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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. 

In models of warm dark matter, there is an appreciable population of high momentum particles in the early universe, which free stream out of primordial over/under densities, thereby prohibiting the growth of structure on small length scales. The distance that a dark matter particle travels without obstruction, known as the free streaming length, depends on the particle's mass and momentum, but also on the cosmological expansion rate. In this way, measurements of the linear matter power spectrum serve to probe warm dark matter as well as the cosmological expansion history. In this work, we focus on ultra-light warm wave dark matter (WWDM) characterized by a typical comoving momentumq_*and massm. We first derive constraints on the WWDM parameter space (q_*,m) using Lyman-αforest observations due to a combination of the free-streaming effect and the white-noise effect. We next assess how the free streaming of WWDM is affected by three modified expansion histories: early matter domination, early dark energy, and very early dark energy. 

Axion-like particles may form a network of cosmic strings in the Universe today that can rotate the plane of polarization of cosmic microwave background (CMB) photons. Future CMB observations with improved sensitivity might detect this axion-string-induced birefringence effect, thereby revealing an as-yet unseen constituent of the Universe and offering a new probe of particles and forces that are beyond the Standard Model of Elementary Particle Physics. In this work, we explore how spherical convolutional neural networks (SCNNs) may be used to extract information about the axion string network from simulated birefringence maps. We construct a pipeline to simulate the anisotropic birefringence that would arise from an axion string network, and we train SCNNs to estimate three parameters related to the cosmic string length, the cosmic string abundance, and the axion-photon coupling. Our results demonstrate that neural networks are able to extract information from a birefringence map that is inaccessible with two-point statistics alone (i.e., the angular power spectrum). We also assess the impact of noise on the accuracy of our SCNN estimators, demonstrating that noise at the level anticipated for Stage IV (CMB-S4) measurements would significantly bias parameter estimation for SCNNs trained on noiseless simulated data, and necessitate modeling the noise in the training data.