# Mass of the universe

1. May 28, 2013

### HowardTheDuck

Hi guys, I have a question about the mass of the universe, and inflation/dark energy.
As I am sure you know, inflation is supposed to stretch the universe so that the visible universe is only a small part of the true size of the universe. This guarantees that the visible universe is flat.

However, and I quote from "Relativity, Gravitation, and Cosmology" by Ta-Pei Cheng, "The Friedmann equation requires a flat universe to have a mass/energy density exactly equal to the critical density. Yet observationally, including both the baryonic and dark matter, we can only find less than a third of this value. Thus it appears that to have a flat universe we would have to solve a missing energy problem." As a result, it is suggested that the value of dark energy must be 75% of all the mass of the universe.

But surely inflation guarantees a flat universe, even if the visible universe only includes a grain of sand? How can cosmologists accept the inflation hypothesis, and then say we need more dark energy to make a flat universe?

Thanks a lot.

2. May 28, 2013

### phinds

The universe is not known to be flat. It IS known to be very close --- I think the deviation from true flat is now under 1% and since that's within the margin of error of the measurements, it COULD be exactly flat. Saying that it categorically IS flat, however, is premature.

3. May 29, 2013

### HowardTheDuck

4. May 29, 2013

### timmdeeg

There is no contradiction. The Inflation provides (among other things) a plausible mechanism to explain the observed flatness (~ very close to flat). Think of the small area of the blown up balloon.
Now, flatness of the universe requires that the sum of the density parameters (matter/energy + lambda) equals 1 over time. Consequently, the ratio of said parameters isn't constant and therefore the ratio of the densities of matter/energy to lambda isn't constant too . Thus, as the matter/energy density decreases due to expansion lamda (dark energy) has to increase.

Last edited: May 29, 2013
5. May 29, 2013

### Chalnoth

Inflation's prediction that the universe will be highly flat is only that: a prediction. There isn't any solid reason to believe that this prediction is sufficient, and so scientists have gone about measuring the flatness of the universe by comparing nearby length scales with far-away length scales, and the answer is the universe is very, very close to flat.

The next question becomes: what are the component of the energy density of the universe? Normal and dark matter only make up about a quarter of the whole, and the rest appears to have a nearly-constant energy density with time (i.e., it doesn't dilute as the universe expands). This is what we call "dark energy", and so far the cosmological constant appears to be our best guess as to what it is.

6. May 29, 2013

### HowardTheDuck

Thanks for your response. But you don't consider inflation. Like I said, inflation guarantees a flat universe - no matter what the matter/energy/lambda values. That's the great appeal of inflation. It always guarantees flatness.

Or am I wrong?

7. May 29, 2013

### phinds

As I understand it, you are wrong.

Inflation flattens things enormously but it does not guarantee absolute flatness.

8. May 29, 2013

### HowardTheDuck

Here's my take on it. I''ve read about a bowling ball analogy for inflation.
Inflation says our visible universe is only a tiny fraction of the true size of the universe which lies outside our visible universe.
If you consider a bowling ball, it obviously has a great deal of curvature. That's the entire universe. It might be curved in any way you like. But if you consider only a tiny patch on the surface of that bowling ball, then it is basically flat. And that is what inflation does - it says our visible universe is just a tiny patch on the bowling ball.
And it doens't really matter what local conditions (matter density) you have in that tiny patch. It will be insignificant compared to the influence of the rest of the bowling ball. And the influence of the rest of the bowling ball is always going to mean that your tiny patch is always flat (or very close to flat).

Have I misunderstood why inflation means the universe is guaranteed to be flat?

I'll admit, it does look like I have misunderstood. I've just read that the density must still be equal to the critical density - even though space is stretched. I can't get my head round that.

Last edited: May 29, 2013
9. May 29, 2013

### Mordred

Inflation and expansion are slightly different. Inflation does address the fine tuning flatness problem but requires a minimal number of e- foldings.
However I've read numerous values for that number. 60 e-folds is one value I recall from memory. Though I have seen higher/lower required values in different inflationary models.

10. May 29, 2013

### phinds

Yes, you have misinterpreted your own analogy. Using your own analogy, why is it that you cannot see that the surface of the bowling ball is NOT flat, it is merely very close to flat?

11. May 30, 2013

### Naty1

Howard:

sort, of but this statement is backwards....the universe was observed to be close to flat....we needed a model to provide that flatness..The Friedman equation [The FLRW λ-CDM cosmological model] does not forecast inflation....Alan Guth forecasted inflation because it seemed to fit observations.....Inflation is a glued on as a front end, an addition to the FLRW model so we can get an overall picture that fits observations....

Wiki says it this way:

and further along:

http://en.wikipedia.org/wiki/Cosmological_inflation

# "problems' means that our models did not match our observations w/o 'inflation'....

12. May 30, 2013

### timmdeeg

You asked "How can cosmologists accept the inflation hypothesis, and then say we need more dark energy to make a flat universe?"

And you are close to an answer. Cosmologists know which combinations of matter/energy density and lambda (means the combination of attractive and repulsive gravitation) makes the universe flat. And in deed observational data from different sources prove (almost) flatness. Inflation is the model according to which this result was expected. What a big success!

13. May 30, 2013

### Chalnoth

No, it doesn't always guarantee absolute flatness. It does guarantee it if inflation lasts long enough, but inflation may not have lasted that long.

14. May 30, 2013

### timmdeeg

It seems interesting to note that if the current energy density is close to the critical density, it must have been much closer to that in the past, because according to the Friedmann equations these values depart from each other over time.

15. May 30, 2013

### Chalnoth

....at least during the matter and radiation domination epochs.

16. Jun 1, 2013

### timmdeeg

The preceding epoch seems rather short. Martin Bojowald says inflation produces matter (pair production) analogously to black holes. But I am not sure whether this is mainstream physics.

If Bojowald is right, matter will be created again, should the dark energy ever cause the universe to expand exponentially. It's just speculation.

Last edited: Jun 1, 2013
17. Jun 1, 2013

### Naty1

Particle production DOES seem to be accepted as mainstream physics when event horizons are present...as in black holes, Hawking radiation, Unruh radiation, whether all that is actually correct is of course a theoretical question so far. Different observers will see different quantum states and thus different vacua....different particle counts....

Similarly, cosmological expansion also results in particle production.....

18. Jun 1, 2013

### Mordred

inflation has several proposed forms of proposed particle production methods depending on which inflation model.
Some examples. Guth's false vacuum. However thats "old inflation". the inflaton field of chaotic eternal inflation. more classically though Parkers radiation is used Which is particle production through inflation/expansion.

19. Jun 2, 2013

### Chalnoth

Yes, this is correct. But the rate of expansion is so fast that this matter is diluted away to nothing and is irrelevant to the evolution of the universe.

The matter around us would have been produced at the end of inflation as the particle driving inflation decayed, not during it.

All that is required for such matter production is a horizon. Which our universe has. But because the magnitude of dark energy is so low, the temperature of that horizon is so minuscule that we're unlikely to ever be able to measure it (the CMB completely and utterly drowns it out).

20. Jun 2, 2013

### timmdeeg

Yes, therefore I was quite astonished to learn that according to Bojowald, see "Once Before Time", the matter production increases during inflation and ends up with the matter the CMB shows, provided the expansion was constantly accelerating. It would mean that the whole matter we see was created by the effect of tidal forces on the vacuum during inflation.

There is no hint that this is proposed by LQG, instead he argues with tidal forces. I have searched for some more background information, but not successful so far.

Would this mean that the quantity of created matter does not grow propertional to the volume?

Last edited: Jun 2, 2013
21. Jun 2, 2013

### Chalnoth

Well, in a sense this is sort of correct, but certainly the matter production at the horizon can't be a part of this increase (that would require an increase in the energy density of the inflaton...I've never heard of an inflation model that posited that).

Rather, the matter production at the horizon (through Hawking radiation) should decrease as inflation progresses, but with a big increase at the end coming from the decay of the inflaton field, not from horizon radiation.

Anyway, it sounds like there is something major being lost here in translation, because as stated so far in this thread, it doesn't make much sense to me at all.

22. Jun 2, 2013

### timmdeeg

In the black hole case matter antimatter particles are created and separated everywhere due to tidal forces (increasingly towards the singularity) whereby the event horizon takes care that the BH radiates. The pairs inside don't contribute.
In contrast the inflation is homogeneous/isotropic and thus the pair production and their separation fills the universe homogeneously.

23. Jun 2, 2013

### Naty1

24. Jun 2, 2013

### Naty1

I believe it was Mordred who recommended the following papers on particle production....I did not keep the discussion link...and have not read them yet....I have read elsewhere that there are some characteristics NOT diluted during inflation...analogous to PArker's abstract comments.... and don't understand how that compares with Chalnoth's post above:

Up until this point I had thought particles were produced continually during inflation.

http://arxiv.org/pdf/1205.5616v1.pdf

Leonard Parker
Physics Department, University of Wisconsin-Milwaukee, Milwaukee, WI 53200, USA
E-mail: leonard@uwm.edu
Abstract. I describe the logical basis of the method that I developed in 1962
and 1963 to deﬁne a quantum operator corresponding to the observable particle
number of a quantized free scalar ﬁeld in a spatially-ﬂat isotropically expanding
(and/or contracting) universe. This work also showed for the ﬁrst time that particles
were created from the vacuum by the curved space-time of an expanding spatially-ﬂat FLRW universe. The same process is responsible for creating the nearly scale-invariant spectrum of quantized perturbations of the inﬂation scalar ﬁeld during the inﬂationary stage of the expansion of the universe…..

Stimulated creation of quanta during inflation and the observable universe
http://arxiv.org/abs/1106.4240
Ivan Agullo, Leonard Parker
(Submitted on 21 Jun 2011)

Inflation provides a natural mechanism to account for the origin of cosmic structures. The generation of primordial inhomogeneities during inflation can be understood via the spontaneous creation of quanta from the vacuum. We show that when the corresponding stimulated creation of quanta is considered, the characteristics of the state of the universe at the onset of inflation are not diluted by the inflationary expansion and can be imprinted in the spectrum of primordial inhomogeneities. …

25. Jun 2, 2013

### Mordred

I can't recall which thread either I've posted those articles a few times.

This thread also has some decent articles. Posted by Marcus (Steinhard) but in particular by Cristco. The arxiv paper "Inflationary encyclopedia" is a pedagonal review of numerous inflationary models to observational evidence using the slow roll aproximation as a standard.

included is Higgs inflation; chaotic eternal inflation, false vacuum; hill inflation, natural inflation etc.
the paper constrains the viable
inflation models to around 60.

this book in particular is an excellent resource for understanding quantum and classic feilds. Whats also nice about it is that its free for distribution and presented in a textbook style. If your interested in learning fields its a handy book to work through.

Last edited: Jun 2, 2013