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26

We need to be precise about the phrase the size of the universe. Specifically I'm going to take it to mean the maximum possible separation between any two points. In an infinite universe two points can be separated by an arbitrarily large distance, so if the maximum distance between two points is finite this means the universe must not be infinite. The ...


11

This claim is simply wrong. The flat hyperplane is of course infinite, but non trivial topologies can be flat and still finite. The simplest example is the 3-torus, but there are even the Klein bottle and the Hantzsche-Wendt manifold. See for example page 27 of Janna Levin - Topology and the Cosmic Microwave Background, which show you ten different closed ...


8

I think the key conceptual hurdle is that the vacuum state is not nothing. Quantum field theory describes matter as excitations in quantum fields. These quantum fields are very strange things, and I don't know of any easy way to explain to a non-physicist what a quantum field is. The key thing is that the quantum fields fill all of spacetime. So a vacuum is ...


6

Actually the "last scattering surface" of the CMB corresponds to the transition of the interstellar/intergalactic medium from an ionized plasma to cooler neutral atoms, about 300 000 years after the big bang. Most atoms have excitation and ionization energies in the visible, so the CMB was probably visible when it formed. We can be a little more precise ...


4

You're actually pretty close to the correct method for estimating the age of the Universe, but $H$ is not constant with time, it is $H=H(t)$. One of the many ways of writing the equation to solve is: $$t(z) = \frac{1}{H_0}\int_z^\infty \frac{dz}{(1+z)E(z)}$$ Here $z$ is redshift; $z\rightarrow\infty$ at the Big Bang, and $z=0$ now, so if you integrate ...


4

The Big Bang didn't occur at a special isolated place in the Universe. It occurred in the whole Universe and every place of it. Every point was an equal player in the Big Bang. Lots of light at various frequencies was produced during the epochs of or after the Big Bang. But it's wrong to imagine that they were coming from a particular distant place. ...


3

The Hubble constant is defined by: $$ H = \frac{\dot{a}}{a} \tag{1} $$ where $a(t)$ is the scale factor as you describe. Acceleration means $\dot{a}$ is increasing, but then of course $a$ is also increasing so how $H$ behaves with time depends on which of the two increases faster. We can calculate how $H$ changes with time simply differentiating equation ...


3

I think that it is important to note that (almost) everyone doing cosmology works within the framework of the FLRW universe. This implies that we assume that the universe is spatially homogeneous and isotropic, i.e. 'every place is the same (at least on large scales)'. Now, think of a flat, finite universe: Is it possible to maintain that all places are ...


3

The centre of mass of a system is simply the weighted average position of the mass distribution in that system. Since the universe is thought to be homogeneous and isotropic, any observer should roughly observe themselves as being at the centre of mass for their observable universe. However, I do not think that is quite the answer you were looking for. From ...


3

One could make an argument that we are just about the size we need to be. There is a fascinating paper from 1980 by William H. Press: Man's size in terms of fundamental constants, where he argues that intelligent beings have to have a scale of $$ L_H \sim \left( \frac{\hbar^2}{m_e e^2} \right) \left( \frac{ e^2 }{ G m_p^2 } \right)^{1/4} \sim a_0 10^9 ...


3

There aren't E and B fields in the entire universe. For example, there are no electric fields inside a conductor. I'm sure there are quite a few other such examples. If you mean "why are there electromagnetic waves throughout the entire universe?", one answer is because the radiation field drops like $1/r$, so the field from a single source never ...


1

Is the universe infinite? Or is it finite? You can relate observational measurements to this question by making an assumption. Namely, if we assume that the cosmological principle holds, then the curvature of the universe that we have measured from our earthly vantage point is true throughout the universe. This allows to extrapolate our measurement of ...


1

Your answer is dependent on many assumption. Your idea of coming back to the starting point was mostly "plausible" before the discovery of dark energy. If the current size and dynamics of spacetime is as we believe as of today, then you will never return back because there will be more space created ahead of you as you travel that what you cover even at the ...


1

The CMB was emitted at an energy of $E_{em}=13.6\text{ eV}$, which is the binding energy of hydrogen. This corresponds to a wavelength of $$ \lambda_{em} = \frac{hc}{E_{em}} \approx 9.12\times 10^{-8}\text{ m}$$ Redshift can be calculated by $$ 1+z = \frac{\lambda_{obs}}{\lambda_{em}} $$ If we observe blue light at 400 nm, we get a corresponding redshift ...


1

Just to add what the other questions say, if the sizes of the atoms were changing, there would have to be some corresponding change in at least one of the fundamental constants. For instance, if the size of the Hydrogen atom changed, then the ground state of the hydrogen atom would no longer be governed by the Bohr radius: $$a_{0} = ...


1

Other answers have made clear the 'flat' only implies infinite given additional assumptions around the topology. In short: A universe which is the same everywhere but not simply connected can be finite. It's worth mentioning that whilst the main working model assumes that the universe is simply connected, the actual topology is an open and serious ...


1

I would like to think about the universe as a balloon's surface. Imagine yourself as a 2D person living on this balloon, can never get out of it. If the balloon expand, you will just see everything is going far away from you, and vice versa. So if you think of Big Bang as a sudden great expansion of the balloon, you - the 2D person on the balloon - will ...


1

You cannot place anything "outside" to observe the big bang because there was no space that thing could have existed in (as you rightly said in your first sentence). So any observer is necessarily right in the middle of the bang happening. The popular science illustrations showing a ball of light expanding are essentially wrong. There is nothing the ball ...


1

John Rennie's answer is good already, but I want to add a single point: These fluctuations are very very short. In quantum mechanics you've got Heisenbergs uncertainty principle, which is often stated as $$ \Delta x \cdot \Delta p \le \frac \hbar 2 $$ and which means, that for any quantum object (think of an electron or a positron created in such a vacuum ...


1

I like this video by MinutePhysics on this topic. It can clarify things as a primer. When you state that the universe expanded at a speed higher than the speed of light, you have to stop and ask what is actually meant by such a statement. What is moving with respect to what? In standard cosmology, we describe the universe expansion by the Hubble rate ...



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