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This paper summarizes the discussions which took place during the PITT-PACC Workshop entitled “Non-Standard Cosmological Epochs and Expansion Histories,” held in Pittsburgh, Pennsylvania, Sept. 5–7, 2024. Much like the non-standard cosmological epochs that were the subject of these discussions, the format of this workshop was also non-standard. Rather than consisting of a series of talks from participants, with each person presenting their own work, this workshop was instead organized around free-form discussion blocks, with each centered on a different overall theme and guided by a different set of Discussion Leaders. This document is not intended to serve as a comprehensive review of these topics, but rather as an informal record of the discussions that took place during the workshop, in the hope that the content and free-flowing spirit of these discussions may inspire new ideas and research directions. 

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 Pulsar timing array observations have found evidence for an isotropic gravitational-wave background with the Hellings–Downs angular correlations between pulsar pairs. This interpretation hinges on the measured shape of the angular correlations, which is predominantly quadrupolar under general relativity. Here we explore a more flexible parameterization: we expand the angular correlations into a sum of Legendre polynomials and use a Bayesian analysis to constrain their coefficients with the 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). When including Legendre polynomials with multipolesℓ≥ 2, we only find a significant signal in the quadrupole with an amplitude consistent with general relativity and nonzero at the ∼95% confidence level and a Bayes factor of 200. When we include multipolesℓ≤ 1, the Bayes factor evidence for quadrupole correlations decreases by more than an order of magnitude due to evidence for a monopolar signal at approximately 4 nHz, which has also been noted in previous analyses of the NANOGrav 15 yr data. Further work needs to be done in order to better characterize the properties of this monopolar signal and its effect on the evidence for quadrupolar angular correlations.