String Theory is a quantum gravity theory which lets us study the universe in a consistent fashion. I am interested in two fundamental questions in cosmology ,which can be addressed under the banner of string cosmology, which are the state of the very early infant universe and the current state of the universe. Starting with the early universe, we first need to ask the question of why do we need string theory aka a quantum theory of gravity to study this stage of our universe. This is because when we try to use our current theories to study the universe we run into several difficulties. These difficulties are a shared motivation of both cosmologists and particle physicists who are interested to study quantum gravity. For my motivations of the problem of quantum gravity and the beauty of string theory read this ().

Let me still highlight the cosmological motivations of quantum gravity and how string theory woes us all! Before, going into that, I should mention few words about what we know about the universe from experiments and theoretical (& mathematical) consistencies. First, we know that the universe is "statistically" homogenous and isotropic which means that on large scales universe appears the same in every direction (focus on the word large scales and if you are confused and want to learn more-read this ()). Second, the energy budget of the universe primarily composed of an unknown form of energy i.e Dark Energy (~70%), unknown form of matter called Dark Matter (~25%) and ordinary matter (you, me, the metals in your phone and everything we see around us) around 5%. Third, we know from observations that it is expanding and the expansion is accelerating! Weird, right? This has several implications. One that the universe is dark energy dominated (as also evident from the energy budget) and also that if we trace back the universe was much smaller and ultimately something closer to our usual storytelling about the BIG BANG!!!!

All these ideas work quite well both experimentally and somewhat theoretically under the framework of Einstein theory of gravity i.e the general theory of relativity. Why the somewhat? Let's dig deeper.

The standard picture of big bang cosmology has several issues (read this to understand the problems of big bang cosmology). What solves the problem is if we propose a theoretical idea called inflation. What inflation says is that in the very early universe we had a rapid expansion phase which caused the universe to expand by a huge margin. To put things into perspective, say at the beginning of inflation the universe was the size of an ant whose average size is around 5mm. By the time inflation ends, this 5mm universe would be around 10^(26)metres and to put things into perspective the distance between earth and sun is around 10^(11) metres. Absurd amount of expansion, right?

If something like that happened, what caused it? The answer cannot be provided properly in either quantum field theory or general relativity. This is where quantum gravity needs to be taken into account. String Theory has interesting answers here. This expansion have natural embeddings or answers in string theory.

There are other problems in the early universe but since I have already given one example here already, lets move to another era of the universe. The late time cosmology or our current state of the universe.

But, we thought current era of the universe is explained by Einsteins GR? Not exactly. Einstein GR does have an explanation for the dark energy but not so much about dark matter . Let's focus on dark energy.

Gravity, as we know, attracts and makes things come together so we would naively expect the expansion which was put in by inflation should decrease and the universe should contract. Rather, we see that expansion is not slowing down, rather it is accelerating! What is this "strong" phenomena which is overcoming gravity and causing the universe to expand (I will try to write about what the universe is expanding into here_) faster and faster?

This expansion can be somewhat explained if we add a term called cosmological constant in Einstein's equation. But, again what is this cosmological constant?Does GR or QFT have an answer? Some answer can be attempted by QFT. In QFT, we can sum over all the vacuum energies (the energy of empty space in some sense) and get some result and try to match right? The extra stuff in QFT or particles of our daily lives maybe something causing the universe to expand. If we follow that route, the predictions we get is off by a factor of 10^(120). I bet we are sorry about this!

This is why physics beyond QFT and GR becomes important and Quantum Gravity effects are thus important and needs to be taken into account to explain these two eras of our universe. Now, what does string theory or it's string cosmology offer to us? Let me try to summarise shortly.

For the early universe, the dynamics of inflation can be captured by a scalar field in a QFT sense. A scalar field is something like the Higgs Boson. This scalar field has natural answers in string. For example, let me give me an example related to my work (). There are extended objects in string theory called branes. To shed some light on this : Particles are 0-dimensional objects and hence D0-branes, strings are 1-dimensional objects and hence D1-branes and we can play this same game and have Dp-branes. In the same way we have anti-particles, we can have anti-Dp branes too! This Dp-brane and anti Dp-brane then attracts and there attraction is described by a scalar field. Not only does this offer a way to describe inflation but it does describe a mechanism to end it as well. (We highlighted some predictions from this scenario in the paper which is under current experimental bounds and has predictions which could be tested in future experiments).

For the late time, string theory - as any theory of quantum gravity should - has some answers. Actually, two answers are mostly discussed. The cosmological constant story or the story of a rolling dynamical scalar field. Let's focus on the cosmological constant one. In string theory, you can compute the cosmological constant in 4 dimensions by looking at the minima of the scalar potential*. String theory has a bunch of scalar fields and the minima of them gives us a cosmological constant. These scalar fields can arise from extra-dimensions and string theory provides a natural mechanism to get those.

Connecting them together,

*This has some technical subtleties.