronger than gravity. We present a comprehensive approach towards an understanding of the full cosmological evolution, including the formation of large-scale neutrino structures. Important effects we account for are local variations in the dark energy and the backreaction on the background evolution, as well as relativistic neutrino velocities. For this aim, we develop a relativistic $N$-body treatment of the neutrinos combined with an explicit computation of the local quintessence field. At its current stage, the simulation method is successful until $z\approx 1$ and reveals a rich phenomenology. We obtain a detailed picture of the formation of large-scale neutrino structures and their influence on the evolution of matter, dark energy, and the late-time expansion of the Universe.

Figure 1

Inconsistency between the assumed background evolution (dashed) and the actual average (solid) taking into account the locally varying cosmon field. For illustration, the figure includes the actual average ${\overline{\rho }}_{\nu }$ of the energy density (dot-dashed).

Figure 2

The neutrino spectrum ${\Delta }_{\nu }$ at $z=1$ for two different resolutions. The vertical dashed line marks the scale $1/\Delta x\approx 0.25h/\mathrm{Mpc}$, roughly corresponding to the cell size of the low-resolution grid.

Figure 3

The evolution of nonlinear neutrino structures in the simulation box, $L=600h^{-1}\mathrm{Mpc}$. The lower four figures show regions in the simulation box where the number density of neutrinos is a factor of $\ge 5$ higher than in the background. We see the process of continuing concentration. In the beginning, the structures were still linear. We show, in the upper figures, a two-dimensional section of the number density (the range goes from 0 to 5 times the background value).

Figure 4

The uppermost figure shows a slice through the number density field of neutrinos (in multiples of the average ${\overline{n}}_{\nu }$). The two lower figures show the number density profile $n_{\nu }(r)$ and the mass profile $m_{\nu }(r)$ of the structure. The dashed lines show the results of a simulation with a lower resolution. The shaded regions indicate the size of a grid cell for each resolution.

Figure 5

The figure shows the number density profile $n_{\nu }$ of an isolated neutrino structure at $a=0.50$ (solid), 0.47 (dashed), and 0.45 (dot-dashed) as a function of the physical distance from its center.

Figure 6

The increase of the equation of state $w_{\nu }$ due to relativistic velocities in the structure formation process. The dashed horizontal line marks the limit $w=1/3$ for highly relativistic particles.

Figure 7

The difference $\Phi -\Psi$ of the two gravitational potentials, scaled by a factor of ${10}^5$, at $z=1$.

Figure 8

Evolution of the deceleration parameter $q$ in our simulation (solid), including the nonlinear backreaction effects, compared to the result obtained by the background equations (dashed).

Figure 9

Evolution of the equation of state of quintessence $w_{\phi }$, the background cosmon field $\overline{\phi }$, and its time derivative ${\overline{\phi }}^{\prime }$ (including backreaction effects: solid; compared to the background equations: dashed).

Figure 10

The evolution of the relative matter spectrum ${\Delta }_m/{\Delta }_m^{\Lambda \mathrm{CDM}}$.

Figure 11

The enhancement of matter bulk velocities $U_l/U_l^{\Lambda \mathrm{CDM}}$ in subboxes of volume $l^3$ for $l=37.5h^{-1}\mathrm{Mpc}$ (solid) and $l=75h^{-1}\mathrm{Mpc}$ (dashed).

Figure 12

The evolution of the gravitational potential $\Psi (z,k)/{\Psi }^{\Lambda \mathrm{CDM}}(z,k)$ for modes $k=0.05h/\mathrm{Mpc}$ (solid) and $k=0.02h/\mathrm{Mpc}$ (dashed).