Accelerated expansion of the universe purely driven by scalar field fluctuations

TL;DR

The paper investigates whether cosmic acceleration can arise purely from scalar-field fluctuations without a designed potential. Using a real scalar field with mass $M$ and curvature coupling $\xi$ in FLRW backgrounds, the authors compute the ensemble-averaged energy density $\langle\rho_i\rangle$ and pressure $\langle p_i\rangle$ for both flat and closed geometries, showing that flat spacetime cannot yield acceleration. In a closed universe, the compact topology introduces a Casimir-like correction that can drive acceleration for sufficiently light fields (with $M<1/a_i$) when a key parameter $x=2\pi I G(1-6\xi)$ satisfies $x>3/2$, and there exists a maximal Hubble rate at $x_*=(3+\sqrt{3})/2$ with $H_* \approx 0.52 M_*$. The work suggests a natural, topology-backed route to inflation or dark energy via a gas of light bosons, while highlighting the need for renormalization analysis and time evolution studies of the initial states.

Abstract

We show that scalar field fluctuations alone can drive cosmic acceleration, provided the universe is spatially closed and the Compton wavelength of the field exceeds the radius of curvature. This mechanism may open new perspectives on inflation and dark energy, which could arise from a gas of sufficiently light bosons in a closed universe.

Figures (2)

• Figure 1: Thermal energy density (left), pressure (center) and equation of state parameter $w_{i}=\langle p_{i}\rangle/\langle\rho_{i}\rangle$ (right) in the high-temperature limit for several values of the non-minimal coupling parameter $\xi$. The usual $\langle\rho\rangle\propto T^{4}$ law (with $w=1/3$) is recovered for the conformal coupling $\xi=1/6$. For other values of $\xi$ (even for $\xi=0$, which corresponds to the field being minimally coupled to gravity), this law gets corrections.
• Figure 2: Hubble rate (left) and equation of state parameter (right) corresponding to the different scalar field masses that allow for accelerated expansion.