And now let's talk about dark energy. Is probably the single most outstanding mystery of physical science, obviously, because we have no idea where it's from. The basic observation really is micro fluctuations which tell us that universe is flat to an amazing precision. And in order for it to be flat, we'd observe the dynamical amount of mass that we see, there has to be exact complement to unity that matches. Today, we're in the regime where it accelerates the expansion of the universe. You can think of this as an elastic force, elasticity of physical vacuum. So the spring the force is bigger the more you compress it or stretch it, all right? So think of it as a negative spring. The more I stretch it, the more it pushes. And it can affect growth of density perturbations, but it's unlike gravity and love that's inversely proportional to the distance squared. This one's actually proportional to the distance. The further away look, the bigger effects you see. And this is why it's only really perceptible in cosmological observations. I've been carelessly mixing cosmological constant and dark energy. And dark energy's a more general term. Whatever it is, it's filling up the universe, but need not be constant. Cosmological called constant, is exactly what the name says. It's the constant uniform energy that adds to your mass density, that's distributed through space. Since space expands, this is yet another example how energy is not conserved in relativistic universes. Because, you get more space, but energy density stays the same. Now first attempt to understand this was due to Soviet physicist Yakov Zeldovich. In Einsteins days vacuum was vacuum, but then quantum physics taught us that actually no, vacuum is filled with virtual particle and anti particle pairs that appear and disappear. Obeying Heisenberg's Uncertainty Principle. And while they exist for a very short period of time, they can count as energy density. And so in principle, you could create energy density vacuum from this. But we don't know how to do this. Because we need quantum theory of gravity in order to make this computation properly. This is now also being used in inflation, it's exactly what inflation tells you, vacuum goes so high and stay to lower entry state. But anyway. We don't have a theory but people tried it and so they tried and made the worst prediction ever. Since the only natural units I could think of for this would be Planck units. Then you get essentially Planck density as prediction, which is 2 times 10 to the 93 grams per cubic centimeter. And that's 123 order of magnitude off from what's measured. And now that's called fine tuning problem. Because you have to somehow get rid of this bulk of potential vacuum energy to one part intent to 123, but this could be just completely wrong reasoning, right? So since obviously universe wasn't planck time old,didn't have this density then the only natrual value is zero right? So whenever you are doing problems and you just can't figure out the answer, zero is always the best answer because then you don't have to worry about units. Not very reliable way to go about faith in the universe. And so people ignored this for awhile until observations showed that it's there. So now we're pretty sure it's there from a variety of different lines of evidence and the question is what is it? And so I said there multiple papers are written on this every day literally. Many thousands of papers are being written about possible nature of dark energy. And I think everybody agrees that we really don't know. Not yet. I mean, some models look more interesting than others, but so far, this is the biggest uncertainty. And all kinds of crazy stuff's been proposed including that, well, these are called multiverse, but landscape to their 10 to power of 500 different universes. Each one of them has different values of constants, including this one and so on. It's very hard to say much more about it, since we only measure one number. That's density, today and forever, actually. The only other possibility that we may have is that if the density were actually changing in time. If it wasn't constant. And so that is done by expressing it through equational state, you may remember is perimeter w, which connects pressure with density and there's generic equational state is written there. So if w is equal to minus 1, then row is constant. And one thing that some people worry about is that it seems weird that we just happen to live in a time where the matter and dark energy are about comparable. I personally don't see this as a problem because it's been this way for the past 10 billion years or so, but some people worry about it. So the version of dark energy that changes in time is called quintessence, and again, nobody has any idea what it could be. But different models make different prediction in terms of how it changes in time. So then the path towards understanding what's going on here is to measure if the energy density is changing in time. And so far all of the measurements from all different kinds of observations zero in on w minus 1. Everything so far is consistent with being constant since the recommendation til the present day. So, I would say chances are pretty good that it really is constant, or constant with such a high precision that it really doesn't matter. And so it remains as an outstanding problem for physics.