Reconsidering a higher-spin-field solution to the main cosmological constant problem

Following an earlier suggestion by Dolgov, we present a model of two massless vector fields which dynamically cancel a cosmological constant of arbitrary magnitude and sign. Flat Minkowski spacetime appears asymptotically as an attractor of the field equations. Unlike the original model, the new model does not upset the local Newtonian gravitational dynamics.

Figure 1

Numerical solutions of ODEs (3.11) with dimensionless cosmological constant $\lambda =\pm 2$, energy density function (3.10a), and model parameter $\delta ={10}^{-10}$. The following auxiliary functions are obtained from $v(\tau )$, $w(\tau )$, and $h(\tau )$: $q_A\equiv \sqrt{{\dot{v}}^2+3h^2{v}^2}$ and $q_B\equiv \sqrt{{\dot{w}}^2+3h^2{w}^2}$. Top row ($\lambda =+2$): The boundary conditions are $\{v(1),w(1)\}=\{8/(3/2-1/100+r/25),8\}$ and $\{\dot{v}(1),\dot{w}(1)\}=\{(3/4+s/2)/(3/2-1/100+r/25),(3/4+s/2)\}$ for integers $r=\pm 1$ and $s=\pm 1$. The corresponding values for $h(1)$ follow from (3.12). The dashed lines in the plots refer to the lowest value of $\dot{v}(1)$ coming from $s=-1$. The scaling of the $v(\tau )$ plot uses the function ${\sigma }_{+}(\tau )\equiv [1+35(\tau -1{)}^2]/[10+100(\tau -1{)}^2+(\tau -1{)}^{2+\overline{p}}]$ and the scaling of the $h(\tau )$ plot uses $\tau /\overline{n}$ with exact parameters $(\overline{n},\overline{p})$ from (3.15). Bottom row ($\lambda =-2$): The boundary conditions are $\{v(1),w(1)\}=\{6,6/(2+r/5)\}$ and $\{\dot{v}(1),\dot{w}(1)\}=\{(1/2+s),(1/2+s)/(2+r/5)\}$ for $r=\pm 1$ and $s=\pm 1$. The scaling of the $v(\tau )$ plot uses the function ${\sigma }_{-}(\tau )$ $\equiv$ $[2+12(\tau -1{)}^2]/[30+120(\tau -1{)}^2+(\tau -1{)}^{2+\overline{p}}]$ and the scaling of the $h(\tau )$ plot uses $\tau /\overline{n}$ with exact parameters $(\overline{n},\overline{p})$ from (3.15).