Pre-inflationary spatial curvature

[timmdeeg]

Prior to expansion the inflaton field had a large potential energy. I wonder whether there are any considerations or calculations to evaluate how to this energy curves the space created by the big bang.

Does it make sense at all to talk about critical vs. actual energy density, the value of the Hubble-Parameter, any time dependence of the scale factor, ... regarding that era?

The big bang was hot and dense. Was does this mean, having in mind that the decay of the inflaton field into particles and radiation happened later? Naively but probably wrong I would say hot and dense means positive curvature. But perhaps, as the nature of said scalar field isn't known, one can only speculate.

Dense should mean pressure. Was there already negative pressure or only later, when the expansion was driven exponentially?

 

[Naty1]

I think you are asking questions that so far have mostly speculative answers...


edit: seems so,

...the nature of said scalar field isn't known, one can only speculate.

from an earlier discussion in these forums [which I did not record]...


Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 7 Sep 2012)
http://arxiv.org/abs/1209.1609

Since the standard inflationary paradigm is based on quantum field theory on classical space-times, it excludes the Planck era. Using techniques from loop quantum gravity, the {inflationary} paradigm is extended ….. from the Planck scale to the onset of slow roll inflation, covering some 11 orders of magnitude in energy density and curvature. This pre-inflationary dynamics also opens a small window for novel effects, e.g. a source for non-Gaussianities, which could extend the reach of cosmological observations to the deep Planck regime of the early universe.

This strong repulsive gravitational force due to quantum geometry is a pre inflationary dynamic applicable from a Planck scale big bounce to the onset of slow roll inflation.

2009 perspective from Steve Carlip that may offer interesting possibilities:


The Small Scale Structure of Spacetime
http://arxiv.org/PS_cache/arxiv/pdf/...009.1136v1.pdf


Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional.

Stephen Hawking and George Ellis prefaced their seminal book, The Large Scale
Structure of Space-Time...

At much smaller scales, on the other hand, the proper description is far less obvious….Indeed, it is not completely clear that “space” and “time” are even the appropriate categories for such a description….Over the past several years, evidence for another basic feature of small-scale spacetime has been accumulating: it is becoming increasingly plausible that spacetime near the Planck scale is effectively two-dimensional. No single piece of evidence for this behavior is in itself very convincing, and most of the results are fairly new and tentative. But we now have hints from a number of independent calculations, based on different approaches to quantum gravity, that all point in the same direction...

 

[timmdeeg]

Naty 1, thanks for your answer and the quotations. I wonder whether some knowledge regarding the nature of said scalar field would help to determine the curvature of that era. Perhaps not, because that's Quantum Regime.

 

[Naty1]

Here are some other related notes I have:

Wikipedia LQC: [Loop Quantum Cosmology]

The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of LQG. In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low space-time curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction and thereby resolving singularities of general relativity. ... In LQC the big bang is replaced by a quantum bounce...

In quantum geometry a discrete formulation leads to a repulsive force at the Planck scale
http://en.wikipedia.org/wiki/Quantum_geometry
http://en.wikipedia.org/wiki/Loop_quantum_cosmology

and there is a rather involved discussion here:
[not too much on curvature...]

Cycles of time--Penrose says his cyclic cosmology obeys thermodynamics.
https://www.physicsforums.com/showthread.php?t=427567&highlight=cycles+time+roger+penrose

...did not look to see who posted this:

I came across this argument in the book The Nature of Space and Time, which is based on a series of lectures given by Hawking and Penrose. Although it relates to Penrose's Weyl curvature hypothesis (WCH), it does not depend on it, and that, to me, makes it a lot more interesting, since I wouldn't bet a six-pack on the validity of the WCH.

As a preliminary, Penrose observes that (in my possibly inaccurate paraphrase):

(1) The Big Bang was not a generic state. A generic Big Bang state would have had a large Weyl curvature, but the universe we see looks nothing like the one that would have resulted from such an initial state. Our Big Bang appears to have had a small or even vanishing Weyl curvature.

(2) The evolution of our universe has led to a state with nonvanishing Weyl curvature. (At black hole singularities, we even have diverging Weyl curvature.)

 

[timmdeeg]

Thanks again.

Let's neglect for the moment any pre-inflationary spatial curvature, assuming it doesn't exist or isn't definable.

Then another question arises:

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

A de Sitter universe is a cosmological solution to Einstein's field equations of General Relativity which is named after Willem de Sitter. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to correspond to dark energy in our universe or the inflaton field in the early universe. According to the models of inflation and current observations of the accelerating universe, the concordance models of physical cosmology are converging on a consistent model where our universe was best described as a de Sitter universe at about a time t = 10^{-33} seconds after the fiducial Big Bang singularity, and far into the future.

So, as the inflation is driven by vacuum energy (the decay of the inflaton field into matter happened at its end) the inflationary universe should be spatially flat, like the de-Sitter universe. Then however, if the inflationary universe is flat anyhow it seems there is no need to argue that due to inflation any pre-existing curvature is flattened out. What do I misunderstand?

 

[Naty1]

10^-33 seconds is about the end of the inflationary era...by then things were apparently pretty flat...I don't know further details about how quickly they 'became flat' during infltion but from discussions in these forums I believe most cosmologists think things were rather highly gravitational, that is spacetime as best we can describe it, was highly curved...asymptotically 'infinite'...before inflation. As already posted, it seems it can be repulsive...maybe two dimensional...whatever that means...

Another view:
Wikipedia LQC: [Loop Quantum Cosmology]

The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of LQG. In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low space-time curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction and thereby resolving singularities of general relativity

In another paper, Guth, Ashtekar say:

Mathematically "..., to obtain the expression of the quantum constraint, one has to first introduce an operator representing curvature of the gravitational connection...An improved Hamiltonian constraint operator is introduced
...This strong repulsive gravitational force due to quantum geometry is a pre inflationary dynamic applicable from a Planck scale big bounce to the onset of slow roll inflation. ... The imposition of the quantum constraint on the homogeneous sector leads one to interpret the background scalar field φ as a relational or emergent time variable with respect to which physical degrees of freedom evolve...the scalar field was shown to serve as an internal clock, thereby providing a detailed realization of the ‘emergent time’ idea

You can interpret this as well as me...
I take it to mean,
"perhaps space and [emergent] time are not at all what we classicaly think they are" or

"we didn't even find time, all we could find was a scalar field that can be interpreted to act as such..."

"Our model ends up with a finite start [bounce] but still appears to replicate current large scale cosmological observations..."

I checked Alan Guth's INFLATIONARY UNIVERSE, my copy 1997...Epilogue

The explorations of variations on the inflationary theme as continued...roughyl 50 different forms of inflation have been studied...double,triple, hybrid inflation, not to mention mutated hybrid inflation, titled hybrid inflation,...cosmologists have also studied inflation that is gravity driven,spindriven, string driven, and vector field driven, as well as inflation that is warm, tepid, and natural.

He goes on to say he worked with Lisa Randall, Harvard, and they had trouble naming a new version of inflation she invented...several names they tentatively picked were already taken and they didn't even know it...[LOL]

I checked Lisa Randalls Book WARPED PASSAGES, 2005 [ which has discouraged me from reading further about particle physics...goodbook, but just too many particles, I got indigestion]

All I could find of direct interest [not very illuminating] :

At Planck scale energy, gravity constructs barriers that make conventional quantum merchanical calculations impossible..the incompatability of QM and gravity also reveals itself itself though non sensical predictions for high energy interactions...of the graviton...

I'm concluding others haven't posted because [a] it's somewhat unsettled science, I haven't said anything too crazy yet...so I better stop.

 

[bapowell]

The vacuum energy of the inflaton field drives the universe towards flatness. The general idea being that the curvature prior to inflation is unimportant; once the inflaton potential energy comes to dominate a region of spacetime, that region inflates and approaches flatness.

 

[timmdeeg]

once the inflaton potential energy comes to dominate a region of spacetime, that region inflates and approaches flatness.

In this view which is the usual one the 'flattening-out' develops over time due to the exponential growth of the scale-factor.

In the other view, mentioned by Wikipedia the inflationary universe behaves like de-Sitterer (empty with a positive cosmological constant only) and thus is spatially flat per se, no development over time.

Is this just a semantic difference?

 

[bapowell]

Pure de Sitter is flat, but inflation is not quite pure de Sitter. In order for inflation to be a dynamical process (start, proceed, end), the vacuum energy must vary (so, not a cosmological constant.)

 

[Naty1]

For those interested, some insights I found interesting here:
from a prior discussion in these forums...

Inflation for Beginners
http://www.lifesci.sussex.ac.uk/home/John_Gribbin/cosmo.htm#Inflation

 

[timmdeeg]

In order for inflation to be a dynamical process (start, proceed, end), the vacuum energy must vary (so, not a cosmological constant.)

Just to make sure that I understand you correctly. Provided the energy density consists exclusively of vacuum energy, then the space is flat during the whole dynamical process, you mentioned . Because flatness depends on the existence of vacuum energy in this case, not however on it's amount. Would this be correct?

 

[bapowell]

Yes. A universe filled with nothing but cosmological constant is flat regardless of the magnitude of this constant.

 

[timmdeeg]

Ok, thanks.

 

[Naty1]

the concordance models of physical cosmology are converging on a consistent model where our universe was best described as a de Sitter universe at about a time t = 10^{-33} seconds after the fiducial Big Bang singularity, and far into the future.

Just to confirm what I think bapowell is implying, that's a misleading statement...not very accurate...in fact it seems refuted by comments later in the article...and that article is critiqued by wikipedia itself...

seems a lot more accurate to state the final stage of the universe will be asymptotically deSitter.