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Models which address both the Hubble and S8 tensions with the same mechanism generically cause a pre-recombination suppression of the small scale matter power spectrum. Here we focus on two such models. Both models introduce a self-interacting dark radiation fluid scattering with dark matter, which has a step in its abundance around some transition redshift. In one model, the interaction is weak and with all of the dark matter whereas in the other it is strong but with only a fraction of the dark matter. The weakly interacting case is able to address both tensions simultaneously and provide a good fit to a the Planck measurements of the cosmic microwave background (CMB), the Pantheon Type Ia supernovae, and a combination of low and high redshift baryon acoustic oscillation data, whereas the strongly interacting model cannot significantly ease both tensions simultaneously. The addition of high-resolution cosmic microwave background (CMB) measurements (ACT DR4 and SPT-3G) slightly limits both model's ability to address the Hubble tension. The use of the effective field theory of large-scale structures analysis of BOSS DR12 LRG and eBOSS DR16 QSO data additionally limits their ability to address the S8 tension. We explore how these models respond to these data sets in detail in order to draw general conclusions about what is required for a mechanism to address both tensions. We find that in order to fit the CMB data the time dependence of the suppression of the matter power spectrum plays a central role. 

We study the nonlinear effects of minimally coupled, massless, cosmological scalar fields on the cosmic microwave background (CMB). These fields can exhibit post-recombination parametric resonance and subsequent nonlinear evolution leading to novel contributions to the gravitational potential. We compute the resulting contributions to the CMB temperature anisotropies through the time-variation of the gravitational potential (i.e., the integrated Sachs-Wolfe (ISW) effect). We find that fields that constitute 5% of the total energy density and become dynamical at zc≃104 can produce marginally observable ISW signals at multipoles ℓ≃2000. Fields that become dynamical at earlier times and/or have initial displacements at a flatter part of their potential, produce ISW contributions that are significantly larger and at higher multipoles. We calculate these dynamics and the resulting evolution of gravitational perturbations using analytic estimates alongside detailed nonlinear lattice simulations, which couple scalar fields and cosmological fluids to a perturbed metric. Finally, we discuss the possibility of detecting these features with future high-resolution CMB observations. 

ABSTRACT Cold Dark Matter with cosmological constant (ΛCDM) cosmological models with early dark energy (EDE) have been proposed to resolve tensions between the Hubble constant $$H_0=100\, h$$ km ṡ−1Ṁpc−1 measured locally, giving h ≈ 0.73, and H0 deduced from Planck cosmic microwave background (CMB) and other early-Universe measurements plus ΛCDM, giving h ≈ 0.67. EDE models do this by adding a scalar field that temporarily adds dark energy equal to about 10 per cent of the cosmological energy density at the end of the radiation-dominated era at redshift z ∼ 3500. Here, we compare linear and non-linear predictions of a Planck-normalized ΛCDM model including EDE giving h = 0.728 with those of standard Planck-normalized ΛCDM with h = 0.678. We find that non-linear evolution reduces the differences between power spectra of fluctuations at low redshifts. As a result, at z = 0 the halo mass functions on galactic scales are nearly the same, with differences only 1–2 per cent. However, the differences dramatically increase at high redshifts. The EDE model predicts 50 per cent more massive clusters at z = 1 and twice more galaxy-mass haloes at z = 4. Even greater increases in abundances of galaxy-mass haloes at higher redshifts may make it easier to reionize the universe with EDE. Predicted galaxy abundances and clustering will soon be tested by the James Webb Space Telescope (JWST) observations. Positions of baryonic acoustic oscillations (BAOs) and correlation functions differ by about 2 per cent between the models – an effect that is not washed out by non-linearities. Both standard ΛCDM and the EDE model studied here agree well with presently available acoustic-scale observations, but the Dark Energy Spectroscopic Instrument and Euclid measurements will provide stringent new tests.