It depends on what you mean by theoretical cosmology. I'll give a list of what I see as the breakdown of the subject, along with a number between 1 and 5 from 1 = extremely competitive to 5 = relatively open to new applicants.
String Theory, (theoretically motivated) models of inflation, other Unified Theory disciplines (quantum gravity, etc), and The Big Questions (time's arrow, causality, 'the beginning', initial conditions, and the flatness problem). The 'Stephen Hawking' definition of cosmology, perhaps. Normally this is essentially high energy physics (or in the case of The Big Questions, quantitative philosophy), where you pay attention to what cosmological data tell you when you invent your models. Found mostly in mathematical physics departments, or perhaps on the HEP floor, but is speculative in the sense that any real cosmological data on these questions are some years out. This is a 1-2, since there's no money, and the money that there is almost exclusively goes to postdocs who have a better handle on the advanced mathematics required.
Traditional 'theoretical cosmology'. Cosmological modeling, building theoretical (computational) models for traditional cosmological observables (CMB, matter power spectrum, supernovae, clustering, etc). Investigating extensions to the standard cosmological (LCDM) model of the universe, and how these extensions would affect observables, as well as phenomenological models of inflation. May also include some data post-processing, beyond the basic statistical methods an observer will employ. Basically, the questions you'd find in a modern cosmology textbook. This is a 2-4, since often you can get paid off of observational grants.
Post analysis of observational data. It's similar to the above, but more nitty-gritty. Use standard (and extended) cosmological models to tease out more (model-dependent) information from datasets by back-tracing cosmological evolution of the signal photons. Gravitational lensing, but also things like matter field reconstruction, the Sunyaev-Zel'dovich effect for cluster counting, etc. I'd also include in this category inventing/working out the details of new cosmological observables, like cosmic shear. I'd say this is a 4-5, since you can almost always get on observational grants for this one, and it has obvious short-term applications.