This question has two parts:
"1: What properties of the marshmallow keep it together?" and then
"2: Given an understanding of what forces are pushing the marshmallow to both expand and contract, how do I make the 'expanding' forces stronger?" Remember, everything is in equilibrium (if it isn't moving) so if the marshmallow isn't expanding or contracting (ie. it's just sitting there looking like a marshmallow) then there must be equal and opposite forces pushing from the 'inside' out and from the outside in.

1. You can think of almost all solids as being held together by a huge number of atoms or molecules held together by springs. Marshmallows are made up of whipped sugar which forms a springy, spongy material with little air pockets (think a bunch of sheets of bubble wrap stacked up on top of each other...but now the bubble wrap is stretchy instead of hard plastic). As a point of fact, even rocks can be thought of this way - the 'springs' are just really, really stiff.

So account for our forces: we have air around the marshmallow pushing on it (remember there's a lot of pressure from air pressing on us all the time) and a springy marshmallow material resisting that air pressure with the help of the air pockets that also push 'out'.

2. So the 'spring' of the white marshmallow sugar material really just wants to stay put - it will resist both expansion and contraction (springs really like to just sit). What we need is for that air to start pushing on the inside of the marshmallow more strongly than the air on the outside is pushing in. As you probably know, air expands when it is heated.

SO! You can either somehow heat the inside of the marshmallow without heating the air around it (microwaves are good at this since microwaves really only heat water and there is water in the white stuff of the marshmallow. When that heats up, it heats up the air inside AND softens the 'springs' of the marshmallow making it easier to expand) -OR- you can reduce the pressure of the air around the marshmallow so that the air on the inside is pushing harder than the air on the outside. Be careful though.. if you cool the marshmallow during this process you'll make it stiff and it won't expand.

If you bite in to a marsh mellow you will notice that kind of looks like a tiny sponge, with stretchy fibery bits and air pockets in between. These are good qualities if you want to make it expand, since the fibers are willing to stretch and the air pockets can help push apart the fibers as the marshmallow grows.

So, the question becomes "what can we do to expand the air pockets in the marshmallow?".

To answer that question we can use a series of equations (Boyle's Law, Charles' Law and the Ideal Gas Law) to see how different factors like pressure and temperature can change volume of air trapped in the marshmallow. Or, we can think about the experiments that were done to come up with all those laws and come up with the same answer without the math. Though math is awesome.

Here are my questions to you:
1) Is cold air more or less dense than warm air? (Charles' Law)
(If you had two balloons ofthe same size but one was filled with really hot air and one with really cold air, which would be heavier?)
(if you had two balloons that were filled with the same amount of air, but the air was hot in one and cold in the other which balloon would be bigger?)
2) Is air under pressure more or less dense than air under low pressure? (Boyle's Law)

If a balloon was attached to an anchor and pulled to the bottom of the sea, would it be bigger or smaller than when it was on the boat?

When a gas is cold the gas molecules do not have as much energy to zip around very quickly, literally, bounce of the walls of the container they are in or each other. This means that they stay closer together and don't take up as much space. You can also push gas molecules together if you reduce the size of their container.

Heat it: put it in the microwave. (This is the classic but you are obligated to clean up any mess you make. Tip: wait till the goo cools down for a bit before cleaning. Sugar burns are not a pleasant way to end an experiment.)

Decrease the surrounding pressure: put it in a vacuum chamber (excellent results but expensive) or in an empty glass bottle and use one of the rubber corks that comes with a pump to reseal wine bottles.

Increase the amount of air in each pocket. (Also true but we did talk about this above.) This is more complicated to pull off and have never seen it done. It requires forcing more gas into each of the tiny pockets inside the marshmallow. I have a few Ideas and I will get back to you...I am off to the lab.Hope this helps.

Answers: cold air is more dense than hot air. The cold balloon would be heavier. The cold balloon would be smaller. Air under pressure is more dense. The balloon would shrink as it was pulled deeper due to the increasing pressure.

Marshmallows are made of sugar, which contains carbon and water. The water evaporates off into water vapor when cooked, but it can't go anywhere inside of the marshmallow, so it puffs it out, taking up more volume but not being able to escape.