Dr. Cuk and Dr. Stewart of the Department of Earth and Planetary Sciences at Harvard University published a paper suggesting a unique tidal evolution of the Moon made possible through the phenomenon of "evection resonance". This is a process whereby the Sun is able to rob the Earth-Moon system of some of its angular momentum during the initial tens of thousands of years after the Moon's formation. This allows for a more rapidly spinning initial Earth than would have otherwise been possible. Dr. Cuk and Dr. Stewart's paper can be found at https://www.sciencemag.org/content/338/6110/1047.
An interesting consequence of this theory is that the orbital evolution of the Moon can now be led through a period of large eccentricity (up to 0.6). This, in combination with the fact that soon after formation the Moon was significantly closer to the Earth than it is today, would have led to a very different Moon than we are used to. With data kindly provided by the authors of the paper we were able to model what the Moon would have looked like in the night sky soon after formation (if anything were around back then to see it!)
Below is a simulation of what the Moon would have looked like 1000 years after formation. The semi-major axis 'a' is stated in units of the semi-major axis of the Moon's current orbit. Notably, due to proximity to the Earth at this stage, the Moon is zooming through its orbit more than 40x faster than it is today.
Next is a simulation 24,000 years after formation. Here things get much more interesting as the eccentricity of the Moon's orbit is now 0.6. This leads to variations in angular size from about 2 degrees at apogee to almost 10 degrees at perigee. The Moon would thus oscillate between appearing 4x larger to almost 20x larger in the sky than it does today! In addition, the large eccentricity of the Moon leads to interesting effects such as the period from full moon to new moon being significantly shorter than that from new to full.
Below is an additional simulation of the Moon, this time 68,000 years after formation, just before it leaves the evection resonance.
Finally, we show the Moon 24,000 years after formation alongside the Moon's orbit today with both simulations normalized such that 1 second of real time corresponds to 10 hours simulation time. The remarkable differences in both angular size and period of orbit are readily apparent.
A summary of various characteristics of the Moon's orbit at the simulated points are given below.
The positions of the stars in the night sky are taken from the Yale Bright Star Catalogue version 5 http://tdc-www.harvard.edu/catalogs/bsc5.html and the constellations were mapped using a data file created by Dr. Mic at Penn State http://physanim.blogspot.ca/2010/12/fun-with-bright-star-catalog.html