How does pressure gravitate? Cosmological constant problem confronts observational cosmology

Abstract

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, $ζ_4 = 0.105 \pm 0.049$ (+highL CMB), or $ζ_4 = 0.066 \pm 0.039$ (+BAO). These represent the most precise measurement of this parameter to date, indicating a mild tension with GR (for $Λ$CDM including tensors, with $ζ_4=0$), and also among different data sets.