# What is the total entropy of the universe today

1. Feb 29, 2012

### avery

hi,
what is the total entropy of the universe today?
thank you

2. Feb 29, 2012

### marcus

Hi, Avery,

These people address the question but only get order-of-magnitude estimates for various components. FWIW I know of them by reputation and respect their expertise.
http://arxiv.org/abs/0801.1847
What is the entropy of the universe?
Paul Frampton, Stephen D.H. Hsu, Thomas W. Kephart, David Reeb
(Submitted on 11 Jan 2008)
Standard calculations suggest that the entropy of our universe is dominated by black holes, whose entropy is of order their area in Planck units, although they comprise only a tiny fraction of its total energy. Statistical entropy is the logarithm of the number of microstates consistent with the observed macroscopic properties of a system, hence a measure of uncertainty about its precise state. Therefore, assuming unitarity in black hole evaporation, the standard results suggest that the largest uncertainty in the future quantum state of the universe is due to the Hawking radiation from evaporating black holes. However, the entropy of the matter precursors to astrophysical black holes is enormously less than that given by area entropy. If unitarity relates the future radiation states to the black hole precursor states, then the standard results are highly misleading, at least for an observer that can differentiate the individual states of the Hawking radiation.
Comments: 5 pages, 3 figures, 1 table, revtex; v3: revised and expanded version, to appear in Class. Quant. Grav

Perhaps it doesn't matter in this case, I don't see how that quantity could be mathematically well-defined unless one had a standard definition of the entropy of the gravitational field---that is, the entropy of the geometry of the universe. Because the geometric entropy would be a significant part of the total.
Geometric entropy is interesting because the high entropy states correspond intuitively to things being clumped and clustered, or to a gravitational field that is pocked and pitted like a road with potholes.
While by contrast the high entropy states for radiation and matter correspond intuitively to stuff being spread out evenly (the way the gas molecules in a box of gas want to be.)

Last edited: Feb 29, 2012
3. Feb 29, 2012

### marcus

Even though I respect the previous authors Frampton et al, I'm inclined to heed what Charley Lineweaver says even more. Lineweaver and Egan (2009) answered Frampton et al and came up with a smarter estimate extending to the cosmic event horizon (the limit of events occurring that we will ever be able to see or that will ever influence us causally in any way.)

http://www.mso.anu.edu.au/~charley/papers/LineweaverEganParisv2.pdf

http://arxiv.org/abs/0909.3983
A Larger Estimate of the Entropy of the Universe
Chas A. Egan, Charles H. Lineweaver
(Submitted on 22 Sep 2009)
Using recent measurements of the supermassive black hole (SMBH) mass function, we find that SMBHs are the largest contributor to the entropy of the observable universe, contributing at least an order of magnitude more entropy than previously estimated. The total entropy of the observable universe is correspondingly higher, and is Sobs = 3.1+3.0-1.7x10104 k. We calculate the entropy of the current cosmic event horizon to be SCEH = 2.6±0.3 x10122 k, dwarfing the entropy of its interior, SCEHint = 1.2+1.1-0.7 x10103 k. We make the first tentative estimate of the entropy of weakly interacting massive particle dark matter within the observable universe, Sdm = 1087-1089 k. We highlight several caveats pertaining to these estimates and make recommendations for future work.
10 pages and 10 figures, ApJ. Accepted 11 Jan 2010.

Last edited: Feb 29, 2012
4. Mar 2, 2012

### clamtrox

If the universe has a cosmological constant, then it also has a de Sitter-horizon, whose entropy is much larger than anything inside. So to answer your question you'd need to know what dark energy is.

5. Mar 2, 2012

### marcus

I don't think we have any convincing evidence that there is a "dark energy". The observed accel. of expan. is simply and neatly explained by a positive cosmological constant Lambda.

This is a constant naturally occurring in the Einst. law of gravity just as the newton constant G occurs. To estimate total entropy we need to measure the constant Lambda, which has been done. We do not need to speculate about what the constant "is".

Google "bianchi prejudices constant" and get http://arxiv.org/abs/1002.3966
a critique of the hype surrounding "dark energy" talk.

6. Mar 2, 2012

### clamtrox

Okay, we have a small mixup in terms. To me, subtracting $\Lambda g_{\mu \nu}$ is such an elementary operation, I count cosmological constant as one model of dark energy. I think you will find that this classification is followed by most authors.

Also I don't think we share the definition of "neat". For example, do you think it's just a coincidence that $\Omega_{\Lambda} \sim \Omega_{M}$? Even worse, is it also a coincidence that currently $Ht \simeq 1$? Just because you think you cannot assign prior probabilities to these parameters (citing the article you linked to), which I completely agree with, you are still left with no explanation for these numerical accidents.

How far are you willing to trust the coincidence explanation? Do you think just because GR allows for different initial conditions, that explains the primordial power spectrum measured from the CMB (therefore making inflation obsolete)?

7. Mar 4, 2012

### marcus

Clamtrox, I highlighted what I was responding to. I don't think you need to know what "dark energy" is in order to estimate the total entropy today.

So I disagreed with you there. You make some other very nice points!

I think (unless I misunderstand you) that we both agree on interpreting "total entropy today" as entropy within today's cosmic event horizon plus that associated with the CEH itself. Call the latter SCEH. Anyway that's how I interpret the question.

The Lineweaver article I linked to has an estimate of SCEH. It dwarfs all the other components of the entropy, as I recall. Sort of like a huge inside-out black hole horizon.
As I recall the radius (proper distance) is a bit over 15 billion ly.

My only observation to you would be that Lineweaver et al do not need to assume anything about "what dark energy is" in order to make their estimate. They can just take the constant Lambda to be what it appears to be, a constant with a certain measured value.
That appears naturally in the Einstein equation because compatible with the symmetry of the theory.

Google "bianchi prejudices constant" and get http://arxiv.org/abs/1002.3966

Last edited: Mar 4, 2012
8. Mar 5, 2012

### clamtrox

Of course it does - just plug a different matter content into Friedmann equation and you get a different horizon size.

I don't understand. Do you think it's completely insignificant that we just happen to be currently expanding freely (within 1% accuracy in LCDM model)?

It seems fairly clear to me that the authors of this article do not appreciate (or intentionally try to misrepresent) the coincidence problem.

I also really dislike their tone considering that rest of their articles are on LQG

9. Mar 5, 2012

### marcus

We seem to be coming from widely different places. The matter content has been measured. The standard LambdaCDM model gives the simplest good fit to the data and Lambda has been measured. From my perspective the distance to the cosmic event horizon is known---as I recall some 15 billion ly.

Your attitude seems to be that we cannot answer the original question because we are free to play around with the matter content and get a different distance to the CEH.

Well...that's how you think about it. Lineweaver, the author I cited, simply answers the question based on standard cosmology. He's a working cosmologist, using the best model so far. He uses the 15 billion ly figure, or thereabouts, as I recall. The answer is provisional, like everything in science---the model subject to improvement of course. But I doubt the rough order of magnitude estimate he gives is going to change much.

10. Mar 6, 2012

### clamtrox

Here again I would say that we "measure" supernova luminosities and redshifts, CMB photon redshifts etc. Then we fit a certain model to these measurements to determine model parameters, like lambda. Likewise, we do not observe acceleration, except within this certain mathematical framework (and indeed you can find some (unrealistic) models which fit the supernovae and CMB data (BAO gives enough tension to rule the simple models out) which are locally decelerating everywhere). In these models you would not have a cosmic event horizon at all.

I think the Lineweaver article is very reasonable, but I also felt like there should be a proviso that this relies heavily on the assumptions put into the standard cosmological model.

11. Mar 6, 2012

### marcus

That suggested proviso strikes me, in turn, as very reasonable. Perhaps we should have a conventional "assuming standard model" ASM tag to stick on our responses to newcomer's questions.

When people ask for numbers here what they get are normally ASM, based on, say, the 5-year or 7-year WMAP reports where the standard cosmology model was fitted to masses of WMAP+BAO+SN data and the best fit parameters were estimated, and so forth. It gets repetitious saying ASM, ASM,... all the time. So a conventional abbreviation would be handy.

As a rule, the things people naturally want to know are all model-dependent, like proper distances, light travel times, age of U, the Hubble parameter itself...

I do sometimes spell that proviso out in words, but it certainly would be convenient (and less distracting to the reader) to have an abbreviation for it.

12. Mar 6, 2012

### marcus

A paper just appeared on the preprint archive today that relates to Bianchi and Rovelli's critique of the hype surrounding the "dark energy" constant, that I mentioned here:
Today's paper is a followup on one the senior author Padilla et al recently published in Physical Review Letters. It offers the prospect that we can isolate the cosmological constant curvature, from the particle theorist's vacuum energy---and do so in an empirically measurable way.

http://arxiv.org/abs/1203.1040
Cleaning up the cosmological constant