Cosmological structure formation with negative mass

We construct a family of models with negative gravitational mass in the context of Newtonian gravity. We focus, in particular, on a model that reproduces the features of the so-called Dirac-Milne universe, a matter-antimatter symmetric universe that was recently proposed as an alternative cosmological scenario [A. Benoit-Lévy and G. Chardin, Astron. Astrophys. 537, A78 (2012)]. We perform one-dimensional N-body simulations of these negative-mass models for an expanding universe and study the associated formation of gravitational structures. The similarities and differences with the standard cosmological model are highlighted and discussed.

Figure 1

Antiplasma case. Left frames: Matter density $\rho (x,t)$ for positive mass (red) and negative mass (blue) particles at four different times. Right frames: Corresponding distributions in the scaled phase space. The small rectangle (right column, third panel) indicates the region that is zoomed in on Fig. 2. Time is measured in years elapsed after the big bang.

Figure 2

Antiplasma case. Zooms of the region denoted by a small rectangle in Fig. 1 (right column, third panel). Left frames: matter density; Right frames: phase space.

Figure 3

Bondi case. Left frames: Matter density $\rho (x,t)$ for positive mass (red) and negative mass (blue) particles at three different times. Right frames: Corresponding distributions in the scaled phase space. Time is measured in years elapsed after the big bang.

Figure 4

Dirac-Milne case. Left frames: Matter density $\rho (x,t)$ for the positive-mass particles at five different times. Right frames: Corresponding distributions in the scaled phase space. The fourth set of frames from the top corresponds roughly to the present epoch.

Figure 5

Dirac-Milne case. Left frames: Matter density $\rho (x,t)$ for the positive-mass particles at three different times. Right frames: Corresponding distributions in the scaled phase space. The figures are zooms of the region denoted by a small rectangle in Fig. 4 (bottom right frame).

Figure 6

Einstein–de Sitter case. Left frames: Matter density $\rho (x,t)$ for the positive-mass particles at five different times. Right frames: Corresponding distributions in the scaled phase space. The third set of frames from the top corresponds roughly to the present epoch.

Figure 7

Einstein–de Sitter case. Zooms of the region denoted by a small rectangle in Fig. 6 (bottom right frame).

Figure 8

Einstein–de Sitter case. Further zooms of the region indicated by a rectangle on Fig. 7.

Figure 9

Time evolution of the thermal peculiar velocities, for the EdS and Dirac-Milne universes.

Figure 10

Power spectra of the matter density for the EdS (top panel) and Dirac-Milne (bottom panel) universes. Time is expressed in years after the big bang. The thick lines correspond to the present epoch ($t=14\times {10}^9\mathrm{y}$).

Figure 11

Wave number corresponding to the peak in the power spectrum for the Dirac-Milne and Einstein–de Sitter universes as a function of time, in comoving coordinates.