# Tag Info

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This is a great question. I know of a couple of really big things about inflation people want to be able to nail down by using the cosmic microwave background. The first is measuring what are known as E- and B- modes, which are the curl-free and divergence-free components to the modes of cmb radiation: Essentially, measuring large scale Gaussian B-modes ...

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Okay, I think I know what Max Tegmark is talking about in the video. He is referring to the fact that, when you observe the cosmic microwave background radiation (CMB) — i.e. the radiation that was "released" when the Universe had expanded and cooled sufficiently to allow protons and electron to combine into neutral hydrogen without immediately being ionized ...

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The simple answer to your question is "yes" - the universe expanded at much greater speeds than $c$ during the inflationary epoch. This period of time was very quick but very dramatic, lasting from about $10^{-36}$ to $10^{-32}$ seconds. The universe expanded, in this very short period, by a factor of $10^{26}$. That's pretty incredible, when you think about ...

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Reason 1: Let's look at the Friedmann equations without the cosmological constant. $$\frac{\dot{a}^2 }{a^2} = \frac{8 \pi G \rho}{3}-\frac{kc^2}{a^2}$$ The term on the LHS is just the Hubble constant squared $H^2$ which can be measured the direct measurement of recession velocity of galaxies The density term can be said to be a combination of $\rho_{... 8 I...think you've got it backwards? Slow-roll inflation is alive and well, unlike models which involve tunneling between two vacua. The model of inflation first proposed by Alan Guth back in 1980 was a tunneling model. But it had a serious problem: it didn't reheat. Tunneling from a false vacuum to a true one (or a lower-energy false one) wouldn't release any ... 8 I don't take this at face value because we should expect more distant objects to have higher observed speeds and therefore higher observed red-shifts. That's true. That was the original Hubble discovery - the farther away things were, the faster they were moving away from us. Here's why. Let's start with a model where the Universe expanded very ... 7 That's a very complicated question! First, let's remember that Moses didn't bring the Law of Conservation of Energy down from Sinai on stone tablets -- it's something that we've observed to be true of the universe today, and which our theories use to make very accurate predictions. But this doesn't mean that it was always true, and particularly that it was ... 6 Conceptually there are several things going on here. Where does energy conservation come from? In modern understanding, energy is the Noether charge of time translation symmetry, as found by Noether's first theorem. But in general relativity, the metric is dynamical, and so in general we simply don't have any time translation symmetry. Static spacetimes do,... 6 My topological defect cosmology is a little rusty, but I'm pretty sure this is how it goes. Start with the fluid equation, $$\dot{\rho} + 3 {\dot{a} \over a} \left( \rho + p \right) = 0,$$ and the equation of state, $$p = w \rho.$$ Plug the equation of state into the fluid equation, assume a constant$w$, and you'll find $$\rho \propto a^{-3(1 + w)}.$$ ... 6 Is Cosmos seriously using that exact number? Egads... if they are, don't take it too seriously, but otherwise they're probably conceptually correct. How do we know it was dark energy? In cosmology, the ΛCDM model fits numerous observations, most notably those observed by the WMAP satellite, but also others, to the Friedmann-Robertson-Walker family of ... 6 What's outside the observable Universe, we can't say anything about, but averaged over large enough scales ($\gtrsim$a billion lightyears), it does indeed seem to be expanding uniformly. However, the presence of mass, or more generally energy, retards the expansion. This means that on the scale of clusters of galaxies, the Universe expands more slowly, and ... 6 Yes, time does run slower for far-away objects, as observed from our point of view; this is a prediction of general relativity. And yes, because expansion accelerates, this time dilation slowly, very slowly, becomes more pronounced (this would happen even if the expansion didn't accelerate, but just continued at the same rate). This time dilation is a well-... 6 Inflation is used to explain why the observable universe is extremely homogeneous. Without inflation, we can do the following crude calculation. The cosmic microwave background was formed about 300,000 years after the big bang, at a redshift of about 1100. Thus causally connected regions at the epoch of CMB formation would have a radius of$\sim 300,000$... 6 Great question! Sorry for this huge response, and it might not be a satisfying answer, but it'll address your questions. Sadly, as with most of astronomy, the Big Bang is surrounded in mystery. It is one of the biggest uncertainties out there, and you'll come to this realization if you've researched it enough. Most of what we can get out of the Big Bang is ... 6 It's a pretty clever idea and a solid question that unseen mass might cause gravity outside the observable that tugs on the universe and might be the cause of dark energy as opposed to some unknown energy that seems to permeate all space. It's not a new idea, but it's worth answering. There's 2, possibly 3 (or 4) pretty big problems to that approach. The ... 6 That is nearly long enough to reach heat-death, which is estimated as about$10^{10^{120}}$. What that means is rather speculative, since it depends on various events that we have never observed, such as the spontaneous formation of black holes by quantum tunnelling. Such events are utterly rare, but are predicted to occur at very long timescales. Any ... 6 Hubble's law $$v=H_0 d,$$ relates the recession velocity$v$of a distant object to it's physical distance$d$. Today, the physical distance coincides, by definiton, to the comoving distance$\chi \equiv d/(1+z)$, but if you want to know how fast two galaxies at a redshift of, say,$z=1$, you must plug in their physical distance at that time (and use$H(z)$,... 5 The critical density of the universe is $$\rho_c=\frac{3H_0^2}{8\pi G},$$ with$H_0=67.8 \frac{\mbox{km}/\mbox{s}}{\mbox{Mpc}}$the Hubble constant and$G=6.673848\cdot 10^{-11}\frac{\mbox{m}^3}{\mbox{kg }\mbox{s}^2}$Newton's gravitational constant. Hence with one parsec$1\mbox{pc}=3.0857×10^{16} \mbox{m}$,$$\rho_c=\frac{3\cdot (67.8\cdot 10^3\cdot \frac{... 5 The surface of the 4-dimensional ball (called 3-sphere) is a slice through the universe as a whole for a fixed cosmic time. This slice describes just three spatial dimensions. The observable universe is a tiny part of this 3-sphere; hence it looks flat (3-dimensional Euclidean space) up to measurement precision (about 0.4% at the moment). Adding time makes ... 5 It's a rather difficult concept to grab but, in short, the image of expansion you have in your mind is wrong. It's not your fault, it's everywhere out there, the inflatable balloon etc. And it's terrible :) Another way to look at it is that the universe properties are changing. Whether it is infinite or finite, its size (as measured within itself) changes. ... 5 The expansion caused by a cosmological constant (a particularly simple version of dark energy) is not exactly Hooke's law, it is an expansion that maintains a fixed Hubble constant. So this means$\mathrm{d}a/\mathrm{d}t = Ha$, for scale parameter$a$and constant$H$. The solution is exponentially growing in time. Hooke's law (without the minus sign) would ... 5 There is in fact a cosmic gravitational wave background. These waves are expected to be stochastic, having originated in the early universe (much earlier than the cosmic microwave background). Random fluctuations were subsequently stretched during inflation, making them observable over many wavelengths. A good and reasonably up-to-date introduction I read is ... 5 Standard cosmological models predicts that the cosmological redshift and the speed of light are wavelength-independent. This result is confirmed observationally e.g. by Ferreras & Trujillo (2016), who used$\sim500\,000$SDSS galaxy spectra down to a precision of$\Delta z \sim 10^{-6}$and$\Delta z \sim 10^{-5}$for galaxies at$z<0.1$and$z>0.1$... 5 tl; dr The universe is probably infinite, but if that's the case it's impossible to verify. If the universe is finite, and small enough, and the global curvature is equal to the curvature of our observable universe, then we will be able to estimate its size. If the global curvature of the universe isn't positive, then the size of the universe is infinite, (... 4 Googling "hyperinflation" mostly returns articles about Zimbabwe and the Weimar Republic, so I'm going to assume that you are referring to what is usually just called (cosmological) inflation. We are still pretty uncertain about when and for how long inflation occured, but we do however have some sort of constraints. In general, inflation is thought to be ... 4 After inflation, the expansion of the universe did indeed slow down. During the inflationary epoch (lasting roughly$1 \times 10^{-33}$seconds), the universe expanded by a factor of$10^{26}$. That's incredible! However, the inflationary epoch didn't last long, and that incredible expansion ended pretty soon after it started. The universe is, as you said, ... 4 Both are true. The universe is "dying" in the sense that stars eventually run out of hydrogen, and there aren't infinite amounts of hydrogen in galaxies to replace old stars. This will take a very long time, but eventually all stars will burn out and new stars will stop forming. This is what the study recently in the news is saying. The universe is ever ... 4 Before the advent of telescopes, we could only look back in time from a few years (for nearby stars) to a few thousand years (for the most distant stars visible to the unaided eye). In addition to this, a handful of galaxies are visible without binoculars, letting us look back a few million years. The first telescopes allowed us to see much farther, like ... 4 To talk about 'the rate of time', we essentially need at least two different time coordinates. For example, this happens in special-relativistic time dilation, which is equivalent to$\mathrm{d}t'/\mathrm{d}t\$ across two different inertial frames. Fortunately, we can do something similar here. Space expands everywhere, also here. And time is inseparable ...

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The CMB lets us measure how close to flat the universe is right now. On the other hand, inflation tries to explain how we got from whatever the early universe was to right now. The motivation for the latter being that even extremely small deviations from perfect flatness in the early universe should have resulted in very obvious deviations from flatness ...

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