Momentum Exchange in the Dark Sector

Abstract

In the era of precision cosmology, the increasing quality and quantity of observational data have begun to reveal hints of physics beyond the standard cosmological model (ΛCDM). Recent measurements of the dark energy equation of state, 𝑤, from the Dark Energy Spectroscopic Instrument suggest that dark energy is not simply a constant background component driving accelerated expansion, but may instead exhibit dynamical behaviour. Furthermore, late-time observations (e.g. from the Dark Energy Survey) consistently measure a lower amplitude of structure growth than what is extrapolated from cosmic microwave background data under standard ΛCDM (the 𝑆8 tension). To address this discrepancy, a compelling possibility is that dark energy and dark matter can interact directly via non-gravitational forces. Specifically, dark scattering models featuring pure momentum exchange between the dark sector components have emerged as a promising solution. By transferring momentum without exchanging energy, these models naturally suppress the growth rate of large-scale structure at late times, potentially alleviating the 𝑆8 tension, without impacting the evolution of the background.
As Stage IV cosmological surveys release data in the coming years, there is strong motivation to test how well dark scattering models fit these measurements and alleviate the 𝑆8 tension. To achieve this, it is important to establish robust theoretical practices for analysing this data, particularly in extreme physical limits where commonly used approximations fail.
In this thesis, we first utilise Fisher forecasting to evaluate the constraining power of upcoming Stage IV spectroscopic surveys on a time-evolving phenomenological dark scattering interaction, 𝜉(𝑧). We demonstrate that by applying a physical positivity prior and parametrising the interaction rate as 𝐴 =
𝜉(1 + 𝑤), next-generation surveys will be able to tightly constrain both the coupling strength and the dark energy equation of state.
Throughout this analysis, we include the full dark energy density and velocity fluid perturbations. We demonstrate that the standard literature approximation of setting these perturbations to zero fails as the equation of state approaches the cosmological constant limit (𝑤 → −1). This failure is driven by a ‘velocity-locking’ effect. On large scales, the dark energy velocity tightly tracks the dark matter, eliminating their relative motion and nullifying the interaction drag. By deriving the scale at which this locking breaks, 𝑘unlock ∝ 1/ 𝑐2(1 + 𝑤), we establish that the onset of power spectrum suppression systematically shifts to smaller scales as 𝑤 → −1. Neglecting perturbations artificially erases this mechanism, leading to severely overestimated interaction constraints.
Finally, we outline a mathematical framework utilising the Time Renormalisation Group method to explicitly incorporate dark energy perturbations into 1-loop power spectrum corrections. This proposed framework establishes the theoretical groundwork necessary to evaluate the 𝑤-dependent velocity-locking effect as it extends into the mildly non-linear regime.
By demonstrating the limitations of standard approximations and detailing a robust non-linear pathway, this thesis provides the theoretical foundation required to accurately evaluate dark sector momentum exchange. This work ensures that future cosmological data can be reliably used to test dark scattering models and determine if an interaction between dark energy and dark matter is responsible for the 𝑆8 tension.

Date of Award	14 Aug 2026
Original language	English
Awarding Institution	University of Portsmouth
Supervisor	Robert Crittenden (Supervisor), Kazuya Koyama (Supervisor) & Marco Bruni (Supervisor)