Non-perturbative effects of vacuum energy on the recent expansion of the universe

TL;DR

The paper presents a non-perturbative mechanism by which vacuum energy from an ultralight quantum field modifies the recent expansion history, producing a transition from matter-dominated to a mildly accelerating de Sitter phase without a cosmological constant. Central to the approach is an $R$-summed effective action derived from a zeta-regularized one-loop action, yielding a renormalizable setup where the late-time dynamics are controlled by a single mass scale $\overline{m}=m/\sqrt{-\bar{\xi}}$ and the present matter density $\Omega_0$, reproducing SN Ia observations with $\overline{m}\sim 10^{-33}$ eV and $\Omega_0<0.4$. The analysis shows the scalar curvature saturates to a nearly constant value after a transition time $t_j$, enabling a consistent open cosmology with age $t_0\gtrsim 13$ Gyr; this framework avoids fine-tuning of a cosmological constant. Overall, the work demonstrates that non-perturbative quantum vacuum effects in curved spacetime can plausibly explain late-time cosmic acceleration and link observable expansion history to fundamental quantum fields.

Abstract

We show that the vacuum energy of a free quantized field of very low mass can significantly alter the recent expansion of the universe. The effective action of the theory is obtained from a non-perturbative sum of scalar curvature terms in the propagator. We numerically investigate the semiclassical Einstein equations derived from it. As a result of non-perturbative quantum effects, the scalar curvature of the matter-dominated universe stops decreasing and approaches a constant value. The universe in our model evolves from an open matter-dominated epoch to a mildly inflating de Sitter expansion. The Hubble constant during the present de Sitter epoch, as well as the time at which the transition occurs from matter-dominated to de Sitter expansion, are determined by the mass of the field and by the present matter density. The model provides a theoretical explanation of the observed recent acceleration of the universe, and gives a good fit to data from high-redshift Type Ia supernovae, with a mass of about 10^{-33} eV, and a current ratio of matter density to critical density, Omega_0 <0.4 . The age of the universe then follows with no further free parameters in the theory, and turns out to be greater than 13 Gyr. The model is spatially open and consistent with the possibility of inflation in the very early universe. Furthermore, our model arises from the standard renormalizable theory of a free quantum field in curved spacetime, and does not require a cosmological constant or the associated fine-tuning.

Figures (4)

• Figure 1: A plot of the LHS (bold-faced curve) and RHS (dashed line) of Eq. (49), as functions of $y$, for $\overline{\xi}=0.033$, $r=10$ and $\Lambda_o=0$. The slope of the dashed line increases as $r$ decreases.
• Figure 2: A plot of the LHS (bold-faced curve) and RHS (dashed line) of Eq. (49), as functions of $y$, with $\overline{\xi} =-0.03$, $r=16$ and $\Lambda_o=0$. As $r$ decreases, the slope of the dashed line increases, and the intersection point is shifted closer to the value $y = -\overline{\xi}^{-1}$. Recall that $r = m^2/m_{Pl}^2$ and $y = R/m^2$.
• Figure 3: A plot of the difference between apparent and absolute magnitudes, as functions of redshift $z$, normalized to an open universe with $\Omega_0 =0.2$ and zero cosmological constant. The points with vertical error bars represent SNe-Ia data obtained from Ref.[5]. The two solid curves represent the values a) $\overline{m} = 3.7 \times 10^{-33}$ eV and $\Omega_0 = 0.4$ (upper solid curve), and b) $\overline{m} = 3.2 \times 10^{-33}$ eV and $\Omega_0 = 0.3$ (lower solid curve). The horizontal dashed line represents an open universe with $\Omega_0 = 0.2$, and the dashed line curving downward represents a matter-dominated flat universe. Smaller values of $\Omega_0$ also would fit the data (see text after Eq. (112)).
• Figure 4: Two plots of the scale factor versus time for a spatially open model universe in which an initially spatially open matter-dominated cosmology evolves to a de Sitter solution. The parameters for the top model are $\overline{m} = 3.7 \times 10^{-33}$ eV and $\Omega_0 =0.4$, and for the bottom model, $\overline{m} = 3.2 \times 10^{-33}$ eV and $\Omega_0 =0.3$. The dashed curves represent a continuation of the open matter-dominated phase.