### Amount of energy of the Big Bang

• What is the currently accepted estimated range of the amount of energy of the Big Bang event?

In joules at some estimated size, so a temperature may be calculated.

For context, I wonder if the temperature of the Big Bang would make its heat radiation wavelength shorter than the Planck length.

• Let's start by making some points clear:

# 1. We don't know what the Big Bang was.

Rather, we know that the Universe is expanding. If you extrapolate backwards, you'd expect the Universe to be denser and denser. More specifically, we talk about this as a change in the scale factor $$a$$, and this gets smaller and smaller as we look further back in time. According to general relativity (our modern theory of gravity), 13.8 billion years ago, $$a$$ should have been $$0$$; however, you can't have a metric with $$a = 0$$.

Thus, we know that general relativity is necessarily incomplete. It breaks down at the conditions of the early universe, so we currently have no physical model to explain that time. Rather, we know that the early universe expanded, and the Big Bang is the time that perplexes cosmologists. Some theories, like quantum gravity, have emerged in an effort to explain the Big Bang; however, we currently have little understanding of what it actually was.

So no, we can't tell you what the energy output of the event was, since we don't know what actually happened.

# 2. The temperature of the early Universe was high

Our theories break down at the Planck epoch of the Universe. The Planck epoch was the earliest epoch of the Universe and lasted until $$10^{-42}$$ seconds after the Big Bang — that's 200 Planck times, which are the shortest meaningful measurement of time.

During this epoch, the entire Universe was at $$1.417×10^{32} \; \mathrm{K}$$, which is the Planck temperature. This is the hottest possible temperature; an object at this temperature will emit photons with wavelengths of a Planck length (you can read more about this in my answer here). The point is that there is no meaningful distance smaller than a Planck length, so the Universe couldn't be hotter than the Planck temperature.

+1 for answering the question, but don't forget that theories break down, and they are only theories. We don't actually know that the temperature of the very early universe was high.

@JohnDuffield The WMAP observations provide strong evidence that the temperature of the early universe was high, ruling out a cold Big Bang. See Komatsu et al. (2010).

I'm sure we'd all agree that the temperature of the early universe was high. But I said _don't forget that theories break down_ and said the _very_ early universe. In fact, I'll go so far as to say this: IMHO the temperature before the big bang was absolute zero.

@JohnDuffield Well, we don't really know what the Big Bang was, so I'm a bit confused as to how you derived that.

It's to do with what Hawking said: the universe is like a black hole in reverse.

PS: I'm not a fan of Hawking, or of Hawking radiation. But I think he was broadly correct when he said the universe is like a black hole in reverse. IMHO pulling away from a black hole through space is something like the universe expanding over time.

Even if 1. and 2. were known, does not knowing *how big* the universe is (total mass or energy) add a third and independent uncertainty?

@uhoh Well, that's if we simply equate "energy of the BB" with "energy of the universe"; the former isn't really well defined. As for the latter, you're right that not knowing the universe would prevent us from finding the total energy. An infinitely large universe would have infinite energy (assuming the cosmological principle), whereas determining the energy density of a closed universe goes hand in hand with determining its radius of curvature, allowing us to get the total energy.

@SirCumference total size of the universe would be *something like* the mass of the matter plus the energy, though I am sure there are better ways to say that. I did not suggest you would equate as you've stated, but I think it's reasonable to expect a larger universe to have a larger energy big bang, no? I still think you need a 3rd uncertainty item for the size of the universe, of which we have no upper limit.

@uhoh Well, "Big Bang" more or less refers to a point in time rather than an event, specifically where we get gravitational and temperature singularities. Now that I think about it, I'd expect the energy of the universe would also approach infinity as we get closer to this time. Whereas cosmological redshift decreases the energy of photons, if we went back in time we'd see the energy being higher than today. At the Big Bang (when the scale factor goes to zero), the wavelength of a photon would go to zero as well, so the energy would be infinite.

Still, wouldn't a larger universe be a "larger infinite" energy? I can never remember, but are there some flavors of infinity that can be larger than others?

@uhoh If you say "infinity" in math, it has (roughly) two distinct meanings based on the context. In set theory, it refers to a quantity of objects, specifically one that's at least as big as the number of integers (there are bigger infinities in that context, which you mentioned). In analysis on the other hand, we mainly just use it to refer to a limit (a sort of unrigorous way of saying the limit diverges). Here we're just considering how energy rises as we consider more and more matter in our universe, so when saying "infinite energy" I mean energy diverges if we make our universe infinite.

@SirCumference okay well I still think that a 3rd source of uncertainty related to the unknown size of the universe is needed, but that's just me.

@uhoh If we're talking about total energy of the universe, then yes. But the energy density of our universe *at the Big Bang* rises to infinity for any size of the universe.