Movements of the continents as the Earth expands. Left: Atlantic Ocean centered; right: Pacific Ocean centered.
The expanding Earth or growing Earthhypothesis asserts that the position and relative movement of continents is at least partially due to the volume of Earth increasing. Conversely, geophysical global cooling was the hypothesis that various features could be explained by Earth contracting.
There are 3 forms of the expanding earth hypothesis.
Earth's mass has remained constant, and thus the gravitational pull at the surface has decreased over time.
Earth's mass has grown with the volume in such a way that the surface gravity has remained constant.
Earth's gravity at its surface has increased over time, in line with its hypothesized growing mass and volume.
Expansion with constant mass
In 1834, during the second voyage of HMS Beagle, Charles Darwin investigated stepped plains featuring raised beaches in Patagonia which indicated to him that a huge area of South America had been "uplifted to its present height by a succession of elevations which acted over the whole of this space with nearly an equal force." While his mentor Charles Lyell had suggested forces acting near the crust on smaller areas, Darwin hypothesized that uplift at this continental scale required "the gradual expansion of some central mass" [of the earth] "acting by intervals on the outer crust" with the "elevations being concentric with form of globe (or certainly nearly so)". In 1835 he extended this concept to include the Andes as part of a curved enlargement of the earth's crust due to "the action of one connected force". Not long afterwards, he moved on from this idea and proposed that as mountains rose, the ocean floor subsided, explaining the formation of coral reefs.
In 1889 and 1909 Roberto Mantovani published a hypothesis of Earth expansion and continental drift. He assumed that a closed continent covered the entire surface of a smaller Earth. Thermal expansion led to volcanic activity, which broke the land mass into smaller continents. These continents drifted away from each other because of further expansion at the rip-zones, where oceans currently lie. Although Alfred Wegener noticed some similarities to his own hypothesis of continental drift, he did not mention Earth expansion as the cause of drift in Mantovani's hypothesis.
A compromise between Earth-expansion and Earth-contraction is the "theory of thermal cycles" by Irish physicist John Joly. He assumed that heat flow from radioactive decay inside Earth surpasses the cooling of Earth's exterior. Together with British geologist Arthur Holmes, Joly proposed a hypothesis in which Earth loses its heat by cyclic periods of expansion. In their hypothesis, expansion led to cracks and joints in Earth's interior, that could fill with magma. This was followed by a cooling phase, where the magma would freeze and become solid rock again, causing Earth to shrink.
After initially supporting continental drift, the late Australian geologist S. Warren Carey advocated expansion from the 1950s (before the development of plate tectonics provided the generally accepted explanation of the movement of continents) to his death, demonstrating that subduction and other events could not balance the sea-floor spreading at oceanic ridges, and piling yet unresolved paradoxes that continue to plague plate tectonics. Starting in 1956, he proposed some sort of mass increase in the planets and said that a final solution to the problem is only possible in a cosmological perspective in connection with the expansion of the universe.
Bruce Heezen initially interpreted his work on the mid-Atlantic ridge as supporting S. Warren Carey's Expanding Earth Theory, but later withdrew his support. The remaining proponents after the 1970s, like the Australian geologist James Maxlow, are mainly inspired by Carey's ideas.
Comic artist Neal Adams, also a proponent, has proposed a mechanism of action. Positron particles, a form of antimatter, appear continuously inside Earth's globe and combine with other particles while releasing gamma rays; Adams says that it also forms new matter, but modern scientists are very confident that no new matter is formed in any of these reactions.
In the last few decades, no credible mechanism of action has been proposed for this addition of new mass, and there is no credible evidence for new mass having been added in the past. The increased gravity of Earth would have altered the orbits of the celestial objects in the Solar System, including Moon's orbit and Earth's own orbit; proponents have no adequate explanation to address this problem. This is a big obstacle for acceptance of the theory by other geologists.
Decrease of the gravitational constant
Paul Dirac suggested in 1938 that the universal gravitational constant had decreased in the billions of years of its existence. This led German physicist Pascual Jordan to a modification of general relativity and to propose in 1964 that all planets slowly expand. Contrary to most of the other explanations this one was at least within the framework of physics considered as a viable hypothesis. 
Measurements of a possible variation of the gravitational constant showed an upper limit for a relative change of 5•10−12 per year, excluding Jordan's idea.
The theory had never developed a plausible and verifiable mechanism of action. During the 1960s, the theory of plate tectonics — initially based on the assumption that Earth's size remains constant, and relating the subduction zones to burying of lithosphere at a scale comparable to seafloor spreading —  became the accepted explanation in the Earth Sciences.
The scientific community finds that significant evidence contradicts the Expanding Earth theory, and that evidence used in support of it is better explained by plate tectonics:
Measurements with modern high-precision geodetic techniques and modelization of the measurements by the horizontal motions of independent rigid plates at the surface of a globe of free radius, were proposed as evidence that Earth is not currently increasing in size to within a measurement accuracy of 0.2 mm per year. The lead author of the study stated "Our study provides an independent confirmation that the solid Earth is not getting larger at present, within current measurement uncertainties".
The motions of tectonic plates and subduction zones measured by a large range of geological, geodetic and geophysical techniques supports plate tectonics.
Imaging of lithosphere fragments within the mantle supports lithosphere consumption by subduction.
Mass accretion on a scale required to change Earth's radius is contradicted by the current accretion rate of Earth, and by Earth's average internal temperature: any accretion releases a lot of energy, which would warm the planet's interior.
Expanding Earth models based on thermal expansion contradict most modern principles from rheology, and fail to provide an acceptable explanation for the proposed melting and phase transitions.
Paleomagnetic data has been used to calculate that the radius of Earth 400 million years ago was 102 ± 2.8 percent of today's radius. However, the methodology employed has been criticised by the Russian geologist Yu Chudinov.
Examinations of data from the Paleozoic and Earth's moment of inertia suggest that there has been no significant change of Earth's radius in the last 620 million years.
Iapetus Ocean: geological, paleontological, paleomagnetic evidences that North America and Europe were separated before Pangaea.
Present day advocates
In 2005 J. Marvin Herndon postulated what he calls whole-Earth decompression dynamics, which he describes as a unified theory combining elements of plate tectonics and Earth expansion. He suggests that Earth formed from a Jupiter-sized gas giant by catastrophic loss of its gaseous atmosphere with subsequent decompression and expansion of the rocky remnant planet resulting in decompression cracks at continental margins which are filled in by basalts from mid-ocean ridges.
Another present day advocate of an expanding Earth is comics artistNeal Adams, who suggests Earth is growing and not merely expanding, and proposes his ideas within a "Growing Earth-Growing Universe" Theory. Adams has made video animations that graphically illustrate his hypothesis, in which new mass is manufactured by a hypothesized electron/positron pair production process within the core of Earth and all celestial bodies.
^ abBucher, K. (2005), "Blueschists, eclogites, and decompression assemblages of the Zermatt-Saas ophiolite: High-pressure metamorphism of subducted Tethys lithosphere", American Mineralogist90: 821, doi:10.2138/am.2005.1718
^McElhinney, M. W., Taylor, S. R., and Stevenson, D. J. (1978), "Limits to the expansion of Earth, Moon, Mars, and Mercury and to changes in the gravitational constant", Nature271 (5643): 316–321, Bibcode:1978Natur.271..316M, doi:10.1038/271316a0
^Schmidt, P. W. and Clark, D. A. (1980), The response of palaeomagnetic data to Earth expansion, Geophysical Journal of the Royal Astronomical Society, 61: 95–100, 1980, doi:10.1111/j.1365-246X.1980.tb04306.x
^Yu Chudinov, Eduction concept of the earth's expansion theory: main grounds, VSP, Utrecht, 2001, ISBN 90-6764-299-1