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									“Warped Reheating in Multi-Throat Brane-Inflation” Before we begin to talk about String Theory and the Universe, let’s discuss something closer to home, literally – you refrigerator. Inflation and Reheating How exactly does your refrigerator cool down your food? The magic is in the properties of gases. If you were to stick your hand into a box full of gas, the first thing you would describe is the gas’s temperature – how hot the gas feels. Microscopically, temperature is just you feeling the energy of impact from the gas molecules hitting your hand, like billions of tiny ping-pong balls bouncing off your hand. The more energy the ping-pong balls have the harder they hit, and the “hotter” the gas feels. The ping-pong balls also hit the walls of the container holding the gas – this is the “pressure” of the gas, it’s desire to push the walls out. Now lets say the walls aren’t very solid (like a balloon) and move outward when hit by a gas molecule (ping-pong ball): just as you use up energy when you push something heavy, the ping-pong balls use some of their energy to move the wall outwards, so the gas will cool down as it expands. But we can reverse this statement as well: as you make a gas expand, it cools down. This is (very) roughly what your refrigerator motor does – it sucks in air from the fridge, forces it to expand and cool down, then pumps it back into the fridge as cold air to cool down your food. This is done in cycles: 1. Take air from the fridge 2. Expand and cool 3. Pump cold air back into fridge 4. Repeat 1-3 until desired temperature reached What does this have to do with the Universe? Well, the Expansion of the Universe Universe is like a big refrigerator motor – it can expand and contract, You can visualize the expansion of cooling or warming the things inside it (by the way, don’t try and take the Universe as a bunch of galaxies the analogy too far – the Universe isn’t expanding because things are painted on the surface of a balloon. As you blow up the balloon, the pushing against its “walls”, in a ironic twist it’s actually expanding Universe expands and the galaxies because of gravity). spread apart from each other. In the standard picture our Universe “started out”* hot and small, and expanded, cooling to today’s temperature of ~3 o above absolute zero – this is what is often called the “Big Bang,” because the hot expansion reminds us of an explosion.** It turns out that despite excellent agreement with our knowledge of the Universe, this scenario doesn’t completely agree with all the observations we see today, and we need to add something else – a period of time very early on of extremely rapid inflation.

Inflation is a special term for “frickin’ huge expansion;” in our case, we need the Universe to expand to ~1022 times it’s previous size in about 10 -36 seconds (i.e. a billionth of a billionth of a billionth of a billionth of a second). Sounds ridiculous, right? Well, for science the question is not how silly the idea sounds, but rather, does the new idea give us predictions? It turns out that inflation does give us predictions, and some of them have been verified, such as the details of the background “glow” of the radiation left over from the early Universe. How do we get inflation? As we’ll see later, inflation happens naturally in string theory models of the Universe. Notice that with so much expansion the Universe will cool down very quickly – so quickly, that without something else happening, there won’t be any stars, galaxies, or planets in the Universe after inflation. This is a major problem, so we need some way to reheat the Universe after inflation. Unfortunately, there are no microwaves, toasters, or ovens big enough to reheat the leftovers of the Universe after inflation – all inflation models must also provide a method for reheating. The general idea is that whatever causes inflation has a lot of energy stored in it, and the release of that energy is what reheats the Universe. For example, in most models of inflation the rapid expansion is caused by the presence of a quantum mechanical field throughout the Universe; after inflation, this field is still there with it’s stored energy, and it causes reheating by decaying into photons, electrons, and other “normal” particles of our world. We’ll talk about another particular method in string theory later. String Theory and (mem)Branes Imagine there’s an ant walking on a really big piece of white toast standing on it’s end. Since it’s an ant, it can only walk along the piece of toast – if it’s a big piece of toast, it’s the whole world as far as the ant is concerned. We can even imagine there being another piece of toast standing on it’s end some distance away, and on this other piece of toast is another ant crawling around. Since the ants are stuck to the toast, they don’t really know that the other exists since they can’t travel to the other piece of toast. But a fly knows better – since it can fly, it knows that the ants are just stuck to the toast. String theory describes the world at the very microscopic level as being made up of tiny vibrating strings. For example, all particles like electrons, protons, photons and Extra Dimension even more exotic particles like gluons and gravitons, are fundamentally made of tiny strings. Some strings are open – they have ends – while others are closed, without endpoints. The open string endpoints must be stuck onto objects called D-membranes, or D-branes for short, much like the ants above were stuck on the pieces of toast. The closed strings, because they don’t have ends, are not stuck to the D-branes and can go wherever they want; they are similar to the fly from above.

In many models of String Theory all the usual stuff we’re made of, electrons, protons, neutrons, are actually made up of open strings (not closed strings), so we’re stuck to these D-branes just like the ants were stuck to the toast! As far as we know we live in 3 space dimensions***: up and down, forwards and backwards, side-to-side. The ants on the toast lived in 2 space dimensions – they could only go back and forth, side-to-side, on the piece of toast. The “up and down” direction was something extra to them – it is what we call an extra dimension. Now, we can’t be stuck to an actual big piece of toast, because we can move in 3 directions, not 2; luck has it, though, that these D-branes can be 3-dimensional. Don’t worry if you can’t visualize a 3-dimensional piece of toast – nobody really can, so we just use toast-like D-branes for our pictures to remind us that we’re stuck to the D-brane. Just like the other direction was an extra dimension to the ant, there are extra dimensions for us as well – in fact, string theory says that there should be around 6 extra dimensions! Remember, we don’t see these extra dimensions because we’re stuck to the D-brane, but some experiments may soon be able to infer their existence****. Also, just as with the ant, there may be other D-branes out there with other Universes on them – if only we could get off our Dbrane we could go and visit them! Brane Inflation Looking around our Universe, the stuff we see is made up mostly of just electrons, protons, and neutrons (which we just further said are made up of strings). But we could imagine (as is often done in Sci-Fi) that there is an “anti-Earth” somewhere made up of anti-electrons, anti-protons, and anti-neutrons, and there might even be an anti-You walking around on the anti-Earth going to it’s anti-Job or anti-School. These “anti-“ particles are called “anti-matter”. What does an anti-electron look like? Well, a normal electron has a negative electric charge and a small mass, and an anti-electron will look exactly the same, have the same mass, just with opposite (positive) charge. Since the electron and anti-electron have opposite charges, the electric force tells us they attract each other (opposites attract), but something strange happens when a particle meets an anti-particle – when they meet, they annihilate each other in an explosive burst of energy! So, if you find an anti-you on an anti-Earth, don’t go rushing to shake their hand – you’ll both explode in a catastrophic burst of energy! The D-branes we’ve been talking about also have a type of electric charge, so if you put a D-brane next to an anti-D-brane they will also attract each other and eventually annihilate in a burst of energy! I mentioned that String Theory requires extra dimensions; different models in String Theory give different shapes for the extra dimensions. We’re going to use a particular model (called KKLMMT or GKP) in which the extra dimensions look like something akin to a Mickey Mouse glove. The fingers of the glove are called “throats” and one of the redeeming features of these throat models is that when a brane and an anti-brane attract each other in a throat, we actually get inflation on any other D-brane! This process is called “brane inflation,” and the glove is a “warped space.”

Now, one troubling question you should be asking yourself is, “but I thought we lived on the D-brane – how can we live on it if it annihilates??!” There are at least two possible solutions to this problem: 1. A stack of D-branes is attracted to the anti-D-brane. Since only one of the Dbranes can annihilate with the anti-D-brane, there’s still at least one brane left over for us to live on. 2. There are other branes elsewhere, like in another throat, on which we live and these branes don’t annihilate. Solution Number 1 is a very difficult problem to solve – some have tried, but most have not been able to give any conclusive answers. Our paper took the approach of Number 2: there are at least two throats, one called the “Inflationary throat (I)” which is where the annihilation happens, and a “Standard Model Throat (SM)” which is where our Universe, the so-called “Standard Model”, is located. Warped Reheating We just saw that inflation can happen in String Theory when a D-brane and antiD-brane approach each other; inflation ends when they annihilate. The annihilation releases a lot of energy in the form of closed strings (the strings have to be closed because the closest D-brane is our Universe, far away in the Standard Model throat), and this energy can be used for reheating our Universe. The only problem is, how are we going to get the energetic closed strings, located in the Inflationary Throat, into the Standard Model throat where they can collide with our D-brane and reheat us? Well, the closed strings will eventually decay down to other special closed strings: the graviton, the particle of gravity, and the Kaluza-Klein graviton, also called the “KK mode”. These closed strings are special because they won’t decay to any other closed strings. The gravitons and KK modes are quantum mechanical objects, and will tunnel quantum mechanically from the Inflationary throat to the Standard Model throat, where they turn into open strings on the D-branes that make up our Universe. When they decay to the open strings, this reheats the Universe, thus we have both inflation and reheating in this model. To summarize, the steps are: 1. D-brane and anti-D-brane attract in the Inflationary throat, causing inflation 2. The D-branes annihilate, creating lots of closed strings 3. The closed strings from step 2.) decay into KK modes and gravitons 4. KK modes and gravitons tunnel to the Standard Model Throat 5. KK modes and gravitons collide with our D-brane, creating open strings and reheating the Universe 6. 13.7 billion years later, here we are asking these questions. The remaining question to ask is: can this process actually work? There cannot be too many gravitons in the early Universe because they don’t reheat the Universe very well and too many of them hanging around causes conflicts with other wellestablished observations. Much of the paper, then involves putting constraints on the lengths of the throats by requiring that we don’t produce too many graviton particles. Our Mickey Mouse Glove model doesn’t just have to have only 2 throats – it can have multiple “fingers”. However, having other throats means that the KK particles we

want to use to reheat our Universe can tunnel into these other throats and get trapped – if the throat is too deep, the KK modes can be trapped for such a long time that by the time they quantum mechanically tunnel back out again it will be too late for reheating, and we will also be in conflict with observations – thus only “short” throats are allowed.

Conclusion and Outlook Ultimately, we found in our paper that given the constraints from the gravitons the early Universe can be reheated from brane-inflation, but only if we allow the throats to be shorter than a certain amount*****. Many interesting problems remain, however. In particular, investigating what happens when stacks of D-branes and anti-D-branes annihilate is a difficult problem and has many applications. Something interesting may also happen when the branes slam into each other at high speeds, and it is unclear if previous conclusions about the closed strings produced by the annihilation still hold. There is also the possibility that these throats change length and grow and shorten with time, which will drastically change the process of inflation and reheating in these types of models.


Stack of D-branes

* I’m not going to speculate on how the Universe started – allow it to start any way you want, i.e. through science or divine intervention, just so long as it starts out hot. Actually, many current models of the Universe don’t even require that it be hot! ** Nobody is actually saying there was an explosion, though. *** Time is often included as a 4th dimension, but it is different from space as you can only travel one direction, forward **** Mostly under very optimistic scenarios only.

***There is some current, unpublished work, that suggests that our approach was too simplistic and a more through analysis relaxes the constraints on the lengths of the throats.

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