Field theories and fluids for an interacting dark sector

We consider the relationship between fluid models of an interacting dark sector and the field theoretical models that underlie such descriptions. This question is particularly important in light of suggestions that such interactions may help alleviate a number of current tensions between different cosmological datasets. We construct consistent field theory models for an interacting dark sector that behave exactly like the coupled fluid ones, even at the level of linear perturbations, and can be trusted deep in the nonlinear regime. As a specific example, we focus on the case of a Dirac, Born-Infeld (DBI) field conformally coupled to a quintessence field. We show that the fluid linear regime breaks before the field gradients become large; this means that the field theory is valid inside a large region of the fluid nonlinear regime.

Figure 1

Comparison of the coupled case (for $C=0.1$) with the uncoupled one. The top left plot compares the evolution of the Hubble parameter for a fixed $H_0$. The top right plot shows the total effective equation of state and the bottom one the behavior of the dark matter and dark energy densities.

Figure 2

Loop corrections to the dark energy mass from a dark matter loop. Both graphs give the same contribution.

Figure 3

Approximate regions of linear and nonlinear regime in $k–t$ plane for the coupled DBI model with $A=30$. The dotted line shows the horizon crossing: $k{c}_{\chi }=aH$. The fluid nonlinear regime starts when $3/2k^2\mathrm{\Phi }{a}_0^{-2}{t}_0^{4/3}{t}^{2/3}>1$. On the other hand, the field nonlinear regime starts when the physical wavelength of its perturbation is smaller than the sound horizon and $k\mathrm{\Phi }{t}_0^{5/3}{t}^{-2/3}>1$.