One effective way of learning about the production and properties of dark matter in the early universe is by extracting information about the primordial dark-matter phase-space distribution from the matter power spectrum. Several years ago a simple empirical formula was introduced which successfully reproduces most of the salient features of the primordial dark-matter phase-space distribution from the matter power spectrum – even in situations in which this distribution is non-thermal, multi-modal, or exhibits other complicated features. Continuing this line of research, we investigate the extent to which machine-learning techniques can improve upon this analytic approach. Interestingly, we find that a one-dimensional convolutional neural network not only succeeds in reconstructing the dark-matter phase-space distribution with greater accuracy, but can also be applied to a broader range of matter power spectra.

As discussed in a number of recent papers, cosmological stasis is a phenomenon wherein the abundances of multiple cosmological energy components with different equations of state remain constant for an extended period despite the expansion of the universe. One of the most intriguing aspects of the stasis phenomenon is that it can give rise to cosmological epochs in which the effective equation-of-state parameter ⟨ w ⟩ for the universe is constant, but differs from the canonical values associated with matter, radiation, vacuum energy, etc. Indeed, during such a stasis epoch, the spatial average of the energy density of the universe evolves in precisely the same manner as it would have evolved if the universe were instead dominated by a perfect fluid with an equation-of-state parameter equal to ⟨ w ⟩. However, as we shall demonstrate, this equivalence is broken at the level of the perturbations of the energy density. To illustrate this point, we consider a stasis epoch involving matter and radiation and demonstrate that within this stasis background the density perturbations associated with a spectator matter component with exceedingly small energy density exhibit a power-law growth that persists across the entire duration of the stasis epoch. This growth can potentially lead to significant enhancements of structure at small scales. Such enhancements are not only interesting in their own right, but may also provide a way of observationally distinguishing between a stasis epoch and an epoch of perfect-fluid domination – even if the universe has the same equation of state in both cases.

We present the current status of the MATHUSLA (MAssive Timing Hodoscope for Ultra-Stable neutraL pArticles) long-lived particle (LLP) detector at the HL-LHC, covering the design, fabrication and installation at CERN Point 5. MATHUSLA40 is a 40 m-scale detector with an air-filled decay volume that is instrumented with scintillator tracking detectors, to be located near CMS. Its large size, close proximity to the CMS interaction point and about 100 m of rock shielding from LHC backgrounds allows it to detect LLP production rates and lifetimes that are one to two orders of magnitude beyond the ultimate reach of the LHC main detectors. This provides unique sensitivity to many LLP signals that are highly theoretically motivated, due to their connection to the hierarchy problem, the nature of dark matter, and baryogenesis. Data taking is projected to commence with the start of HL-LHC operations. We summarize the new 40m design for the detector that was recently presented in the MATHUSLA Conceptual Design Report, alongside new realistic background and signal simulations that demonstrate high efficiency for the main target LLP signals in a background-free HL-LHC search. We argue that MATHUSLA's uniquely robust expansion of the HL-LHC physics reach is a crucial ingredient in CERN's mission to search for new physics and characterize the Higgs boson with precision.

Stasis is a unique cosmological phenomenon in which the abundances of different energy components in the universe (such as matter, radiation, and vacuum energy) each remain fixed even though they scale differently under cosmological expansion. Moreover, extended epochs exhibiting stasis are generally cosmological attractors in many BSM settings and thus arise naturally and without fine-tuning. To date, stasis has been found within a number of very different BSM cosmologies. In some cases, stasis emerges from theories that contain large towers of decaying states (such as theories in extra dimensions or string theory). By contrast, in other cases, no towers of states are needed, and stasis instead emerges due to thermal effects involving particle annihilation rather than decay. In this paper, we study the dynamics of the energy flows in all of these theories during stasis, and find that these theories all share a common energy-flow structure which in some sense lies between particle decay and particle annihilation. This structure has been hidden until now but ultimately lies at the root of the stasis phenomenon, with all of the previous stases appearing as different manifestations of this common underlying structure. This insight not only allows us to understand the emergence of stasis in each of these different scenarios, but also provides an important guide for the potential future discovery of stasis in additional cosmological systems.

We present the Conceptual Design Report (CDR) for the MATHUSLA (MAssive Timing Hodoscope for Ultra-Stable neutraL pArticles) long-lived particle detector at the HL-LHC, covering the design, fabrication and installation at CERN Point 5. MATHUSLA is a 40 m-scale detector with an air-filled decay volume that is instrumented with scintillator tracking detectors, to be located near CMS. Its large size, close proximity to the CMS interaction point and about 100 m of rock shielding from HL-LHC backgrounds allows it to detect LLP production rates and lifetimes that are one to two orders of magnitude beyond the ultimate sensitivity of the HL-LHC main detectors for many highly motivated LLP signals. Data taking is projected to commence with the start of HL-LHC operations. We present a new 40m design for the detector: its individual scintillator bars and wavelength-shifting fibers, their organization into tracking layers, tracking modules, tower modules and the veto detector; define a high-level design for the supporting electronics, DAQ and trigger system, including supplying a hardware trigger signal to CMS to record the LLP production event; outline computing systems, civil engineering and safety considerations; and present preliminary cost estimates and timelines for the project. We also conduct detailed simulation studies of the important cosmic ray and HL-LHC muon backgrounds, implementing full track/vertex reconstruction and background rejection, to ultimately demonstrate high signal efficiency and ≪ 1 background event in realistic LLP searches for the main physics targets at MATHUSLA. This sensitivity is robust with respect to detector design or background simulation details. Appendices provide various supplemental information.

A variety of scenarios for early-universe cosmology give rise to a population of primordial black holes (PBHs) with a broad spectrum of masses. The evaporation of PBHs in such scenarios has the potential to place the universe into an extended period of "stasis" during which the abundances of matter and radiation remain absolutely constant despite cosmological expansion. This surprising phenomenon can give rise to new possibilities for early-universe dynamics and lead to distinctive signatures of the evaporation of such PBHs. In this paper, we discuss how this stasis epoch arises and explore a number of its phenomenological consequences, including implications for inflationary observables, the stochastic gravitational-wave background, baryogenesis, and the production of dark matter and dark radiation.

A variety of processes in the very early universe can give rise to a population of primordial black holes (PBHs) with an extended mass spectrum. For certain mass spectra of this sort, it has been shown that the evaporation of these PBHs into radiation can drive the universe toward an epoch of cosmological stasis which can persist for a significant number of $e$-folds of cosmological expansion. However, in general, the initial mass spectrum which characterizes a population of PBHs at the time of production can subsequently be distorted by processes such as mergers and accretion. In this paper, we examine the effects that these processes have on the spectra that lead to a PBH-induced stasis. Within such stasis models, we find that mergers have only a negligible effect on these spectra within the regime of interest for stasis. We likewise find that the effect of accretion is negligible in many cases of interest. However, we find that the effect of accretion on the PBH mass spectrum is non-negligible in situations in which this spectrum is particularly broad. In such situations, the stasis epoch is abridged or, in extreme cases, does not occur at all. Thus accretion plays a non-trivial role in constraining the emergence of stasis within scenarios which lead to extended PBH mass spectra.

This document 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.

Many theories of physics beyond the Standard Model predict the existence of large or infinite towers of decaying states. In a previous paper [K. R. Dienes et al., Phys. Rev. D 105, 023530 (2022)], we pointed out that this can give rise to a surprising cosmological phenomenon that we dubbed "stasis" during which the relative abundances of matter and radiation remain constant across extended cosmological eras even though the universe is expanding. Indeed, such stasis epochs are universal attractors, with the universe necessarily entering (and later exiting) such epochs for a wide variety of initial conditions. Matter/radiation stasis is therefore an important and potentially unavoidable feature of many BSM cosmologies. In this paper we extend our arguments to universes containing significant amounts of vacuum energy, and demonstrate that such universes also give rise to various forms of stasis between vacuum energy and either matter or radiation. We also demonstrate the existence of several forms of "triple stasis" during which the abundances of matter, radiation, and vacuum energy all simultaneously remain fixed despite cosmological expansion. We further describe several close variants of stasis which we call "quasi-stasis" and "oscillatory stasis," and discuss the circumstances under which each of these can arise. Finally, we develop a general formalism for understanding the emergence of stasis within BSM cosmologies irrespective of the number or type of different energy components involved. Taken together, these results greatly expand the range of theoretical and phenomenological possibilities for the physics of the early universe, introducing new types of cosmological eras which may play an intrinsic and potentially inevitable role within numerous BSM cosmologies.

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

It has recently been shown that extended cosmological epochs can exist during which the abundances associated with different energy components remain constant despite cosmological expansion. Indeed, this "stasis" behavior has been found to arise generically in many beyond-the-Standard-Model theories containing large towers of states, and even serves as a cosmological attractor. However, all previous studies of stasis took place within nonthermal environments, or more specifically within environments in which thermal effects played no essential role in realizing or sustaining the stasis. In this paper, we demonstrate that stasis can emerge and serve as an attractor even within thermal environments, with thermal effects playing a critical role in the stasis dynamics. Moreover, within such environments, we find that no towers of states are needed-a single state experiencing two-body annihilations will suffice. This work thus extends the stasis phenomenon into the thermal domain and demonstrates that thermal effects can also generally give rise to an extended stasis epoch, even when only a single matter species is involved.

It has recently been realized that many theories of physics beyond the Standard Model give rise to cosmological histories exhibiting extended epochs of cosmological stasis. During such epochs, the abundances of different energy components such as matter, radiation, and vacuum energy each remain fixed despite cosmological expansion. In previous analyses of the stasis phenomenon, these different energy components were modeled as fluids with fixed, unchanging equations of state. In this paper, by contrast, we consider more realistic systems involving dynamical scalars which pass through underdamping transitions as the universe expands. Indeed, such systems might be highly relevant for BSM scenarios involving higher-dimensional bulk moduli and inflatons. Remarkably, we find that stasis emerges even in such situations, despite the appearance of time-varying equations of state. Moreover, this stasis includes several new features which might have important phenomenological implications and applications. For example, in the presence of an additional "background" energy component, we find that the scalars evolve into a "tracking" stasis in which the stasis equation of state automatically tracks that of the background. This phenomenon exists even if the background has only a small initial abundance. We also discuss the intriguing possibility that our results might form the basis of a new "Stasis Inflation" scenario in which no ad-hoc inflaton potential is needed and in which there is no graceful-exit problem. Within such a scenario, the number of e-folds of cosmological expansion produced is directly related to the hierarchies between physical BSM mass scales. Moreover, non-zero matter and radiation abundances can be sustained throughout the inflationary epoch.

Many theories of BSM physics predict the existence of large or infinite towers of decaying states. In a previous paper (arXiv:2111.04753) we pointed out that this can give rise to a surprising cosmological phenomenon that we dubbed "stasis" during which the relative abundances of matter and radiation remain constant across extended cosmological eras even though the universe is expanding. Indeed, such stasis epochs are universal attractors, with the universe necessarily entering (and later exiting) such epochs for a wide variety of initial conditions. Matter/radiation stasis is therefore an important and potentially unavoidable feature of many BSM cosmologies. In this paper we extend our arguments to universes containing significant amounts of vacuum energy, and demonstrate that such universes also give rise to various forms of stasis between vacuum energy and either matter or radiation. We also demonstrate the existence of several forms of "triple stasis" during which the abundances of matter, radiation, and vacuum energy all simultaneously remain fixed despite cosmological expansion. We further describe several close variants of stasis which we call "quasi-stasis" and "oscillatory stasis" and discuss the circumstances under which each of these can arise. Finally, we develop a general formalism for understanding the emergence of stasis within BSM cosmologies irrespective of the number or type of different energy components involved. Taken together, these results greatly expand the range of theoretical and phenomenological possibilities for the physics of the early universe, introducing new types of cosmological eras which may play an intrinsic and potentially inevitable role within numerous BSM cosmologies.

Neutral particles are notoriously difficult to observe through electromagnetic interactions. As a result, they naturally elude detection in most collider detectors. In this paper, we point out that neutral particles that interact through a dipole interaction can nevertheless be detected in far-forward detectors designed to search for long-lived particles (LLPs). In contrast to previous analyses that focused on neutral particles with elastic interactions, we consider inelastic interactions. This naturally leads to LLPs, and we demonstrate that FASER (and future experiments at the Forward Physics Facility) will be able to probe substantial regions of the associated parameter space. In particular, we find that FASER is capable of probing the region of parameter space wherein thermal freeze-out gives rise to an $\mathcal{O}$(GeV) dark-matter candidate with the appropriate relic abundance, as well as regions of parameter space that are difficult to probe at fixed-target experiments. FASER and its successor experiments may therefore play a critical role in the discovery of such a dark-matter candidate.

In the path towards a muon collider with center of mass energy of 10 TeV or more, a stage at 3 TeV emerges as an appealing option. Reviewing the physics potential of such muon collider is the main purpose of this document. In order to outline the progression of the physics performances across the stages, a few sensitivity projections for higher energy are also presented. There are many opportunities for probing new physics at a 3 TeV muon collider. Some of them are in common with the extensively documented physics case of the CLIC 3 TeV energy stage, and include measuring the Higgs trilinear coupling and testing the possible composite nature of the Higgs boson and of the top quark at the 20 TeV scale. Other opportunities are unique of a 3 TeV muon collider, and stem from the fact that muons are collided rather than electrons. This is exemplified by studying the potential to explore the microscopic origin of the current g-2 and B-physics anomalies, which are both related with muons.

The phrase"more is different"is often used to refer to the new, unexpected collective phenomena that can arise when the number of states in a given system is large. In this contribution to the Snowmass 2021 Study, we describe 13 unexpected collective phenomena that can arise when the dark sector contains a large number of states, contrary to the usual assumptions. These 13 take-away lessons stretch across all of the domains of relevance for dark-matter physics, including collider signatures, direct-detection signatures, indirect-detection signatures, new perspectives on dark-matter complementarity, and even unexpected astrophysical and cosmological phenomena that transcend those normally associated with single-component dark-matter scenarios. These lessons -- and the phenomena on which they are based -- thereby illustrate the need to maintain a broad perspective when contemplating the possible signatures and theoretical possibilities associated with non-minimal dark sectors.

We summarize progress made in theoretical astrophysics and cosmology over the past decade and areas of interest for the coming decade. This Report is prepared as the TF09 "Astrophysics and Cosmology" topical group summary for the Theory Frontier as part of the Snowmass 2021 process.

We report on recent progress and next steps in the design of the proposed MATHUSLA Long Lived Particle (LLP) detector for the HL-LHC as part of the Snowmass 2021 process. Our understanding of backgrounds has greatly improved, aided by detailed simulation studies, and significant R&D has been performed on designing the scintillator detectors and understanding their performance. The collaboration is on track to complete a Technical Design Report, and there are many opportunities for interested new members to contribute towards the goal of designing and constructing MATHUSLA in time for HL-LHC collisions, which would increase the sensitivity to a large variety of highly motivated LLP signals by orders of magnitude.

One signature of an expanding universe is the time variation of the cosmological abundances of its different components. For example, a radiation-dominated universe inevitably gives way to a matter-dominated universe, and critical moments such as matter-radiation equality are fleeting. In this paper, we point out that this lore is not always correct and that it is possible to obtain a form of "stasis" in which the relative cosmological abundances Omega(i) of the different components remain unchanged over extended cosmological epochs, even as the universe expands. Moreover, we demonstrate that such situations are not fine-tuned but are actually global attractors within certain cosmological frameworks, with the universe naturally evolving toward such long-lasting periods of stasis for a wide variety of initial conditions. The existence of this kind of stasis therefore gives rise to a host of new theoretical possibilities across the entire cosmological time-line, ranging from potential implications for primordial density perturbations, dark-matter production, and structure formation all the way to early reheating, early matter-dominated eras, and even the age of the Universe.