According to Asian source, Hitachi Displays, Ltd. and Sony Mobile Display Corporation started to ship 4-inch LCD for new iOS device and LCD for iPad 3. These 2 companies will be merged their business with Toshiba Mobile Display Co., Ltd., as "Japan Display" in 2012 spring.
If Apple does indeed go from the current 3.5-inch screens to a larger 4-inch screen size, in order to prevent fragmentation of their development ecosystem, they'd have to keep the same 940x640 resolution. That would reduce the pixel density, which would get the internet up in arms over "Retina display" labels. However, retina display is a function of both density and distance, so a) the density could remain good enough for Apple to stick with the marketing term, or b) the distance a slightly larger device is held at could render the practical result the same (see the iPad for an example of how far a 9.7-inch display can be comfortably held).
Again, the only other alternative is to box old apps, the way iPhone apps are boxed on the iPad, which would maintain compatibility with old apps, but would still fragment new apps -- larger resolutions wouldn't play nicely on older devices.
Along with LTE radios, however, larger screens are one of the few hardware features Apple competitors use as differentiators. We've heard plenty of LTE iPhone rumors, so it's no wonder the 4-inch rumors are hot on their heels.
Macotara also said a new display technology was in the works for iPad 4.