Over many years I have helped in the development of a methodology to constrain the cosmological parameters while also testing Einstein’s theory of gravity. In 2010, Yong-Seon Song and I began our work in using the anisotropy clustering of galaxies in redshift-space, to obtain information on the growth of structures using the Sloan Digital Sky Survey (SDSS) Luminous Red galaxy DR7 sample (arxiv:1001.1154). We showed that through the growth of structure, the non-Hubble flow velocities of galaxies are effected and this in turn changes the clustering pattern of the galaxy density field in redshift-space. However, the precision that we can measure this clustering was ultimately limited by the size of the galaxy sample and also by our ability to theoretically model the non-linear clustering signal.

In advancing forward, we next used the SDSS galaxy cluster sample, which should be less contaminated by non-linear, redshift-space distortion, effects (arxiv:1006.4630). However this sample was smaller and more sparse resulting in larger statistical noise that made it difficult to place tight constraints on the growth rate. We returned to this work in 2014, using more accurate theoretical predictions for the density and velocities fields in the mildly non-linear regime (provided by the TNS model, arxiv:1006.0699), applied to the SDSS CMASS DR9 sample of galaxies. We also realized that the anisotropy of the clustering signal also depends on the cosmological model used to convert galaxy (RA, dec, redshift) positions into comoving coordinates; the so called Alcock-Paczynski (AP) effect. We were thus able to constrain both the growth of structure and the AP effect thus simultaneously probing gravity and the large scale ‘averaged’ cosmological background via the distance measures, DA and H-1 (arxiv:1311.5226). This work was followed up using the SDSS DR11 CMASS catalogue, which provided a much larger cosmological volume and we were able to test the LCDM model to higher precision in a model independent approach (arxiv:1407.2257).

In 2015, using a consistent modified gravity perturbation theory, we could place limits on the allowed parameter space of the f(R) model (arxiv:1507.01592). We found, with the 95% confidence upper limit |fR0| <8×10-4, which supports validity of Einstein’s GR. However in the future, with larger data-sets, tighter constraints may be placed on particular models of modified gravity. In fact, this particular methodology of combining the growth rate and the large scale structure information via the AP effect has numerous applications and will continue to be even more useful in the future with data coming from DESI and eventually LSST. As an example, currently Minji Oh (KASI, UST PhD student) is finishing a paper, using this methodology for measuring the sum of Neutrino masses, an exciting result which should appear later this year (Oh, Song 2016 arxiv:1607.01074).

In a related work I am also developing a model independent method to recover DA and H-1, using the AP effect, while making minimal assumptions on systematic uncertainties like the bias, non-linear clustering and non-linear velocities of galaxies inside clusters (arxiv:1603.02389, arxiv:1504.00740 and arxiv:1609.05476).