Mass of the Universe: Dark Energy, Inflation & Observations

[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.

 

[Mordred]

Obviously, the Hawking radiation with a temperature which is proportional to its surface gravity on the event horizoncan give some insight on the deep relationship between gravity and thermodynamics. Indeed, the thermodynamics of black hole has already been constructed with the Bekenstein entropy of a black hole [3–6]. Note that, the Hawking radiation is usually investigated from the eventhorizon of a stationary black hole. In fact, it can also be obtained from the cosmological horizon of a spacetime such as the cosmological horizon of de Sitter spacetime.



Therefore, Hawking radiation may also exist in a FRW universe. By considering that the FRW universe is also a spherical symmetric spacetime and with an apparent horizon, therefore, the above discussion on the apparent horizon of dynamic spherical symmetric black hole spacetime can be generalized to the FRW universe.

the above is two quotes from the Hawking radiation in an FRW universe. The paper later shows the tunnelling via the cosmological horizon.

 

[timmdeeg]

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...

I agree and don't remember that I said something different. The particle separation correlating to tidal forces is a picture, which Bojowald and others are using.

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.

I am not sure about your point. Do you say there is no pair production inside the event horizon?

Of course, matter/radiation can't escape.

 

[Naty1]

My post #17


timedeeg posts

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

my reply

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...

I should have clarified that the particle production a/w event horizons does NOT involve matter/anti matter particle separation...As stated elsewhere that is a heuristic non mathematical 'intuitive' explanation.

A better way to think about it is this: [These are from several prior discussions, quotes from various experts here, that I put together to form a bigger perspective

There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields

..The expansion of geometry itself, especially inflation, can produce matter.
Other theoretical cases of geometric circumstances create real (not virtual) particles, like Hawking radiation at a BH horizon and Unruh radiation caused by an accelerating observer. With the Unruh effect, it is theorized that two adjacent observers, one inertial and one accelerating will measure different temperatures and make different counts of particles. In other discussions in these forums, there are theories that at the Hubble radius the accelerating Hubble Horizon is sufficient for the production of particles.

[Apparently Hubble and event horizon coincide for exponential inflation.]

Quantum fluctuations in the inflationary vacuum become quanta [particles]
at super horizon scales. ...The evolution of quantum fluctuations, from their birth [at Planck Scale] in the inflationary vacuum and their subsequent journey out to superhorizon scales where they become real life perturbations, is perhaps my favorite calculation in physics.

Here is how those last two circumstances can be thought to produce particles, without particle/aniparticle separation:

An unbounded quantum ['particle'] perturbation is not detectable as a real particle...it is a wave, a field, everywhere to infinity... The emergence of an event horizon bounds that perturbation and causes a detectable particle to emerge...one of finite wavelength...only certain frequencies/wavelengths are allowed...analogous to a loosely waving string...fix the ends and you can create detectable excitations...sounds...Or via quantum mechanics, put a particle in a box...or a potential well...and decrease the size of the container or change the potential of the well... new excitations emerge...frequencies are 'confined' via harmonic oscillations according to the potential or box size...make the container smaller
and Heisenberg uncertainty causes momentum increases...