How does pressure gravitate? Cosmological constant problem confronts
  observational cosmology
  An important and long-standing puzzle in the history of modern physics is the
gross inconsistency between theoretical expectations and cosmological
observations of the vacuum energy density, by at least 60 orders of magnitude,
otherwise known as the \textit{cosmological constant problem}. A characteristic
feature of vacuum energy is that it has a pressure with the same amplitude, but
opposite sign to its energy density, while all the precision tests of General
Relativity are either in vacuum, or for media with negligible pressure.
Therefore, one may wonder whether an anomalous coupling to pressure might be
responsible for decoupling vacuum from gravity. We test this possibility in the
context of the \textit{Gravitational Aether} proposal, using current
cosmological observations, which probe the gravity of relativistic pressure in
the radiation era. Interestingly, we find that the best fit for anomalous
pressure coupling is about half-way between General Relativity (GR), and
Gravitational Aether (GA), if we include \textit{Planck} together with
\textit{WMAP} and BICEP2 polarization cosmic microwave background (CMB)
observations. Taken at face value, this data combination excludes both GR and
GA at around the 3-sigma level. However, including higher resolution CMB
observations ("highL") or baryonic acoustic oscillations (BAO) pushes the best
fit closer to GR, excluding the Gravitational Aether solution to the
cosmological constant problem at the 4--5-sigma level. This constraint
effectively places a limit on the anomalous coupling to pressure in the
parametrized post-Newtonian (PPN) expansion, $\zeta_4 = 0.105 \pm 0.049$
(+highL CMB), or $\zeta_4 = 0.066 \pm 0.039$ (+BAO). These represent the most
precise measurement of this parameter to date, indicating a mild tension with
GR (for $\Lambda$CDM including tensors, with $\zeta_4=0$), and also among
different data sets.
