[bubal7 (OP)]

How to change water density dissolving salt or changing the temperature. This is the typical experiement of the egg and salt water, but also heating the water. Hot water is less dense and so the egg sinks.

[CliffordK]

Interesting ideas.

Also, over time, the eggs also tend to loose moisture (their air pocket grows).  This doesn't necessarily mean the egg has gone bad, but the density of the egg may vary with time.

Salt, of course, not only changes water's density, but it will also affect the boiling point and melting point.

Alcohol also has a slightly lower density than water.  One might see a difference in the way the egg is sitting in the water if placed in a strong alcoholic drink.

[imatfaal]

A fresh hen's egg sink in cold normal water.  As Clifford says it will gain a larger and larger airpocket over time as it draws in air through the porous shell.

Salty water is just dense enough to allow the egg to displace a greater mass of salty water than it's own mass and thus an egg that sinks in pure water might float in salty water. 

If an egg was placed in a mixture of alchohol and water - which will be less dense than water the fresh egg (which sinks in pure water) will definitely sink.  The fresh egg in the boozy mixture will displace a mass of water less than its own mass and will thus sink to the bottom - it will sink quicker than in pure water, although probably not noticeably. 

If the volume of the egg X density of water is less than the mass of the egg then it will sink.
If the volume of the egg X density of water is greater than the mass of the egg then the egg will float.  And the volume of the portion under the surface X density of water will equal the mass of the egg - thus the buoyancy upwards is equalled by the force downwards and the egg finds an equilibrium