The Structure of Structure Formation Theories

TL;DR

This work formalizes structure-formation models as governed by the stress history of the dark sector within covariant gravity, showing that linear perturbation evolution is fully determined by initial conditions and stress histories. It develops a comprehensive covariant perturbation framework, detailing gauge choices, stress classifications (adiabatic, entropic, sonic, anisotropic) and their impact on curvature and observables, with analytic solutions for multi-component systems and smooth components. A key contribution is the demonstration that ΛCDM-like phenomenology can be exactly mimicked by a single-component general dark matter (GDM) with appropriate equation of state and zero comoving sound speed, underscoring potential degeneracies in interpreting cosmological data and guiding reverse-engineering of the dark sector. The results provide concrete, testable links between dark-sector physics, transfer functions, and CMB/LSS observables, offering a principled path to constrain or reveal exotic stresses via upcoming observations.

Abstract

We study the general structure of models for structure formation, with applications to the reverse engineering of the model from observations. Through a careful accounting of the degrees of freedom in covariant gravitational instability theory, we show that the evolution of structure is completely specified by the stress history of the dark sector. The study of smooth, entropic, sonic, scalar anisotropic, vector anisotropic, and tensor anisotropic stresses reveals the origin, robustness, and uniqueness of specific model phenomenology. We construct useful and illustrative analytic solutions that cover cases with multiple species of differing equations of state relevant to the current generation of models, especially those with effectively smooth components. We present a simple case study of models with phenomenologies similar to that of a LambdaCDM model to highlight reverse-engineering issues. A critical-density universe dominated by a single type of dark matter with the appropriate stress history can mimic a LambdaCDM model exactly.

Figures (18)

• Figure 1: Taxonomy of structure formation. Models can be classified by their initial conditions (adiabatic or isocurvature), perturbation type (passive or active), and clustering properties of the dark matter (clustered or smooth on large-scale structure scales). Passive fluctuations involve stress responses to other perturbations and can support scalar ("S") or scalar and tensor ("ST") components. Active stresses generate fluctuations and generally possess vector components as well ("SVT"). We will examine the extent to which this traditional categorization is useful in predicting model phenomenology.
• Figure 2: Scalar, vector, tensor decomposition. At the top of the tree of possibilities for structure formation models is the assumption that general relativity holds in the cosmological context and universe is homogeneous and isotropic in the mean with linear perturbations initially. Without further assumptions, the linear fluctuations may be expanded in scalar, vector, and tensor modes that do not interact while the fluctuations remain linear.
• Figure 3: Scalar perturbations. It is useful to subdivide the stress-free class of scalar perturbations from the general possibilities. A "stress-free" perturbation has dimensionless stresses (${S}$,${S_\Pi}$) that are much smaller than the comoving curvature perturbation ${\zeta}$. Note that the stress-free perturbation condition does not preclude background or "smooth" stress.
• Figure 4: Vector perturbations. Vector perturbations simply decay from their initial value in the stress-free limit. The integral solution in the presence of vector stress is given in § \ref{['sec:vectorstress']} and applies to defect models.
• Figure 5: Tensor perturbations. Tensor perturbations propagate as free gravity waves in the stress-free limit as is the case of a matter-dominated expansion. The integral solution in the presence of stresses is given in § \ref{['sec:tensorstress']} and may be applied to propagation during radiation domination as well as defect sources.