The Bondi universe: How negative mass drives the cosmological expansion

TL;DR

This work addresses the cosmic acceleration problem by proposing a Bondi universe with equal positive and negative Bondi masses, analyzed through linear Vlasov–Poisson theory and long-time 1D exact N-body simulations. It demonstrates a double coincidence: a transition from a weakly to a strongly coupled gravitational regime occurs concurrently with a shift from coasting ($a(t) \propto t$) to accelerating expansion, mediated by Bondi runaway acceleration once stable positive/negative mass pairs form. The simulations reveal three expansion phases—ballistic, random-walk acceleration, and uniform acceleration—whose onset coincides with the coupling parameter crossing unity, linking nonlinear dynamics to cosmic acceleration without dark energy. These results suggest a dark-energy–free mechanism for late-time acceleration and motivate extending the analysis to higher dimensions and relativistic gravity to assess observational implications.

Abstract

We identify a new cosmological coincidence that parallels the well-known matter/dark-energy coincidence: the present-epoch transition of the universe from a weakly coupled (collisionless) to a strongly coupled (collisional) gravitational regime. Within a cosmological model containing equal amounts of positive and negative Bondi masses -- consistent with the weak equivalence principle and momentum conservation -- we show that this coupling transition naturally coincides with the shift from a coasting to an accelerating expansion. A linear response analysis of the corresponding Vlasov-Poisson system reveals that mixed positive-negative mass configurations are always unstable, with growth rates that increase at shorter wavelengths, thereby driving the system toward strong coupling. Using long-time, exact one-dimensional N-body simulations, we demonstrate that the universe undergoes three successive expansion phases: an initial ballistic regime, an intermediate random-walk acceleration driven by sporadic Bondi encounters, and finally a uniformly accelerating phase triggered by the formation of stable positive/negative mass pairs. The onset of this last phase occurs precisely when the coupling parameter crosses unity, linking the two cosmological coincidences through a single dynamical mechanism. These results suggest that cosmic acceleration may arise from the nonlinear dynamics of a gravitationally neutral mixed-mass universe, without invoking dark energy or a cosmological constant.

Figures (10)

• Figure 1: Time evolution, on a log-log scale, of the root-mean-square displacement $\sigma_{X}(t)$ for an initially collisionless system with velocity dispersion equal to $\sigma_{V}(0) = 10^4$ (red dots). The function is $\sigma_{X}(t)$ is fitted with three different power laws of the type $t^{\alpha}$ in the regions delimited by the arrows. The values of $\alpha$, computed via a least-square method, are found to be: $\alpha =1.02$ ($10<t<100$), $\alpha =1.57$ ($10^3<t<10^6$), and $\alpha =1.92$ ($10^7<t<10^8$). The black straight lines represent the corresponding power laws.
• Figure 2: Time evolution, on a log-log scale, of the root-mean-square displacement $\sigma_{X}(t)$ for several simulations with initial velocity dispersions in the range $1 \le \sigma_{V}(0) \le 10^5$. Although the initial evolutions are different, they all converge to the power law $\sigma_{X}(t) \thicksim t^2$, for times $t \gtrsim 10^7$.
• Figure 3: Time evolution, on a log-log scale, of the root-mean-square velocity $\sigma_{V}(t)$ for several simulations with initial velocity dispersions in the range $1 \le \sigma_{V}(0) \le 10^5$. Although the initial evolutions are different, they all converge to the power law $\sigma_{V}(t) \thicksim t$, for times $t \gtrsim 10^7$. This power law is represented by the continuous black line.
• Figure 4: Particle density (left panels) and phase space distributions (right panels) for an initially weakly correlated system with velocity dispersion $\sigma_{V}(0) = 10^4$. Positive mass particles are depicted in red, while negative mass particles are depicted in blue. The straight lines in the phase-space plots represent the slope $H= \alpha/ t$ of the filament (instantaneous Hubble parameter), where the product $H t$ is expected to approach the exponent $\alpha$ of the expansion law. Note that both the position and velocity scales change over time, in order to capture the expansion of the system.
• Figure 5: Particle density (left panels) and phase space distributions (right panels) for an initially strongly correlated system with velocity dispersion $\sigma_{V}(0) = 10$. Positive mass particles are depicted in red, while negative mass particles are depicted in blue. The straight line in the phase-space plot at $t=10^8$ represents the slope $H= \alpha/ t$ of the filament (instantaneous Hubble parameter), where the product $H t$ is expected to approach the exponent $\alpha$ of the expansion law. Note that both the position and velocity scales change over time, in order to capture the expansion of the system.