Decelerated Expansion

The currently understood chronology of the universe has two periods of deceleration after inflation, the radiation-dominated era and the matter-dominated era.

The radiation-dominated era was very short at about 47,000 years, during which the value of the equation of state parameter w=1/3.  Using the equations discussed in Equations for Cosmological Expansion, we find that dH_RE/dt=-2H² and H=1/(2t).

The matter-dominated era extended from 47,000 after the Big Bang to about 4 billion years ago, during which the equation of state parameter w=0.  Using the equations discussed in Equations for Cosmological Expansion again, we find that dH_ME/dt=-3H²/2 and H=2/(3t).

In Inflation, I conclude that having an expansion in the order of 10²⁶ over the 10^-32s available would require a Hubble parameter value of H=~10⁶¹km/s/Mpc.  This is about the same magnitude of Hubble parameter as in the first unit of Planck time.  So, if the deceleration was from that value, it would be as if the clock had been turned back to t=t_PL, so by about 10^-32s.  After that, the expansion of the universe during the radiation-dominated era would be at half pace, H=1/(2t), expanding by half the speed of light, for 47,000 years, reaching about 23,500 light years in radius in addition to the approximately 10^-10 light seconds it was at the end of the inflationary era.  If everything went back to “normal” then (with H=1/t), then the universe would be 23,500 light years smaller than we would have expected, but this is a small fraction of the expected 13.77 billion light years (~0.00017% smaller, or basically indistinguishably smaller).

Then, in the matter-dominated era, the expansion of the universe would be at a rate of 2/3 of the speed of light, for a period of approximately 9.8 billion years, resulting in a radius of about 6.6 billion light years (swamping any delta caused by inflation for 10^-32s or slower expansion during 47,000 years of radiation-dominated era).

The combined effect would look like this, using the same notion as per the Inflation post (approximately):

The H value at the end of that process would be approximately that expected at about 14.7 billion years (assuming a constant H=1/t), or 66.5km/s/Mpc.

To get to where we would expect to be today, assuming a constant H=1/t over 13.77 billion years, it would look like this:

This would imply that a radius at 13.77 billion light years would be receding away from us at about 1.8 times the speed of light.  However, that if objects at (r_H=)13.77 billion light years remove were receding away at 1.8 times the speed of light, that is equivalent to H=128km/s/Mpc, which is not what we measure.  Note however, that this here illustrates a period of faster expansion, not of expansion that accelerates.  I will look at the dark-matter-dominated era with what appears to be accelerated expansion next.

Equations for Cosmological Expansion

I am going to get to a discussion on accelerated expansion in a later post, but I want to get into the equations now for use in both that discussion and one on “decelerated expansion”.  Unfortunately, it’s just the nature of the beast that I have to jump the gun on myself a little when I do this.  It’s also the case that easily accessible explanations are somewhat disparate being split across many webpages.  So, what I intend to do is bring a number of threads together in one place.

Here, it is stated that:

The acceleration equation describes the evolution of the scale factor with time

 

Then, later, it is stated that:

The most important property of dark energy is that it has negative pressure (repulsive action) which is distributed relatively homogeneously in space.

From this it follows that:

Assuming a flat universe (which is consistent with measurements) and noting that a flat universe is always flat, ρ=ρ_c=3H²/8πG.  So:

To be clear, a here is the scale factor and ä is the second time derivative of that scale factor.  An a with a single dot is the first time derivative of the scale factor and is used to defined the Hubble parameter:

The scale factor relates the change in proper distance between two objects over time, using the equation x(t)=a(t)x_o, or a(t)=x(t)/x_o, where x_o is the distance at some reference time (notionally t_o).

Note that there is a more easily generated notation for first and second time derivatives, namely da/dt and d²a/dt².  The widespread use of d to mean distance and ä to mean d²a/dt², where a is usually acceleration (or d²x/dt²), does not help things.  It’s almost like the people involved want to unnecessarily complicate things.  Rewriting the equation above using this notation:

Also,

So

In other words, the Hubble parameter gives us the speed of recession of an object, say a galaxy, divided by the distance of that object.  The use of the scale factor is just a minor complication of this concept.  (The most recent equation there is just a restatement of Hubble’s Law.)

At one point in the past, cosmologists were so convinced that the expansion of the universe was decreasing, they created a “deceleration parameter”, q, where:

And

 We know that, if H=1/t, then dH/dt=-1/t²=-H².  From this, we can see that if dH/dt=-H².b, where b is a constant, then H=1/(t.b).

Using the acceleration equation above, and the definition of the Hubble parameter:

 Therefore:

 Which implies that:

This Hubble parameter equation is invalid where the equation of state parameter w=-1, but note that if w=-1, then dH/dt=0, meaning that H=H_ic, which is to say some initial constant value and the acceleration involved is enough to precisely balance the inherent deceleration as t increases.  Note that normally, I’d use the subscript _o, but in this instance H_o is the value of the Hubble parameter today, not at some initial time.

There are effectively three zones established around two points, w=-1 and w=-1/3.

If w<-1, then it is understood that there is “phantom energy” which will lead to an eventual Big Rip.  The value of dH/dt becomes positive meaning that value of H increases with time.  This is what would happen with the value of H, assuming a current value of H=71 at 13.77 billion years and w=-1.03:

 

Precisely when the Big Rip happens depends a little on the magnitude of the delta-t (dt) used.  The larger the delta used, the further away the Big Rip seems, but it appears to be in the order of about 300 billion years away as dt approaches a unit of Planck length.  The time left before a Big Rip halves, approximately, if we use an equation of state parameter value of w=-1.06 and extends out towards infinity as the equation of state parameter approaches w=-1.

If w=-1/3, then we’d have the simple equation H=1/t, which would look like this:

 

As w→-1 from above, that curve would become less steep, approaching a flat line at the opening value (set at 71).

 

For values of w>-1/3, the curve would become steeper, for example:

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Since H=(dx/dt)/x, if H=1/t, then H=c/r_H, where r_H is the Hubble radius (or Hubble length).  The implication of this is that there is a horizon receding away at the speed of light.  If, however, H=1/(2t), that horizon would be receding away at half the speed of light, and so on.

Note that while it is generally said that the radiation-dominated and matter-dominated eras have “decelerated expansion”, this is a little inaccurate.  Expansion is slower in those eras, but in reality for a given state of equation parameter w=-1, the rate of expansion is fixed and for higher values of the equation of state parameter the rate at which the Hubble parameter decreases is accelerated.

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So, in brief:

• w<-1 – H increases until (eventually) an asymptotic point is reached, and the universe ends in a Big Rip.

• w=-1 – H remains constant.

• -1<w<-1/3 – H would decrease relatively gradually, at a greater rate as w→-1/3.  Effectively, it would be as if time were progressing more slowly, and “future” values of H would be reached later than would have been the case than when w=-1/3.

• w=-1/3 – H∝1/t, so that the Hubble parameter is related to the age of the universe.  It would be equal to the inverse age of the universe if it were always the case that w=-1/3, otherwise it would be equal to the inverse of the universe plus some offset related to the initial time that w=-1/3 and the value of H at that time.

• w>-1/3 – H would decrease more rapidly, increasingly so as the value of w increased. Effectively, it would be as if time were progressing more rapidly, and “future” values of H would be reached earlier than would have been the case than when w=-1/3.

More Inflation - the Inflaverse

There seem to be at least two ways of viewing inflation.  There is the inflationary epoch, which I talked about in the imaginatively titled post Inflation, and then there is eternal inflation.  In the first, you have our universe beginning shortly before the Big Bang (for reasons unknown) and, in the second, you have what I call the inflaverse, which is a greater universe in which inflation goes on forever for the most part and our universe (“the universe”) condenses out of it due to some mechanism.  We’d not be the only universe, so this is a form of multiverse theory (or rather the multiverse is an apparently unavoidable consequence of the model).  So you would have the multiverse consisting of a multitude of universes that are totally disconnected (sorry MCU fans) immersed in an eternally inflating inflaverse.

 

A mechanism by which our universe could condense out of the inflaverse was raised in Does Inflation have a Homogeneity Problem?  An event of vacuum decay (or collapse) could lead to a bubble of spacetime that is not inflating but instead is expanding out at the speed of light.

 

Note that the time of the inflaverse would not be the same as the time of the universes that it spawns.  It would be reasonable to think of universal time as orthogonal to inflaversal time, in which case we could find ourselves in a situation in which the bubble of spacetime that expands out from the vacuum decay event would expand in both a positive and negative direction (with those assignments being arbitrary).

 

To remain flat (so that the density equals the critical density), the twin universes would accrue mass-energy at a rate equivalent to one unit of Planck mass per unit of Planck time, divided equally between the two.  Or as modified by periods of deceleration and/or acceleration (since the mass-energy density is related to the Hubble radius).

 

In the following posts, I am not going to consider the inflaverse version of inflation in the first fraction of a second of our universe.  I’m going to assume that however it happened, at the beginning of the radiation-dominated era the conditions are such that either could have happened immediately prior.

Inflation

This, and the following posts, are expansions on and clarifications of the concerns raised at Avoiding a Contravention of the Extended Consistency Principles.

During the inflationary epoch, between 10^-36s after the Big Bang and approximately 10^-32s later, it is understood that the universe expanded by a factor of at least e⁶⁰=~10²⁶.

In my hypothesis of universal expansion, as described in earlier posts and occasionally referred to as FUGE – Flat Uniform Granular Expansion, the radius of the universe expands by 1 unit of Planck length every unit of Planck time.  A FUGE universe, at 10^-36s after the Big Bang, would have had a radius of 10^-36 light seconds.  In that case, at the end of an inflationary epoch with expansion by a factor of 10²⁶, that universe would have a radius in the order of at least 10^-10 light seconds (which is about 30mm).

There are widely varying estimates for how large the universe was before and/or after inflation.  Some say the size of a grapefruit (after), Alan Guth says a marble (after), some say it was almost infinitesimally small at the beginning (in the order of a Planck length, making the post inflation size in the order of 10^-5 m – diameter or radius, it doesn’t really matter which), and a Forbes article says that the universe was about two AUs across at 10^-12s after the Big Bang (which would imply inflation by a factor of 10¹⁵).

Note that, for the universe to remain flat, this would result in the introduction of a quite substantial amount of mass-energy, equivalent to 10¹⁸ kg (or about 1/10³⁴ of the total mass today) in a period of about 10^-32s, or 10⁵⁰kg/s.  Compare this with the current rate, assuming an age of the universe of 13.77 billion years and H=71km/s/Mpc, of 2.02x10³⁵kg/s.

If, at the end of an inflationary epoch with an expansion by a factor of 10²⁶ in 10^-32s, the universe flipped back to FUGE – that is flat uniform granular expansion, then the universe today would be … pretty much indistinguishable from what we observe.  It would have a radius that is 3cm greater than we would expect in purely FUGE universe, which larger by a factor of about one part in 10²⁷ and the density would be greater by 10^-61kg/m³ (or by one part in 10³⁴), both of which are practically unmeasurable.

So, basically, perhaps inflation happened.  Perhaps it didn’t.  But either way, if the universe otherwise expanded in accordance with the FUGE hypothesis, it could be just as it is observed today.  We could enormously simplify the scenario, by imagining two straight lines with the combined equation r=±ct (t is along the horizontal axis, r is along the vertical axis, c is a conversion factor [and the speed of light]):

This is for values of t between 0 and 20.  Say that we introduce some “inflation” at t=2, then we get:

When we consider a range of t=[0,20], the inflation looks obvious, even with inflation in the order of only 10³.  But when we consider massively greater values of t, we begin to see that the curves are indistinguishable from r=±ct, with t=10⁶:

If we used equivalent scales, it would be inflation of 10²⁶ at t=2 and a final value of t=10⁴³, we get this:

 

This is totally indistinguishable from r=±ct, for sufficiently high values of t (anything above the square root of the order of magnitude of the inflation would be sufficient, assuming that the inflation happens sufficiently early).

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There are two broad options for what would have happened to the Hubble parameter during an inflationary period.  Either its value snapped to a single value for about 10^-32s, enough to expand the universe out by a factor of 10²⁶ and then relaxed back to some much lower value, or the equation of state parameter flipped below w=-1 for about 10^-32s and then back to above w=-1.

The single value of H required would be enough expand x=10^-36 light seconds into dx=10^-10 light seconds in dt=10^-32 seconds.  Recalling from the previous post that:

We find that H=~10⁵⁸/s=~10⁶¹km/s/Mpc.

If it is a question of the equation of state parameter flipping to below w=-1, then the value needed would be around w=-1.00003 because H is already incredibly high at 10^-36s. But it would have to flip back pretty much instantaneously or it would overshoot.  That is to say, the conditions in the universe that manifest an equation of state parameter of w=~-1.00003 would need to able to change, everywhere in the universe, simultaneously (because you get an inhomogeneity problem otherwise), within less than 10^-33s (or the universe is ripped apart).  Of course, the value of the equation of state parameter could ramp down and ramp back up again to get the amount of inflation that we need, but again you have a simultaneity problem which is precisely what inflation is trying to avoid (see Does Inflation have a Homogeneity Problem?).

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Note that while the above indicates that, were inflation to have happened, it would be unlikely that we would be able to observe any effect so far as the size or density of the universe goes, there are arguments out there that inflation is not necessary in the first place.  Recall that inflation was introduced as a concept to explain why the cosmic microwave background is so uniform.  There is a paper that argues that gravity is all that is needed to explain homogeneity of the universe and another that argues that an “anti-cosmos” would negate any requirement for inflation.  The latter was referenced at the end of Half a Problem Solved, where I quoted the statement "a CPT-respecting universe naturally expands and fills itself with particles, without the need for a long-theorized period of rapid expansion known as inflation".

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After the inflationary epoch, it is understood that there were two periods of decelerating expansion, the radiation-dominated era and the mass-dominated era, and then the current, dark-matter-dominated era in which the expansion of the universe is understood to be accelerating.  I’ll take a look at these soon, but first I need to introduce the equations for cosmological expansion and then I need to touch on the inflaverse (as raised in Does Inflation have a Homogeneity Problem?).

Avoiding a Contravention of the Extended Consistency Principles

In the previous post, I concluded that there is an apparent contravention of what I called the extended consistency principles and asked whether that contravention might be resolved?  I think it might.  To explain, I need to beg the indulgence of the reader, to just go with me in the scenario below (at least until I mention Sean Carroll).  There are some issues that might come up, a few of which I am already aware of and have resolved, but I can address them at a later stage.

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Let us say that there are two conjoined volumes, joined at a null point.  Initially, they are infinitesimally small (ie tending towards zero volume, perhaps even at zero volume) and empty.  Imagine that we can look very, very closely at these volumes at an angle such that they appear to be two areas, purely for illustrative purposes, as below.  (Alternatively, you could imagine a variant of the image illustrating the history of the universe show in the previous post, extending downwards as well as upwards. Just don’t include the exponential curvature.) 

 

Let us say then, that we allow a certain amount of mass-energy into these volumes over the smallest meaningful period of time.  Say that amount is one unit of Planck mass-energy over one unit of Planck time and let us share the mass-energy evenly between the two volumes. 

 

Let us also say that, with every unit of Planck time, the radius of each volume increases by one unit of Planck length.

The equations for Planck mass, Planck time and Planck length are as follows:

This means that after one Planck time, there are (notionally) two tiny volumes of V=4/3.π.l_p³ inside each of which is half a Planck mass (½m_p).  That means there’s a (notional) density of:

After a certain number of Planck times, let us say ꬱ=8.0619x10⁶⁰, the density will be:

Now, these values are:

Planck time – t_P = 5.39x10^-44 s

Gravitational constant – G =6.674x10^-11 m³/kg/s²

Pi – π = 3.14159 (-ish)

Plugging them in, we get 9.47x10^-27 kg/m³.  This is precisely the critical density calculated for of our universe – at this time.  It should be noted that there are other values given, such as by NASA (in 2013), who gave the critical density as 9.9 x 10^-30 g/cm³ but note that they also say that “WMAP determined that the universe is flat, from which it follows that the mean energy density in the universe is equal to the critical density”.  Most of the results that come up, when you search for <<most recent value of the density of the universe>>, are for the critical density, but given that the consensus is that the universe is flat, then the density and the critical density are the same anyway.

Note also that, expressed in energy density, this is 0.85133x10^-9 J/m³ (which is approximately the estimated value for vacuum energy, at 10^-9 J/m³).

The only question of course is: what is 8.0619x10⁶⁰ Planck times in more recognisable units?  It is, of course, 13.77 billion years – the age of our universe as calculated by WMAP.

I just want to summarise here for a moment and make some comments.

In the previous section, I indicated that it would appear that (given the inflationary model of cosmology) we are in a privileged era, because the Hubble parameter is roughly equivalent to the age of the universe.  There are some related facts, so these can’t be thought of as additive coincidences: the universe is (currently) flat, which means that the density is equal to the critical density and the density of the universe is equivalent to the density of a Schwarzschild black hole with a radius of the age of the universe multiplied by the speed of light (which is a consequence of the universe being flat).

However, if the expansion of the universe is currently accelerating (and went through exponential expansion early), then there would not have been any era in the past nor will there be any era in the future when the density would be critical, unless something very strange was happening with the quantity of mass-energy in the universe.  Note that, in the link to Sean Carroll’s article on why we are not inside a black hole, he notes (without support or clarification, unfortunately) “that a spatially flat universe remains spatially flat forever”.  This aligns with the extended consistency principles, but the inflationary cosmological model doesn’t – again unless something odd is happening with mass-energy.

Fortunately, something odd is happening with mass-energy, basically that energy changes when spacetime changes – which is to say that density of the mass-energy of the universe is maintained at the critical density or, as the universe increases in size, the amount of energy increases (at what rate is not explained by Carroll).

Note that this does not mean that the laws of conservation of energy and momentum are broken in such a way that you can get free energy.  What it does mean is that the notion of allowing 1 unit of Planck mass-energy into the universe per unit of Planck time is not a contradiction of existing laws of physics.  Existing laws of physics already imply that mass-energy is being added at rate necessary to ensure that the universe remains flat.

That said, the way that mass-energy would need to enter the universe in order to keep an inflationary/accelerated expansion universe flat (noting that “a spatially flat universe remains spatially flat forever”) would not be consistent.  What we would see is an initial period of exponentially accelerating increase in the mass-energy (well above one unit of Planck mass-energy per unit of Planck time), the rate would then slow down for a while (to less than one unit of Planck mass-energy per unit of Planck time) and then, later, resume a more leisure acceleration (reaching a rate today that is, coincidentally, one unit of Planck mass-energy per unit of Planck time) and, according to predictions, continue to accelerate (to eventually significantly exceed one unit of Planck mass-energy per unit of Planck time).

Perhaps, if the rate of mass-energy entering the universe is entirely governed by rate of expansion (whatever that may be at the time), then I guess that flatness could be maintained.  However, it would not be such that the amount of energy in the universe were proportional to the age of the universe, ever, except for right now.  And the rate at which mass-energy enters the universe would never equal one unit of Planck mass-energy per unit of Planck time, except for right now.  Which puts us back in the situation of being in a privileged era.

There is another issue that I touched on only very lightly.  I pointed out that the critical density, right now, expressed in terms of energy density, is 0.85133x10^-9 J/m³.  In what has been referred to as “the worst theoretical prediction in the history of physics”, quantum field theory calculates a value for the vacuum energy that is 120 orders of magnitude higher than measured (which is in the order of 10^-9 J/m³, and thus in the order of critical density but expressed in terms of energy rather than mass).

Purely out of curiosity at the time, a while ago, I pondered what the energy density would be after the very first unit of Planck time and used my method to get the answer 5.5331x10¹¹² J/m³, which is (approximately) 6.4994x10¹²¹ times higher than currently measured (or within spitting distance of 120 orders of magnitude).  It may come as no surprise to some that this multiplier is the square of 8.0619x10⁶⁰ which the more keen-eyed will remember is the value I assigned to ꬱ above and is the number of units of Planck time in 13.77 billion years.  So again, we look like we might be in a privileged era (since some argue that the vacuum density is invariant and this coincidence would therefore only occur right now).

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We would not, however, be living in a privileged era – if we were to be living in a two volume universe with smooth consistent expansion, at one unit of Planck length per unit of Planck time, with one unit of Planck energy entering per unit of Planck time (divided equally between the volumes).  If that were the case, then we get the results that we observe without needing to contravene the extended consistency principles.  No matter where or when an observer found herself observing the universe, the universe would be at critical density (which would the density of a Schwarzschild black hole with a radius equal to the age of the universe at the time observed multiplied by the speed of light), a Hubble parameter value that would be the inverse of the age of the universe, the rate at which mass-energy entering the universe would always be one unit of Planck mass-energy per unit of Planck time and, I fully expect, the vacuum energy would be in the ball-park of the critical density (the most significant difference being the units in which they are expressed).

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The very keen eyed will notice that I use the symbol ꬱ rather than the more easily found æ.  Initially, I took this out of the equation generated in Word, because the rendering looks pretty awful but I have since resurrected it for consistency (which I had lost having inadvertently reverted to using the easy option in later articles).

I prefer ꬱ because it hints at age with the a, along with a reflection of it extending into the other direction, as an echo of the notion of two equal but opposite universe halves, extending in different directions from the same null point (without necessarily being perfect reflections of each other). 

Does Inflation have a Homogeneity Problem?

Inflation is proposed as a solution to the horizon or homogeneity problem.  The problem is the cosmic microwave background (CMB) is extremely homogenous, pretty much the same no matter which direction you look despite the areas we are looking at not having been in anything near close proximity since 300,000 years after the Big Bang about 13.77 billion years ago.  That is to say, these regions that we are looking at are not “causally related”.

 

The generally accepted solution to the problem is that from about 10^-36s after the Big Bang, during a period of about 10^-32s, the universe expanded by a factor of at least 10²⁶.  (These are folds of expansion, so I am reading it as the radius is increased by that factor.  If they are talking about volume, then the radius increases by about 10⁹, but the sizes generally talked about imply radius, for example Guth estimates that universe could have been about marble size after inflation starting from one billionth the size of a proton and this is consistent with talking about the radius.)

 

Recall that nothing travels faster than light (in space) which is part of the reason that we have the horizon problem with causally independent patches of the sky looking the same.  But if space is expanding as fast as proposed for the inflationary epoch, then the pre-CMB isn’t going to be causally related then either - so how was the slowdown of the exponential inflationary expansion orchestrated?  It would have to be exquisitely fine-tuned so that the smoothness we see today is maintained or some bits of space would be expanding slightly faster than others during the slowdown.  It’s not like there’s a mechanism that can operate on the entire universe simultaneously because there is no simultaneity per Relativity.  Even if there were a notional code to expand this much for this long and no longer, there’s a problem in assuming that all the notional clocks would remain precisely in sync.

 

Perhaps there’s an answer to this, but it’s not immediately obvious to me.

 

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I posted a version of this question to Reddit at r/AskPhysics and got a couple of interesting responses.

 

The first, from Aseyhe, pointed at the graceful exit problem and the models designed to avoid it.  I still have a problem with the array of (notional) clocks all ticking in sync while the inflaton field evolves to a point where inflation stops, simultaneously, everywhere (in our universe, but not in the greater “inflaverse”, a term that I can’t find anywhere else, but by which I mean the portion of an eternal inflation universe is still evolving, retaining the term “universe” to refer more easily to what we might otherwise need to refer to as “our universe”).  Any deviation from perfect simultaneity of the deceleration process, given the rate of inflation (equivalent to about H=10⁶⁰), would have led to gaping holes in the CMB.  The poster u/Aseyhe was confident that the (notional) clocks would tick in unison because they would not deviate from the state that they were in “before inflation scattered them”.  I can understand that, but the CMB is not perfectly homogenous and isotropic, there’s reason to believe that there could have been zones in which time would have been progressing slightly differently due to admittedly miniscule irregularities in the distribution of mass-energy.  Look at the CMB to see what I mean (from ESA where you can download a more detailed image):

The accompanying text reads:

 

The anisotropies of the Cosmic microwave background (CMB) as observed by Planck. The CMB is a snapshot of the oldest light in our Universe, imprinted on the sky when the Universe was just 380 000 years old. It shows tiny temperature fluctuations that correspond to regions of slightly different densities, representing the seeds of all future structure: the stars and galaxies of today.

 

Now, it’s true that the CMB is from 380 thousand years after inflation is thought to have ended, but to avoid an inhomogenous CMB the homogeneity and istropy at the beginning of inflation would not just have to have been “pretty good”, it would have to have been perfect.  And it’s that that I struggle with.  I do understand that we are talking about 10^-36s after the Big Bang (although that concept once we bring the inflaverse into the discussion seems a bit rubbery), but recall that 10^-36s is in the order of about a billion units of Planck time.  A billion iterations of anything would seem enough to introduce slight inhomogeneities.

 

Then there was turnpikelad, who talked about the end of inflation being the same thing as false vacuum collapse.  I think “similar to” or “driven by” would be better than “the same thing as” since false vacuum decay (rather than collapse) is the sort of thing behind potential ends of the universe, such as proton decay (and eventual heat death).  It’s also thought, by some, to be the driver behind cosmic inflation, which would align better with what turnpikelad seemed to be saying.

 

Anyway, the intriguing notion raised by turnpikelad was that “the inflaton field can collapse at any point at any time” and “(that) collapse spreads from that point in a perfectly spherical bubble at the speed of light”.  So a universe expanding with the speed of light, one which, after a period of 13.77 billion years would have a radius of 13.77 billion light years and, if the equation of state parameter w=-1/3, would have a Hubble parameter of about H=71km/s/Mpc and, if flat, would have a density equal to the critical density, which is the density that we appear to have.  Like our universe.

 

It's not precisely the universe that I imagined at Imagine a Universe, but it’s another way to get to what we appear to have.  And I don’t see that it’s impossible to have a universe condensing from the inflaverse that spouts off into two equal but opposite time directions.  It’s even possible that the mirrored universes of the CPT symmetry model of Boyle, Finn and Turok might be compatible with being spawned from an inflaverse.