Early dark energy beyond slow-roll: Implications for cosmic tensions

In this work, we explore the possibility that early dark energy (EDE) is dynamical in nature and study its effect on cosmological observables. We introduce a parametrization of the equation of state allowing for an equation of state w differing considerably from cosmological constant (cc, w=-1) and vary both the initial wᵢ as well final wf equation of state of the EDE fluid. This idea is motivated by the fact that in many models of EDE, the scalar field may have some kinetic energy when it starts to behave like EDE before the cosmic microwave background (CMB) decoupling. We find that the present data have a mild preference for non-cc early dark energy (wᵢ=-0.78) using Planck+BAO+Pantheon+SH₀ES datasets, leading to Δχₘᵢₙ² improvement of -2.5 at the expense of one more parameter. However, wᵢ is only weakly constrained, with wᵢ<-0.56 at 1σ. We argue that allowing for wᵢ≠-1 can play a role in decreasing the σ₈ parameter. Yet, in practice the decrease is only ~0.4σ and σ₈ is still larger than weak lensing measurements. We conclude that while promising, a dynamical EDE cannot resolve both H₀ and σ₈ tensions simultaneously.