Tests and Gravity Beyond GR

Research on gravity tests links a specified departure from GR to a well-posed prediction and a calibrated observation. There are several ways to enter that chain: derive a controlled solution, measure an approximation’s failure, reproduce a bound, or determine what a test can miss. Choose a project by the link you can make reliable.

The six records retain their 2026-08-20 evidence cutoff. Each contains a practical entry project before the detailed assessment. The suggested extensions have unchecked novelty; a current literature search and discussion with a suitable supervisor should precede a thesis commitment.

Compare the six directions

Direction and finite question	First calculation	What the next stage requires
Propagation: which speed, dispersion, or damping law is constrained?	Reconstruct the GW170817 speed interval and delay sensitivity	A source model, or a different waveform/population likelihood for dispersion and damping
Scalarization: can an allowed compact object develop scalar charge?	One stellar equilibrium and scalar-charge sequence	Stability, equation-of-state uncertainty, and a theory-specific observable
Black-hole hair: which non-GR solutions are dynamically and observationally viable?	A small-coupling radial solution with residual checks	Formation, hyperbolicity, boundary matching, and controlled waveform predictions
Strong-field null tests: what departures can a statistic reveal or absorb?	A released residual plot and a controlled injection	Calibrated sensitivity across noise and waveform systematics
Screening: does one model connect local and cosmological regimes?	A resolved spherical screening transition	Environmental inputs and consistent parameter translations
Dark-matter alternatives: can one relativistic model fit multiple scales?	One galaxy fit with nuisance sensitivity	Lensing, clusters, cosmology, and a fixed action and matter content

Choose an entry route

Analytic theory: the propagation-delay exercise is the lightest entry. Hair and scalarization demand variational calculus, boundary-value problems, and perturbation or bifurcation theory. If your first goal is to understand a mechanism, choose a spherical or small-coupling baseline whose limiting behavior can be independently derived. Do not begin by promising a generic merger calculation.

Numerical modeling: screening and stellar scalarization provide finite radial problems before full simulations. You should already know how a small discrete residual can coexist with a wrong boundary condition or an unresolved layer. Seek a supervisor who can assess the physical branch and effective-theory regime. Three-dimensional evolution adds formulation and hyperbolicity risks beyond ordinary resolution checks.

Inference: null tests and galaxy fits are natural starting points if you understand priors, posterior prediction, and selection. A replot of public samples is useful training; a new bound requires a likelihood that responds correctly to known signals. GR waveform systematics and astrophysical nuisance parameters are part of the tested hypothesis, not corrections to postpone until after a result.

Laptop-sized entry work exists in every row. It does not imply that the whole programme is cheap: cosmological simulation grids, binary mergers, and large injection campaigns require maintained software, storage, computing allocations, and collaborators who know the relevant data.

How the questions connect

1. For compact objects, use the scalarization background, then the Damour–Esposito-Farèse → Shao sequence in the scalarization record. Extract a charge definition and its timing observable. Follow with the hair project’s Sotiriou–Zhou → stability-paper sequence, keeping matter coupling and curvature coupling separate.
2. For gravitational-wave tests, start with the propagation project’s GW170817 calculation, explicitly writing the emission-delay assumption. Move to the null-test project’s official residual products and eccentricity injections. Identify what is modified during propagation, what changes generation, and what the best-fit source parameters can absorb.
3. For local-to-cosmological models, follow the screening project’s field equation and environmental boundary conditions before reading its Euclid code comparison. Then use the galaxy-fit project in the dark-matter-alternative record. Extract the additional matter, lensing law, and cosmological evolution a full replacement claim would need.

A constraint travels only with its theory and domain. A massless neutron-star dipole bound cannot be pasted onto an arbitrary curvature-coupled black hole. A galaxy interpolation law does not specify a relativistic cosmology. A screening solution does not by itself settle tensor propagation.

Turn interest into a research proposal

Prepare a short proposal naming one action or observable, one primary baseline, the exact public inputs, the finite output, and one condition that would make you stop or pivot. The leaf projects supply examples. Bring a baseline result to a supervisor before expanding to a large parameter scan.

A possible contribution could be an independently checked approximation boundary, a calibrated blind direction in a test, or a theory translation that removes a false disagreement. First establish that the result is not already known. If numerical health, environmental classification, or data access prevents the intended inference, narrow the question to that obstacle. Passing one necessary test is useful progress; it does not establish that the entire theory is viable.