The next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys will observe is to use cosmological perturbation theory for linear structures on horizon-sized scales, and Newtonian gravity for non-linear structures on much smaller scales. We propose a two-parameter formalism that generalizes this approach, thereby allowing interactions between large and small scales to be studied in a self-consistent and well-defined way. This uses both post-Newtonian gravity and cosmological perturbation theory, and can be used to model realistic cosmological scenarios including matter, radiation and a cosmological constant. We find that the resulting field equations can be written as a hierarchical set of perturbation equations. At leading-order, these equations allow us to recover a standard set of Friedmann equations, as well as a Newton-Poisson equation for the inhomogeneous part of the Newtonian energy density in an expanding background. For the perturbations in the large-scale cosmology, however, we find that the field equations are sourced by both non-linear and mode-mixing terms, due to the existence of small-scale structures. These extra terms should be expected to give rise to new gravitational effects, through the mixing of gravitational modes on small and large scales -effects that are beyond the scope of standard linear cosmological perturbation theory. We expect our formalism to be useful for accurately modelling gravitational physics in universes that contain non-linear structures, and for investigating the effects of non-linear gravity in the era of ultra-large-scale surveys.

Controlled experiments show that arbuscular mycorrhizal fungi (AMF) can increase competitiveness of exotic plants, potentially increasing invasion success. We surveyed AMF abundance and community composition in Centaurea stoebe and Potentilla recta invasions in the western USA to assess whether patterns were consistent with mycorrhizal-mediated invasions. We asked whether (1) AMF abundance and community composition differ between native and exotic forbs, (2) associations between native plants and AMF shift with invading exotic plants, and (3) AMF abundance and/or community composition differ in areas where exotic plants are highly invasive and in areas where they are not. We collected soil and roots from invaded and native forb communities along invasion gradients and in regions with different invasion densities. We used AMF root colonization as a measure of AMF abundance and characterized AMF communities in roots using 454-sequencing of the LSU-rDNA region. All plants were highly colonized (>60%), but exotic forbs tended to be more colonized than natives (P < 0.001). We identified 30 AMF operational taxonomic units (OTUs) across sites, and community composition was best predicted by abiotic factors (soil texture, pH). Two OTUs in the genera Glomus and Rhizophagus dominated in most communities, and their dominance increased with invasion density (r = 0.57, P = 0.010), while overall OTU richness decreased with invasion density (r = −0.61, P = 0.006). Samples along P. recta invasion gradients revealed small and reciprocal shifts in AMF communities with >45% fungal OTUs shared between neighboring native and P. recta plants. Overall, we observed significant, but modest, differences in AMF colonization and communities between co-occurring exotic and native forbs and among exotic forbs across regions that differ in invasion pressure. While experimental manipulations are required to assess functional consequences, the observed patterns are not consistent with those expected from strong mycorrhizal-mediated invasions.

A variety of gauges are used in cosmological perturbation theory. These are often chosen in order to attribute physical properties to a particular choice of coordinates, or otherwise to simplify the form of the resultant equations. Calculations are then performed with the understanding that they could have been done in any gauge, and that transformations between different gauges can be made at will. We show that this logic can be extended to the domain of large density contrasts, where different types of perturbative expansion are required, but that the way in which gauges can be chosen in the presence of such structures is severely constrained. In particular, most gauges that are commonly considered in the cosmology literature are found to be unviable in the presence of nonlinear structures. This includes spatially flat gauge, synchronous gauge, comoving orthogonal gauge, total matter gauge, N-body gauge, and the uniform density gauge. In contrast, we find that the longitudinal gauge and the Newtonian motion gauge are both viable choices in both standard cosmological perturbation theory, and in the post-Newtonian perturbative expansions that are required in order to model non-linear structures.

We consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used to derive the relativistic equations of Eulerian hydrodynamics in realistic cosmological scenarios that contain radiation and a cosmological constant, as well as matter that has been allowed to clump into galaxies and clusters of galaxies. These equations can be used to evolve energy densities and velocities in the presences of small-scale non-linear structures, and on scales all the way up to the horizon and beyond. The leading-order part of these equations reproduces the expected Newtonian equations, while subsequent orders prescribe relativistic corrections. We demonstrate that these evolution equations are consistent with maintaining the Einstein constraints, and hence that the system as a whole is mathematically well posed. The relativistic corrections that we derive are found to exhibit non-trivial interactions between perturbations on different scales, as well as the mixing of scalar, vector and tensor modes. They deviate from those that occur in both post-Friedmann and standard cosmological perturbation theory approaches, and point towards new relativistic effects that could be measurable by upcoming ultra-large-scale surveys. * Electronic address: c.s.gallagher@qmul.ac.uk † Electronic address: t.clifton@qmul.ac.uk

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