I will discuss attempts to modify Einstein’s theory of General Relativity to explain current observational puzzles in cosmology. Focusing on the late-time acceleration of the universe, I will discuss guiding principles in modifying General Relativity, the theoretical issues that arise, and the fundamental problem of distinguishing such approaches from dark energy in the context of a modern effective field theory approach.

The tradition of a strict conceptual dichotomy between space(time) and matter--all entities and structures in our universe are to be categorised and conceptualized as either spacetime or matter, never both, never neither--originates with Democritus’ atomism--everything in our universe is ultimately reducible to either atoms (matter) or void (space)–and has reigned supreme ever since Newton. The framework of Newtonian mechanics typically includes a collection of point particles (representing e.g. the planets) that obey an action-reaction principle, carry energy and have mass, as well as a static, immutable space, which was often thought of as the arena or theatre in which the play performed by the planets unfolds. This picturesque way of thinking about Newtonian space is echoed by the famous container metaphor according to which space is conceived of as a container for matter, i.e. the contained (Sklar, 1974).
Although this strict conceptual dichotomy did make a lot of sense in the context of our pre-20th-century worldview, this paper contends that it is no longer tenable, and even a hindrance to further progress. More precisely, each of the main ingredients--General Relativity, inflation, dark matter and dark energy--of our highly-successful and well-established standard model of cosmology that was developed over the course of the 20th century puts pressure on the outdated Newtonian idea that the space(time) and matter concepts can and should be strictly distinguished.
This paper focuses on 1) comparing dark matter to its modified gravity alternatives, as well as 2) comparing various models of dark energy, including a cosmological constant and modified gravity alternatives. Dark energy is typically referred to as the intrinsic energy of spacetime, but ‘carrying energy’ is also a paradigmatic property of matter--some models even associate a mass with dark energy. Then again, the simplest interpretation of dark energy as a cosmological constant suggests that it has to do with the nomological structure rather than the gravitational/spacetime structure or the matter content of the universe. This paper analyses the various senses in which dark matter and dark energy and the respective modified gravity alternatives suggest a breakdown of the traditional spacetime-matter dichotomy. It furthermore investigates the consequences of these breakdowns for the philosophical debate between substantivalism and relationalism about spacetime. To the extent that dark matter and dark energy are not pure spacetime or pure matter but a mixture of both, the container metaphor clearly makes no sense anymore--what would it even mean for these entities to be both the container and contained in itself--and hence the traditional substantivalist and relationalist positions do not straightforwardly apply to theories including these entities (contra Baker, 2005).

My talk will revisit the foundations of Teleparallel Gravity (TPG), an alternative theory of gravity, observationally indistinguishable from General Relativity (GR). In contrast to the latter, gravity in TPG isn’t conceptualised as a manifestation of spacetime curvature. Instead, TPG’s gravitational degrees of freedom appear to be encoded in a suitable--the so-called Weitzenbock--connection’s torsion (a salient feature of non-Riemannian geometries in virtue of which parallelograms formed by parallel-transported vectors do fail to close). In the first part of my talk I shall try to carefully reconstruct TPG’s conceptual structure and interpretation.
For this, it will prove useful to articulate the sense in which TPG--but arguably not GR--can be said to be a gauge theory, akin to (yet not exactly the same as) classical Yang-Mills theories. This will clarify the status of TPG’s spacetime structure in particular. On one common view, TPG’s spacetime structure is that of a Weitzenbock spacetime: the spacetime’s structure is supposed to be that of a manifold, endowed with a Weitzenbock connection. Does this position do justice to TPG? A related, and often simultaneously endorsed, claim purports that whereas GR geometrises gravity, TPG does not: the latter is a force theory; that is, in TPG gravity remains a force. How do these two views go together? Does the failure to geometrise gravity in the manner exemplified by GR indeed imply, as seems to be typically assumed in the literature, that in TPG gravity is force? More fine-grained taxonomies of degrees of geometrisation render this questionable. Or should we--yet another position one finds in the literature--regard merely as a notational variant of GR, an alternative representation of the same theory, with all differences solely pertaining to means of mathematical form, not to physical content?
In the second part of my talk, I shall critically examine conceptual advantages (both inherent ones and advantages over GR) with which TPG tends to be touted, such as its separation of gravity and inertia, or the fact that it admits of a well-defined status of a gravitational energy-stress tensor. While I urge that TPG be taken seriously, my analysis regarding its alleged superiority over GR will be largely deflationary. An exception is the coherence of principles that TPG achieves via its gauge theoretical structure.
The third and final part of my talk will draw some broader philosophical lessons from my results. In particular, I shall draw attention to the relevance of TPG to the standing of conventionalism about (spacetime) geometry--a philosophical stance that, to my mind, deserves a place at the table of the Modified Gravity/Dark Energy debate

Comparisons of gravitational theories and the structures they posit have a long and fruitful history in the philosophy of physics literature. Studying the relation between General Relativity (GR) and Newton-Cartan theory (NCT), for example, has been a valuable means to deepen our understanding of the ontology and structures each theory posits. Similarly, investigation of the relation between GR and its modified gravity counterparts have been of recent interest (see, e.g., Knox (2011) for a comparison of GR and Teleparallel Gravity, a relativistic theory of gravity that allows for non-vanishing torsion, as well as Duerr (2021) for a comparison of GR and f(R) gravity, a theory that is arguable the most natural extension of GR). Here, I investigate 1) the relationship between NCT and a classical theory of gravity with possibly non-vanishing torsion and 2) the relation between such a classical theory of gravity and Teleparallel Gravity.
I first develop a theory of Newtonian Gravity with possibly non-vanishing torsion. This is done by following the procedure Trautman Recovery Theorem---a theorem that, in the torsion-free context, establishes the relation between NCT and Newtonian Gravity. Here, by relaxing the conditions on the possible derivative operators to allow those with torsion, I recover a theory of gravity with possibly non-vanishing torsion from NCT. For the second part of the project, I consider the classical limit of Teleparallel Gravity, i.e., as the speed of light becomes unbounded. Knowing that GR reduces to NCT as the light cones are "opened up," I consider what the result of a similar procedure is on Teleparallel Gravity. The spacetime I recover is a classical spacetime with possibly non-vanishing torsion.
Overall, this project is in the spirit of Read and Teh (2018). However, while they adopt the tetrad formulations of the theories and employ the teleparallel Bargmann–Eisenhart solution to show the reduction relation, I remain closer to typical formulations of GR and NCT. This methodology, I argue, allows for a more straightforward comparison of the theories. This project not only helps us better understand the concepts in gravitational theories, it also presses us to consider how theoretical terms operate within/amongst theories of gravity. In each theory, terms like "curvature'' and "force'' are mathematically and conceptually redefined. However, the limiting relations amongst the theories (established through, e.g., recovery or by taking the classical limit) trouble the idea that the terms operate only within the limited context of each theory.