Constraints on the spacetime dynamics of an early dark energy component

We consider an Early Dark Energy (EDE) cosmological model, and perform an analysis which takes into account both background and perturbation effects via the parameters $c_{eff}^2$ and $c_{vis}^2$, representing effective sound speed and viscosity, respectively. By using the latest available data we derive constraints on the amount of dark energy at early times and the present value of the equation of state. Our focus is on the effect that early dark energy has on the Cosmic Microwave Background (CMB) data, including polarization and lensing, in a generalized parameter space including a varying total neutrino mass, and tensor to scalar ratio, besides the 6 standard parameters of the minimal cosmological model. We find that the inclusion of Baryonic Acoustic Oscillations (BAO) data and CMB lensing significantly improves the constraints on the EDE parameters, while other high redshift data like the Quasar Hubble diagram and the Lyman-$\alpha$ forest BAO have instead a negligible impact. We find ${\Omega }_{eDE}<0.0039$ and $w_0<-0.95$ at the $95\%$ C.L. for EDE accounting for its clustering through the inclusion of perturbation dynamics. This limit becomes weaker ${\Omega }_{eDE}<0.0034$ if perturbations are neglected. The constraints on the EDE parameters are remarkably stable even when $\Sigma m_{\nu }$, and $r$ parameters are varied, with weak degeneracies between ${\Omega }_{eDE}$ and $r$ or $\Sigma m_{\nu }$. In general we expect smaller values for the upper limits on the total amount of EDE with an increasing neutrino mass, while with a decreasing value of the tensor to scalar ratio we expect the 2$\sigma$ upper limits on EDE to increase. We compare this EDE model with a simple $w$CDM with zero dark energy at early times and we find $\sim 1$–$2\%$ different upper limits on total neutrino mass and $\sim 0.1$–$0.2\%$ difference on the equation of state at the present time. Perturbation parameters are not constrained with current data sets, and tensions between the CMB derived $H_0$ and ${\sigma }_8$ values and those measured with local probes are not eased. This work demonstrates the capability of CMB probes to constrain the total amount of EDE well below the percent level.