Mass of the Universe: Dark Energy, Inflation & Observations

[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.

 

[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.

 

[HowardTheDuck]

Thanks for your reply.

 

[timmdeeg]

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?

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.

 

[Chalnoth]

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?

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.

 

[HowardTheDuck]

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.

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?

 

[phinds]

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?

As I understand it, you are wrong.

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

 

[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.

 

[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.

 

[phinds]

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

.

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?

 

[Naty1]

Howard:

... 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?

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:

Inflation answers the classic conundrum of the Big Bang cosmology: why does the universe appear flat, homogeneous, and isotropic in accordance with the cosmological principle when one would expect, on the basis of the physics of the Big Bang, a highly curved, heterogeneous universe?

and further along:

Motivations
Inflation resolves several problems in the Big Bang cosmology that were discovered in the 1970s.[14] Inflation was first discovered by Guth while investigating the problem of why we see no magnetic monopoles today; he found that a positive-energy false vacuum would, according to general relativity, generate an exponential expansion of space. It was very quickly realized that such an expansion would resolve many other long-standing problems#. These problems arise from the observation that to look like it does today, the universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation attempts to resolve these problems by providing a dynamical mechanism that drives the universe to this special state, thus making a universe like ours much more likely in the context of the Big Bang theory.

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

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

 

[timmdeeg]

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.

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!

 

[Chalnoth]

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?

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.

 

[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.

 

[Chalnoth]

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.

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

 

[timmdeeg]

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

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.

 

[Naty1]

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

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...

 

[Mordred]

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.

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

 

[Chalnoth]

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.

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.

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

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).

 

[timmdeeg]

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.

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.

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.

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

 

[Chalnoth]

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.

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.

 

[timmdeeg]

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.

How about this version?:

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.

 

[Naty1]

There is an excellent discussion of particle production here:


https://www.physicsforums.com/showthread.php?t=590798&page=2

Particle creation in an accelerating Universe?

 

[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:

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.

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. …

 

[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.

https://www.physicsforums.com/showthread.php?t=688176

this book in particular is an excellent resource for understanding quantum and classic fields. 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.

 

[timmdeeg]

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. …

Very interesting article, thanks.

 

[Chalnoth]

How about this version?:

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.

It's not quite that simple either, though, because the Hawking radiation at the cosmological horizon is observer dependent, rather like the radiation from the Unruh effect.

 

[Chalnoth]

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. …

Right. These two descriptions are how I understood it: the horizon particle production is a source of perturbations, not a source of the matter that is around today.

 

[Naty1]

edit: I see Chronos posted while I was composing...beat me by 1 minute!

I posted above:

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

and the first Parker paper confirms that...

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

…inflationary expansion of the universe leads to a spectrum of perturbations that can seed the cosmic inhomogeneities we observe today….It has been argued that the exponential expansion during inflation will dilute any possible quanta present in the initial state …..However, as first pointed out in [references provided in the paper] the gravitationally-induced spontaneous creation of quanta in a general expanding universe is accompanied by the corresponding stimulated process if there are quanta already present in the initial state. The stimulated creation process during inflation is governed by the same quantum amplification factor as is responsible for the spontaneous creation of quanta of the perturbation field from the vacuum. This amplification factor grows enormously during inflation and compensates for the dilution of the quanta initially present, keeping their average number density constant during inflation…..

So I definitely don't understand Chronos post yet:

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.

One possibility: stimulated 'quanta' maybe different than 'matter' ??

 

[Naty1]

My understanding [flawed though it may be!] originated with this insight:


It's from bpowell, pst # 17, linked to previously in this thread,

https://www.physicsforums.com/showthread.php?t=590798
Particle production in an accelerated universe

Gravitational particle production by accelerated expansion is what gives rise to the primordial perturbations (except in modern parlance we no longer speak of particles, but fluctuations.) The idea is usually pitched in terms of particle/anti-particle pairs that pop out of the vacuum, only to get pulled apart by the rapidly inflating background. Eventually they are pulled outside the horizon, never to meet again. Of course, this description has the same conceptual shortcomings as the description of the Hawking effect in terms of particle/anti-particle pairs -- it isn't quite right.

The easiest way to "see" how inflationary spacetimes lead to particle production (more precisely, have a de Sitter temperature), is to observe that physical length scales, λ∼a(t) , grow at a faster rate than the Hubble scale, d H ∼H −1 when the universe is accelerating (w<−1/3 )

d dt (d H λ )=d dt (1 aH )∝1+3w

In the case of pure de Sitter expansion, H = const, so that d H is shrinking in comoving coordinates and the above expression is < 0. Physically, the λ here is the wavelength of a Fourier mode comprising a quantum fluctuation: once it gets stretched so that λ>d H , it becomes frozen-in as a classical perturbation.

That's the quick story. It's a nice exercise though to work through the evolution of a scalar field fluctuation during inflation, from its birth in the vacuum out to superhorizon scales if you haven't done it. What you find once you've done this is that you end up with a spectrum of perturbations across a range of length scales. For a massless scalar, you find that the amplitude of the fluctuation at horizon crossing is H/2π . This should look familiar.

 

[Naty1]

To Mordred [just a lighthearted note]

The arxiv paper "Inflationary encyclopedia" is a pedagonal review of numerous inflationary models to observational evidence using the slow roll aproximation as a standard.

If that is this...

Encyclopaedia Inflationaris

Jerome Martin, Christophe Ringeval, Vincent Vennin
(Submitted on 15 Mar 2013)

I want to complain...its 300 PAGES! OMG!

Listen up, Mordred, this is a hobby, not a lifecourse for me...I am too old for that...I need time to argue with the wife, walk my Yorkies, drink some wine, and continue cutting down trees leaned by Hurricane Sandy here in the northeast US from last October...

 

[Mordred]

Lol the fields book is longer. The inflationary article took me a couple of weeks to read I'm still working on the fields book along with a thesis paper from a forum member

what I find makes the inflation article handy is the listing of the various equations involved in each inflation model. As well as the brief explanations of each.

helps sort through the a lot of the garbage and misunderstandings from the web.

 

[timmdeeg]

It's from bpowell, pst # 17, linked to previously in this thread,

https://www.physicsforums.com/showthread.php?t=590798
Particle production in an accelerated universe

The easiest way to "see" how inflationary spacetimes lead to particle production (more precisely, have a de Sitter temperature), is to observe that physical length scales, λ∼a(t) , grow at a faster rate than the Hubble scale, d H ∼H −1 when the universe is accelerating (w<−1/3 )

d dt (d H λ )=d dt (1 aH )∝1+3w

In the case of pure de Sitter expansion, H = const, so that d H is shrinking in comoving coordinates and the above expression is < 0

That goes more into details but seems in accordance with Bojowald's popular science book. H = const means that during inflation the universe expanded exponentially.

 

[Mordred]

the attached article has some of the involved perturbation theory including slow roll approximation

the link below comes from this thread
https://www.physicsforums.com/showthread.php?t=680932

it covers Unruh/hawking radiation and cosmological horizons

https://www.physicsforums.com/attachment.php?attachmentid=57177&d=1364417183

unfortunately one file I wanted to upload is too big so I'll hunt for a copy of it online :inflationary constraints"

edit: that was easy to find as its an arxiv article "Planck results constraints on inflation"
http://arxiv.org/abs/1303.5082

I may have other perturbation related articles in my 12 GB archive of pdf files, when I get a chance I'll dig around and see if any are worth mentioning

these two are more a historical reference the first is by Copeland the second is Guth's pbs personal site on false vacuum.

http://arxiv.org/abs/astro-ph/9401011
http://www.pbs.org/wnet/hawking/mysteries/html/uns_guth_1.html

this one may come in handy can't recall the details though lol
http://arxiv.org/abs/1007.4044v3
Hawking radiation from the cosmological horizon in a FRW universe

that looks like the main ones of interest from my data base anything further would be repeat information

 

[Naty1]

timedeeg:

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.

This account misses the mark for at least two reasons. First the particle anti particle separation at a boundary is not a mathematically based phenomena...Hawking himself used it as an intuitive way to describe quite different mathematics...and said so...and his actual explanation has been posted in these forums...

Bapowell:

The actual picture of the Hawking effect in terms of virtual particles is actually rather murky;... he instead examined the asymptotic transformation of a field fluctuation brought in from far away, past a black hole, and back out to very far away. If the initial field fluctuation far away was in its vacuum state, the final fluctuation far away generally is not (as a result of its gravitational interaction with the black hole). John Baez has a nice write up about this:

http://www.weburbia.com/physics/hawking.html

Hawking's own words:

. Just
outside the event horizon there will be virtual pairs of particles, one with negative
energy and one with positive energy. The negative particle is in a region which
is classically forbidden but it can tunnel through the event horizon to the region
inside the black hole where the Killing vector which represents time translations
is spacelike. ... Instead of thinking of negative
energy particles tunneling through the horizon in the positive sense of time one
could regard them as positive energy particles crossing the horizon on pastdirected
world-lines and then being scattered on to future-directed world-lines by
the gravitational field. It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally."

So he offered two intuitive pictures...neither based on his own mathematical calculations.

Secondly, there is no matter within the event horizon ['towards the singularity']...and even if there were, nothing inside can get outside where we might observe it. As explained elsewhere by PeterDonis,my interpretation, if a phenomena isn't in the past lightcone of infalling matter/energy, it's not part of the black hole description. At least not as described by GR.