Joel Primack's research has mainly been in relativistic quantum field theory and in cosmology and particle astrophysics, a field that he has helped to create. In collaboration with UCSC astronomers George Blumenthal and Sandra Faber and others, he developed the ``Cold Dark Matter'' (CDM) theory, which has helped to set the agenda for theoretical and observational cosmology for two decades. More recently, he has been using the largest supercomputers as well as analytic and semi-analytic techniques to investigate the implications of various hypotheses regarding the identity of the dark matter for the formation and distribution of galaxies. He also works on science and technology policy and on the cultural implications of the ongoing revolution in cosmology. He has developed computer games for teaching relativity and quantum mechanics, and cosmological computer visualizations. Primack was director of the 1986 Theoretical Advanced Study Institute at UCSC, and co-director of the 1995 Enrico Fermi school on Dark Matter at Varenna, Italy. He is P.I. of grants from NSF and NASA, and he and others at UCSC raised funds from NSF in 1997 create the UCSC Scientific Visualization Laboratory and in 2001 to create the UCSC UpsAnd Beowulf Computer Laboratory.

In the 1970s, Primack helped to create what is now called the Standard Model of particle physics; for example, in 1972, with Ben Lee and Sam Trieman he did the first calculation of the mass of the charmed quark using renormalizable electroweak theory. Primack's recent research has concentrated on the nature of the dark matter that comprises most of the mass in the universe. He and Heinz Pagels were the first to suggest that the dark matter might be the lightest supersymmetric partner particle. He also investigated the possibility that some of the dark matter might be light neutrinos (hot dark matter). He and his students and other collaborators have analyzed many variants of CDM - especially CDM with less than a critical density of matter and a compensating cosmological constant (CDM) - and confronted the predictions of these models with a wide range of observational data. With his former graduate student Rachel Somerville (UCSC PhD 1997, now at Space Telescope Science Institute), Primack developed new techniques for semianalytic modeling of galaxy formation. He and his former graduate student Ari Maller (PhD 1999, now a postdoc at the University of Massachusetts) are investigating implications of gas clouds at high redshift. Primack, his students, and his former graduate students James Bullock (PhD 1999, Hubble Fellow at Harvard 2002-04, now an assistant professor at the University of California, Irvine) and Risa Wechsler (Hubble Fellow at the University of Chicago) have been investigating high-redshift galaxies using the high-resolution simulations of Anatoly Klypin (New Mexico State University) and Andrey Kravtsov (University of Chicago). Another project with Bullock and Somerville involves working out the absorption of high-energy gamma rays as a probe of galaxy formation.