Phenomenology of gravitational aether as a solution to the old cosmological constant problem

One of the deepest and most long-standing mysteries in physics has been the huge discrepancy between the observed vacuum density and our expectations from theories of high energy physics, which has been dubbed the old cosmological constant problem. One proposal to address this puzzle at the semiclassical level is to decouple quantum vacuum from spacetime geometry via a modification of gravity that includes an incompressible fluid, known as gravitational aether. In this paper, we discuss classical predictions of this theory along with its compatibility with cosmological and experimental tests of gravity. We argue that deviations from general relativity (GR) in this theory are sourced by pressure or vorticity. In particular, the theory predicts that the gravitational constant for radiation is 33% larger than that of nonrelativistic matter, which is preferred by (most) cosmic microwave background (CMB), Ly-$\alpha$ forest, and ${}^7\mathrm{Li}$ primordial abundance observations, while being consistent with other cosmological tests at $\sim 2\sigma$ level. It is further shown that all parametrized post-newtonian parameters have the standard GR values aside from the anomalous coupling to pressure ${\zeta }_4$, which has not been directly measured. A more subtle prediction of this model (assuming irrotational aether) is that the (intrinsic) gravitomagnetic effect is 33% larger than GR prediction. This is consistent with current limits from LAGEOS and Gravity Probe B at $\sim 2\sigma$ level.

Figure 1

Allowed regions with $2\sigma$ lines for D/H, $Y_p$ and ${}^7\mathrm{Li}/\mathrm{H}$ are shown. The upper and lower horizontal dashed lines indicate GR and gravitational aether predictions, respectively. The thickness of $Y_p$ means the uncertainty in measurements of neutron lifetime [24, 25]. We can translate the vertical axis into $\Delta N_{\nu }$ by using a relation $G_N/G_R\simeq 1/(1+0.135\Delta N_{\nu })$.

Figure 2

Constraints at the 95% confidence level for $G_N/G_R$ from WMAP 7-year (background, green), $\mathrm{WMAP}+\mathrm{ACT}+\mathrm{SPT}$ (middle, blue) and $\mathrm{WMAP}+\mathrm{ACT}+\mathrm{SPT}+\mathrm{Sne}+\mathrm{BAO}+\mathrm{\text{Hubble}}$ data (front, red). The white lines show the 68% confidence levels. Note that the gravitational aether prediction is $G_N/G_R=0.75$, while in general relativity $G_R=G_N$.

Figure 3

Constraints at the 95% confidence level for $G_N/G_R$ from $\mathrm{WMAP}+\mathrm{ACT}+\mathrm{Sne}+\mathrm{Ly}-\alpha$ (background, green) and $\mathrm{WMAP}+\mathrm{ACT}+\mathrm{SPT}+\mathrm{Sne}+\mathrm{Ly}-\alpha$ (front, red). The white lines show the 68% confidence levels. Note that the gravitational aether prediction is $G_N/G_R=0.75$, while in general relativity $G_R=G_N$.