New perspective on the relation between dark energy perturbations and the late-time integrated Sachs-Wolfe effect

Abstract

The effect of quintessence perturbations on the integrated Sachs-Wolfe (ISW) effect is studied for a mixed dynamical scalar field dark energy (DDE) and pressureless perfect fluid dark matter. A new and general methodology is developed to track the growth of the perturbations, which uses only the equation of state (EoS) parameter ${w}_{\mathrm{DDE}}(z)\ensuremath{\equiv}{p}_{\mathrm{DDE}}/{\ensuremath{\rho}}_{\mathrm{DDE}}$ of the scalar field DDE, and the initial values of the relative entropy perturbation (between the matter and DDE) and the intrinsic entropy perturbation of the scalar field DDE as inputs. We also derive a relation between the rest-frame sound speed ${\stackrel{^}{c}}_{s,\mathrm{DDE}}^{2}$ of an arbitrary scalar field DDE component and its EoS ${w}_{\mathrm{DDE}}(z)$. We show that the ISW signal differs from that expected in a $\ensuremath{\Lambda}\mathrm{CDM}$ cosmology by as much as $+20%$ to $\ensuremath{-}80%$ for parametrizations of ${w}_{\mathrm{DDE}}$ consistent with SNIa data, and about $\ifmmode\pm\else\textpm\fi{}20%$ for parametrizations of ${w}_{\mathrm{DDE}}$ consistent with $\mathrm{SNIa}+\mathrm{CMB}+\mathrm{BAO}$ data, at 95% confidence. Our results indicate that, at least in principle, the ISW effect can be used to phenomenologically distinguish a cosmological constant from DDE.