The Hubble Constant and Subatomic Particles

[Enola Straight]

It is a given that the universe is expanding at a rate proportional to the Hubble Constant...IIRC something like 70 ly per Megaparsec.

Galaxies are expanding away from each other at this rate, therefore, logically, objects inside these galaxies are also expanding at this rate
(but because they are closer to each other, not so far so fast)

What happens after a couple hundred billion or trillion years? Will space expand to such a degree that subatomic distances are affected? What happens if an electron gets too far from the atomic nucleus, or the quarks that make up protons and neutrons get too far from each other?

[Kuroneko]

It is a given that the universe is expanding at a rate proportional to the Hubble Constant...IIRC something like 70 ly per Megaparsec.

Ignoring some caveats, such as the Hubble constant not being constant or those being the wrong units, essentially yes.

Galaxies are expanding away from each other at this rate, therefore, logically, objects inside these galaxies are also expanding at this rate (but because they are closer to each other, not so far so fast)

Not necessarily. Gravitationally bound objects can not only remain bound, but even contract.

What happens after a couple hundred billion or trillion years? Will space expand to such a degree that subatomic distances are affected? What happens if an electron gets too far from the atomic nucleus, or the quarks that make up protons and neutrons get too far from each other?

If the expansion is due to the cosmological constant Λ, which can be re-interpreted as "dark energy" of pressure -Λ and energy density Λ (in units of of G=c=1), this will never happen. If Λ>0 and there is additional dark energy to lower the pressure-to-energy-density ratio below -1, this will occur.

[Feil]

Your second statement is incorrect, Enola.

Think of it as two small magnets next to one another (one galaxy) on a rubber sheet that's being stretched in all directions, and another two magnets a meter away (another galaxy). The attractive force of each pair magnets keeps them stuck together no matter how far we stretch the rubber sheet, but the distance between the two pairs is sufficiently great that whatever attractive force is present is insufficient to cause them to move towards one another faster than the rubber sheet expands between them.

Galaxies are stuck together on the universal rubber sheet by gravity; subatomic particals by electromagnetism and nuclear forces.

[Winston Blake]

Your second statement is incorrect, Enola.

Think of it as two small magnets next to one another (one galaxy) on a rubber sheet that's being stretched in all directions, and another two magnets a meter away (another galaxy). The attractive force of each pair magnets keeps them stuck together no matter how far we stretch the rubber sheet, but the distance between the two pairs is sufficiently great that whatever attractive force is present is insufficient to cause them to move towards one another faster than the rubber sheet expands between them.

Galaxies are stuck together on the universal rubber sheet by gravity; subatomic particals by electromagnetism and nuclear forces.

What if said magnets are stationary relative to each other, e.g. Earth not being sucked into the Sun? I think he's actually got the basic idea of the Big Rip:

First, the galaxies would be separated from each other. Arguably, this is what is happening right now, with galaxies that move outside the observable universe (approximately 13.7 billion light years away). About 60 million years before the end, gravity would be too weak to hold the Milky Way and other individual galaxies together. Approximately three months before the end, the Solar system will be gravitationally unbound. In the last minutes, stars and planets will be torn apart, and an instant before the end, atoms will be destroyed.

[Kuroneko]

The problem is that the big rip cannot occur if the Hubble constant is actually a constant. It needs to be accelerated for it to work.

[SyntaxVorlon]

The problem is that the big rip cannot occur if the Hubble constant is actually a constant. It needs to be accelerated for it to work.

Which can occur as it's really a parameter, which is why we can take the big rip seriously.

But as far as the short term goes, that is the next 10^15 maybe 10^20 years, if I remember correctly, the universe will be fine.

[Admiral Valdemar]

Kuroneko, with your massive physics addled brain, what is your thought on the Hubble Constant (or not, as the case may be)?, since I hear that the cyclical universe model would explain the matter-energy being reset, but the "constant" diminishing.

In fact, what does that even mean? Will there be a point when the constant is zero and the supposed infinite cycle ends?

[kheegster]

Kuroneko, with your massive physics addled brain, what is your thought on the Hubble Constant (or not, as the case may be)?, since I hear that the cyclical universe model would explain the matter-energy being reset, but the "constant" diminishing.

In fact, what does that even mean? Will there be a point when the constant is zero and the supposed infinite cycle ends?

The Hubble 'constant' is simply a value for the expansion of the Universe at the present time. At different periods of the universe this value was different, off the top of my head something like

H^2 = H0^2(omega_m*a^-3 + omega_r*a^-2 + omega_lambda*a^-1)

for a flat universe, where H is the Hubble parameter, H0 the Hubble constant and a the scale factor of the universe (taking the convention that a = 1 at the present time).

As for the cyclic universe models, I'm unaware of the Hubble contant having any special properties at all, and AFAIK the cycle is indeed infinite, at least for the Steinhardt-Turok models. I have a stack of papers on this that I have to read, so I'll have to get back to you in a few days....

[Admiral Valdemar]

That's what I'm having trouble understanding. I read somewhere that the same Steinhardt-Turok universe cycle was infinite, but that the H number was diminishing over time, as each cycle was reset. That doesn't make a whole lot of sense to me, given it would seem to suggest a limit to the number of cycles any one brane can have before it's kaput.

If the value did change, then that would imply the expansion varies with each incarnation of the universe, rather than, say, changing over the period of one universe cycle.

I'll have to read up on that again, because it may just be me mixing two string theories together in my head.

[kheegster]

That's what I'm having trouble understanding. I read somewhere that the same Steinhardt-Turok universe cycle was infinite, but that the H number was diminishing over time, as each cycle was reset. That doesn't make a whole lot of sense to me, given it would seem to suggest a limit to the number of cycles any one brane can have before it's kaput.

If the value did change, then that would imply the expansion varies with each incarnation of the universe, rather than, say, changing over the period of one universe cycle.

I'll have to read up on that again, because it may just be me mixing two string theories together in my head.

No. Within each cycle the process is the same. In the current period we live in, the Hubble parameter is increasing as the expansion of the universe accelerates until the universe gets smoothed out and matter and radiation gets diluted into emptiness. But as the universe starts to reach the top of the potential well, the acceleration starts to slow down, i.e. the Hubble parameter starts to decrease until it hits zero and then goes negative as the universe starts contracting towards the Big Crunch. The Hubble parameter describes the expansion of the universe, nothing more.

Can you believe I have to give a talk on the Steinhardt-Turok model in 2 weeks?

[Admiral Valdemar]

So, I assume the Big Crunch is favoured rather than heat-death or the Big Rip here then. Has there actually been much more elucidation on what the true fate of the universe is then or is it still purely hypothetical with several possible endings?

[kheegster]

So, I assume the Big Crunch is favoured rather than heat-death or the Big Rip here then. Has there actually been much more elucidation on what the true fate of the universe is then or is it still purely hypothetical with several possible endings?

The Big Rip would not happen unless a 'cosmic fluid' with pressure < -energy density is found (dark energy has pressure = -energy density, while radiation has pressure = 1/3 * energy density), so it's a purely hypothetical concept with no evidence supporting it.

AFAIK the inflatory Big Bang theory makes no prediction regarding the fate of the Universe, whereas the Steinhardt-Turok model solves the problems that inflation was introduced to deal with (e.g. the horizon and flatness problems), yet predicts the history of the universe as a whole.

[kheegster]

I forgot to say... the Universe is observed to be flat, and since the expansion of the universe is currently observed to be expanding, we would expect the Universe to end up in heat death.

At present, there are no widely accepted models for the Universe which say otherwise.

[Kuroneko]

Which can occur as it's really a parameter, which is why we can take the big rip seriously.

It's possible, but there is absolutely no reason to think it is the case. Even just accelerated expansion is not enough--see the last part of my first post in this thread.

Kuroneko, ... what is your thought on the Hubble Constant (or not, as the case may be)?, since I hear that the cyclical universe model would explain the matter-energy being reset, but the "constant" diminishing. In fact, what does that even mean? Will there be a point when the constant is zero and the supposed infinite cycle ends?

I'm pretty sure that's not correct. IIRC, in the (non-singular) cyclic model, the dark energy decays, leading to a slowed expansion and eventual recollapse (which can be described by a Hubble parameter), but it is remade in the next cycle.

[Feil]

What if said magnets are stationary relative to each other, e.g. Earth not being sucked into the Sun?

Earth isn't moving fast enough to maintain an orbit any higher than this one. If you increased the distance between the Earth and the Sun (which, arguably, is being done all the time as the universe expands), Earth would fall right back into its orbit again. If the displacement were sufficient, Earth would fall into a new orbit, but its mean distance from the Sun would stay the same. Of course, since the increase in the amount of universe between the Earth and the Sun is both constant and very small, the orbit never changes at all--it's as though a very, very slight force were opposing the sun's gravity to a slight degree.

Alternately speaking, Earth is being sucked into the sun; we're just falling over the edge.

The Big Rip has already been covered.

[Enola Straight]

Due to the Hubble Constant...with farther-away galaxies receding from us faster than nearer galaxies...the observable universe has a kind of event horizon; at a far enough distance some galaxies ave a receding velocity equal to the relative speed of light.

If current universal models are correctin having an increasing expansion rate, then the lightspeed event horison would be closer.

Does this mean the universe is shrinking?

[kheegster]

Due to the Hubble Constant...with farther-away galaxies receding from us faster than nearer galaxies...the observable universe has a kind of event horizon; at a far enough distance some galaxies ave a receding velocity equal to the relative speed of light.

If current universal models are correctin having an increasing expansion rate, then the lightspeed event horison would be closer.

Does this mean the universe is shrinking?

Actually the definition of the cosmic horizon is the point where the recession speed of the distant object is c . So we'll get this effect even if there is no acceleration of the expansion.

Since the distance of to the cosmic horizon is about 13 billion light years (from d = c / H0, with H0 ~70km/s/Mpc), this is by coincidence about the age of the Universe, which suggests that we are near the turnover after which the visible universe shrinks.

[Kuroneko]

Not quite. The set of points at which the recession velocity is c is the Hubble sphere. The cosmological horizon is the boundary of observability. Those are not the same thing by far, although they can be. The misconception is probably due to an overemphasis on de Sitter spacetime, which is interesting but far from representative of all cases. However, since it's simple, I'll try to explain in terms of de Sitter rather anything more complicated.

Consider an observer taken to be at the origin in the standard de Sitter spacetime (Λ>0 vacuum). Since every spacetime is locally Minkowski, one can determine whether an object "sufficiently close" to the observer is comoving with it, and extend this process to get a family of observers defining the so-called "comoving coordinates". In these coordinates, lightlike geodesics toward the origin arriving at t = t_0 take the form of exponential curves r=T_0[exp(-t/T_0) - exp(-t_0/T_0)], so any object comoving with the observer disappears behind a horizon in finite proper time (the horizon is, of course, found in the limit of t_0→∞). In this sense, "the universe is shrinking", but this is very misleading.

In terms of (spatial) geodesic distance between the observer and the object, aka "proper distance", the distance increases exponentially without bound, according to R = R_1exp(t/T_0). In case of de Sitter spacetime, then, the Hubble sphere stays at a constant proper distance and actually coincides with the cosmological horizon. However, the Hubble parameter is constant in this spacetime. What if it's not? Then it is possible for the Hubble sphere to recede faster than lightspeed, making the cosmological horizon outside the Hubble sphere--in other words, superluminal objects become observable. This is quite natural in decelerating universes, but can also happen in accelerating universes.