Strict creationist Russell Humphreys has proposed a cosmological model which claims to solve the problem of distant starlight for young earth supporters. The "starlight problem" as it has come to be known, is that light reaching the earth from stars millions of light years away would seem to imply that the universe is at least millions of years old. Humphreys' model holds that the earth is near the center of the universe, and that due to relativistic principles relating to gravity, light, and time dilation, only a few thousand years of time would transpire on earth while the rest of the expanding universe experienced billions of years of time. Humphreys described his model in a paper at a creationist conference in 1994 (Humphreys 1994a), and in a book entitled Starlight and Time published the same year (Humphreys 1994b).
Although soon hailed by many creationists as a landmark resolution to the starlight problem, the work has been severely criticized by physicists and astronomers. They report that it contained serious flaws in its math and physics, and is demonstrably incorrect (Conner and Page, 1998). In response, Humphreys has made a number of modifications to his model (Conner and Ross, 1999). However, critics assert that the modifications actually deepen the problems and errors. Although Humphreys denies this and insists that his model is still valid (Humphreys, 2002), it is overwhelmingly rejected by the scientific community (Isaac, 2006).
Other proposed solutions to the starlight problem, such as the suggestion that God created light from stars already en-route to earth, have been seriously questioned on logical and theological grounds even by other creationists (as it would imply that events often depicted in such light that never happened, making God a deceiver). Thus, the starlight problem seems to remain a major challenge to the young earth position.
Conner, Samuel, and Don N. Page, "Starlight and Time is the Big Bang," Creation Ex Nihilo Technical Journal, v. 12, n. 2 (August 1998), pp. 174194.
Conner, Samuel R., and Hugh Ross, 1999, The Unraveling of Starlight and Time. Web article at: http://www.reasons.org/resources/apologetics/unravelling.shtml
Humphreys, Russell, 1994, "Progress toward a young-earth relativistic cosmology," in R. E. Walsh (ed.) Poceedings of the Third International Conference on Creationism (Pittsburgh, PA: Creation Science Fellowship), pp. 267-286.
Humphreys, Russell, 1994, Starlight and Time (Colorado Springs, CO: Master Books, 1994).
Humphreys, D. Russell, 2002, Seven years of Starlight and Time.
Isaac, Mark, 2006, Creationists claim CE412. http://www.talkorigins.org/indexcc/CE/CE412.html
The Distant Starlight Problem, by Christopher M. Sharp
The Unraveling of Starlight and Time, by Samuel R. Conner and Hugh Ross
Exchanges between Hugh Ross and Russell Humphreys
The following essay addresses the geocentric tenet of Humphreys' cosmology:
Geocentrism: Was Galileo Wrong? by Robert C. Newman
Humphreys also makes a number of other astronomical claims supposedly demonstrating a young world, which are refuted in: "Creation Physicist" D. Russell Humphreys, and his Questionable "Evidence for a Young World" by David E. Thomas
Wikipedia's overview of the "Starlight problem."