Inflation and negative pressure
The attractive gravitational force subsides and the universe continues to expand at a rapid rate
About 7 billion years ago, ordinary gravitational attraction became weak enough for the universe’s repulsive forces to once again become dominant, and since then the rate of the universe’s expansion has been continually increasing. This was confirmed observationally in 1929, when the astronomer Edwin Hubble discovered that whichever way he looked, every distant galaxy was moving away from us and each other, rather like raisins in rising dough. Furthermore, the rate of the galaxies’ recession was proportional to their distance. For example, galaxies 100 million light-years away are moving at about 5.5 million miles per hour, those that are 200 million light-years are moving twice as fast and so on.[1] Hubble’s observations have allowed astronomers to calculate a precise expansion rate for the universe, known as the Hubble constant which has since been refined to a precision of 3%[2] (± 0.11 Ga[3]). Hubble’s discovery that the universe is expanding has been described as one of the great intellectual revolutions of the twentieth century[4].
What were the contributing factors behind this expansion?[5]
The answer lies in the equations of General Relativity. Regular mass-energy (galaxies, stars, planets) will cause the universe to contract, but uniform energy and negative pressure yield repulsive gravity, and by including pressure as a source for gravity, Einstein opened up the possibility that a system with very large negative pressure could have zero or even negative gravitational mass that repels instead of attracts. Regions with slightly more energy - those with slightly more mass (via E=mc²) - exert a slightly stronger gravitational pull, attracting more particles from their surroundings and growing larger, evolving into galaxies and the stars within them. In fact, the very existence of galaxies, stars, planets and life itself derives from microscopic quantum uncertainty amplified by inflationary expansion, but without the presence of this extra mass in sufficient quantity, the uniform energy and negative pressure of a quantum field (or cosmological constant) results in a repulsive gravity driving things further apart.
As we will see when looking at general relativity in more detail (at /converting-the-thought-experiment-into-mathematical-equations.html and /the-cosmological-constant-and-the-expansion-of-space.html), Einstein’s original equation looked something like this: Gμν = 8πTμν where the left hand side refers to the geometry of spacetime - its curvature at a given point - and the expression on the right describes the distribution of the energy and momentum of spacetime. In other words, the equation describes how the distribution of matter and energy determines the curvature of spacetime.
If you find these concepts difficult to grasp, then you are in good company. Einstein himself was unhappy that his equations showed that the universe was expanding - essentially because of the relative absence of matter which would otherwise have exerted a gravitational pull. This offended his understanding of a fixed, static, unchanging universe, which everyone “knew” to be the case merely by looking skywards at night. Bear in mind that in Einstein’s early years, the existence of galaxies other than our own was unknown. Einstein wanted to keep the universe he grew up with – the static, stable majestic cosmos of Newton. This was the way people of the early twentieth century thought of the universe, as a placid, unchanging system[6]. But his equations needed a little help to achieve this object because in their pure form they suggested this model of the universe would be unstable.
So he inserted into his equations a carefully crafted calculation governing gravity’s repulsive push – a constant, lambda (Λ), whose value he admitted was “at present unknown” - so that his equation now came out looking something like:
Gμν – Λgμν = 8πTμν. This constant exactly balanced its attractive side thereby resulting in the desired static universe he was seeking. This theoretical construct was discredited some years later by Hubble’s observations that the universe was indeed expanding.
In Newton's law of gravity, pressure plays no role - the strength of gravity depends solely on mass. In Einstein's law of gravity, however, the strength of gravity depends not just on mass but also on acceleration, energy density and pressure. In this way, pressure has two effects: direct (caused by the action of the pressure on surrounding material) and indirect (caused by the gravitation that the pressure creates). Negative pressure, also known as a “false vacuum”, pulls instead of pushes much like a stretched rubber band. It has vacuum energy: energy that is present even in apparently empty space thereby creating a repulsive force. So a false vacuum is like a vacuum (i.e. no ordinary matter or radiation), but it has this extra energy density p which is a constant. Its mass energy is proportional to its volume through E=mc², which means that it also has a gravitational effect on the expansion of the universe, but the effect of vacuum energy is the opposite of that of matter. Matter causes this expansion to slow down and can eventually stop and reverse it. On the other hand vacuum energy causes the expansion to accelerate, as in inflation, acting just like Einstein’s cosmological constant.
Most hot gases have positive pressure. The kinetic energy of the motion of the atoms and radiation pushes outwards on the container housing it, say a balloon, but an implosive gas has negative pressure, and a balloon containing such a gas would collapse inward, because the outside pressure (zero or positive) would exceed the inside pressure (negative). But imagine now the whole of space filled with an implosive gas. There is no bounding surface and no external pressure. The gas still has negative pressure, but it has nothing to push against, so it can exert no direct effect. It has only the gravitational effect – that is, repulsion. The repulsion stretches space, increasing its volume and, in turn the amount of vacuum energy. The tendency to stretch is therefore self-reinforcing and the universe expands at an accelerating pace.
Where does the energy come from?
The best known possibility is that it is inherent in the fabric of space, and even if a volume of space were utterly empty - without any matter and radiation - it would still contain this energy. All this is inherent in Einstein’s equations.
Reduced to its mathematical essentials, in Einstein's law of gravity the sign of the gravitational force is determined by the algebraic combination of the total energy density plus three times the pressure (three because there are three dimensions of space): in other words g (gravity) = energy density (p) + 3 x the pressure (P). If the pressure is positive, as it is for ultra-relativistic material such as light, radiation, photons, neutrinos and matter from the early universe (all moving at the speed of light) and to a lesser extent ordinary matter (moving at much less than the speed of light), the combination is positive and gravitation is attractive. But if the pressure is sufficiently negative, it can cancel out the energy density, nullifying gravity in the process like the cosmological constant; and if the pressure is negative and bigger still, then the sign of the gravity-generating term in Einstein's equation actually reverses, and if it drops below the proportion of 1:3, instead of gravity attracting, it repels. Vacuum energy meets this condition, provided its density is positive. This is a consequence of the law of conservation of energy, according to which energy cannot be destroyed[7].
In the end, Einstein had to fall back into line after corroborative evidence that the universe was indeed expanding was provided by technology in the form of Hubble’s telescope. He thereafter considered his ‘cosmological constant’ his greatest mistake and hoped everyone would forget the whole sorry episode, and for a time everyone did, but the inflationary cosmology model brought to life in the 1980s revealed that although Einstein was correct on the basic principle behind the notion of a cosmological constant, gravity’s negative or repulsive strength turned out to be far greater than the so-called ‘constant’ he had so carefully constructed [8].
Another take
Let's have a look at what another informed observer has to say.
As Carlos Calle points out [9], in Newton’s universe normal attractive gravity comes from the masses of the planets, stars, and galaxies, but in Einstein’s universe, the planets, stars, and galaxies attract each other with additional gravity from all the forms of energy that they have and from the positive pressures that they exert. In 1917, when Einstein was developing his model, no one knew about negative pressure, but his equations told him that negative pressure was a possibility. Without negative pressure, which produces repulsive gravity, Einstein’s universe — like Newton’s — could collapse, but if the universe had the right amount of this antigravity, it would counterbalance the pull of gravity, preventing the universe’s collapse and maintaining its “perfect, static equilibrium”.
- That’s what Einstein's cosmological constant accomplished.
By adding this term, Einstein’s universe became filled with this exotic form of energy that created antigravity and maintained the universe in balance. For Einstein, the cosmological constant exerts a repulsive gravitational force: it creates antigravity. If Einstein hadn’t included the term in his equations, he would’ve realized that to prevent the gravitational collapse, the stars in the universe had to be moving away from each other. He would’ve predicted the expansion of the universe 12 years before Hubble discovered it! [10]
- The key to how the cosmological constant works is the contribution to gravity from negative pressure.
The negative pressure, which creates repulsive gravity, is constant throughout the universe; it doesn’t decrease with distance, like the part of gravity that comes from ordinary matter does, and it doesn’t need the presence of matter or energy to operate. The cosmological constant operates in empty space - it’s a property of empty space.
- The rate of expansion of the universe depends on a battle between two giants: the attractive and the repulsive parts of gravity.
As the universe expands and the galaxies move farther apart, the attractive part of gravity decreases. However, the repulsive part of gravity is the same throughout the universe and stays fairly constant even with the expansion. Which part wins out depends on how close the galaxies are to each other.
When our universe was starting out, its galaxies were closer together than they are now. As a result, regular attractive gravity was much stronger than repulsive gravity and held the galaxies more tightly together, slowing the universe’s expansion. But after some time — about 5 billion years — the galaxies were far enough apart for the attractive part of gravity to decrease and match the strength of the repulsive gravity. At this point, the two cancelled each other out; galaxies no longer felt gravitational force of any kind from other galaxies, but, even with no gravitational force, the galaxies kept moving away from each other, according to Newton’s first law.
- Reviving the Cosmological Constant: Einstein Was Right After All
Something is pushing the galaxies apart now. Some source of energy is fuelling the expansion of the universe. And it permeates the universe. What can it be? It turns out that the best way to explain the runaway expansion of the universe is with Einstein’s cosmological constant.
So, the cosmological constant fills the universe with repulsive gravity — just what’s needed to speed up the expansion.
The key to how the cosmological constant works is the contribution to gravity from negative pressure. The negative pressure, which creates repulsive gravity, is constant throughout the universe; it doesn’t decrease with distance, like the part of gravity that comes from ordinary matter does. And it doesn’t need the presence of matter or energy to operate. The cosmological constant operates in empty space; it’s a property of empty space. [11]
And as we now know, since the universe was about 7 billion years old, its expansion rate has in fact been speeding up, and that something with negative mass and negative gravity - dark energy, the cosmological constant, something akin to Hubble’s constant, call it what you will – appears to be the culprit.
The governing principles behind negative pressure and repulsive gravity are also succinctly illustrated in the following graph:
Explanation: Whether a lump of energy exerts a
gravitationally attractive or repulsive force depends on its pressure. If the
pressure is zero or positive, as it is for radiation or ordinary matter,
gravity is attractive. (The downward dimples represent the potential energy
wells.) Radiation has greater pressure, so its gravity is more attractive. For
quintessence, a dynamic quantum field not unlike an electrical or magnetic
field, the pressure is negative and gravity is repulsive (the dimples become
hills).
Source: “Quintessential Universe”, Scientific American, January 2001 by Jeremiah P. Ostriker and Paul J. Steinhardt: http://dhushara.freehosting.net/book/upd/aug201/cos4.htm
A sidelight
An interesting sidelight to all of this is that Hubble appears to have been entirely ignorant of Einstein's theory. At least there is no evidence that he was cognisant of it. As Bill Bryson says, he was a much better observer than a thinker[12]. It was in fact a Belgian priest-scholar by the name of Georges Lemaître (1894-1966) who was the first to marry up Einstein's theoretical work with Hubble's observations and produce his own Big Bang theory of the origin of the Universe, which he called his "hypothesis of the primeval atom" or the "Cosmic Egg"[13].
Lemaître was also the first to postulate what is now known as Hubble's Law and made the first estimation of what is now called the Hubble's constant, which he published in 1927, two years before Hubble's. It would take the inadvertent discovery of the Cosmic Background Microwave Radiation by Penzias and Wilson in 1964 before the Big Bang theory achieved a status among scientists which may be described as respectable, but as so often happens too little of the credit has devolved upon the Belgian priest who was the first to propound it theoretically.
[1] Green (2005), 219.
[2] Edward J Weiler, Hubble – A Journey through Space and Time, Abrams, New York, 105.
[3] Ga (for gigaannum), is a unit of time equal to one billion years: 109 years (one billion on the short scale, one milliard on the long scale). It is commonly used in scientific disciplines such as cosmology and geology to signify extremely long time periods in the past. For example, the formation of the Earth occurred approximately 4.57 Ga (4.57 billion years) ago.
[4] Hawking, 39; Greene (2005), 229.
[5] For the following explanation, see http://www.physicsforums.com/archive/index.php/t-91108.html, contribution by stevebd1; also “Repulsion in Einstein Theory of Gravity”: http://bustard.phys.nd.edu/Phys171/lectures/repulse.html.
[6] John Farrell, The Day Without Yesterday, Lemaître, Einstein, and the Birth of Modern Cosmology, Thunder's Mouth Press, New York, 2005, 31.
[7] As per [5] above.
[8] Greene’s colourful description in The Fabric of the Cosmos (2005). In 1931 Einstein removed the constant from his theory for good. Seventy years later, to explain the data from measurements of supernovae, astronomers restored it: Robert P. Crease, The Great Equations – Breakthroughs in Science from Pythagoras to Heisenberg, Norton, New York, 2008, Ch 8, p 200, fn 34.
[9] Einstein For Dummies, (Kindle Locations 4974-4984), Wiley 2005 Kindle Edition.
[10] Ibid, Kindle Locations, 4969-4970.
[11] Ibid, Kindle Locations, 5031-5043.
[12] Bill Bryson, A Short History of Nearly Everything, Broadway Books, 2003, 131.
[13] https://en.wikipedia.org/wiki/Georges_Lemaître
Source: “Quintessential Universe”, Scientific American, January 2001 by Jeremiah P. Ostriker and Paul J. Steinhardt: http://dhushara.freehosting.net/book/upd/aug201/cos4.htm
A sidelight
An interesting sidelight to all of this is that Hubble appears to have been entirely ignorant of Einstein's theory. At least there is no evidence that he was cognisant of it. As Bill Bryson says, he was a much better observer than a thinker[12]. It was in fact a Belgian priest-scholar by the name of Georges Lemaître (1894-1966) who was the first to marry up Einstein's theoretical work with Hubble's observations and produce his own Big Bang theory of the origin of the Universe, which he called his "hypothesis of the primeval atom" or the "Cosmic Egg"[13].
Lemaître was also the first to postulate what is now known as Hubble's Law and made the first estimation of what is now called the Hubble's constant, which he published in 1927, two years before Hubble's. It would take the inadvertent discovery of the Cosmic Background Microwave Radiation by Penzias and Wilson in 1964 before the Big Bang theory achieved a status among scientists which may be described as respectable, but as so often happens too little of the credit has devolved upon the Belgian priest who was the first to propound it theoretically.
[1] Green (2005), 219.
[2] Edward J Weiler, Hubble – A Journey through Space and Time, Abrams, New York, 105.
[3] Ga (for gigaannum), is a unit of time equal to one billion years: 109 years (one billion on the short scale, one milliard on the long scale). It is commonly used in scientific disciplines such as cosmology and geology to signify extremely long time periods in the past. For example, the formation of the Earth occurred approximately 4.57 Ga (4.57 billion years) ago.
[4] Hawking, 39; Greene (2005), 229.
[5] For the following explanation, see http://www.physicsforums.com/archive/index.php/t-91108.html, contribution by stevebd1; also “Repulsion in Einstein Theory of Gravity”: http://bustard.phys.nd.edu/Phys171/lectures/repulse.html.
[6] John Farrell, The Day Without Yesterday, Lemaître, Einstein, and the Birth of Modern Cosmology, Thunder's Mouth Press, New York, 2005, 31.
[7] As per [5] above.
[8] Greene’s colourful description in The Fabric of the Cosmos (2005). In 1931 Einstein removed the constant from his theory for good. Seventy years later, to explain the data from measurements of supernovae, astronomers restored it: Robert P. Crease, The Great Equations – Breakthroughs in Science from Pythagoras to Heisenberg, Norton, New York, 2008, Ch 8, p 200, fn 34.
[9] Einstein For Dummies, (Kindle Locations 4974-4984), Wiley 2005 Kindle Edition.
[10] Ibid, Kindle Locations, 4969-4970.
[11] Ibid, Kindle Locations, 5031-5043.
[12] Bill Bryson, A Short History of Nearly Everything, Broadway Books, 2003, 131.
[13] https://en.wikipedia.org/wiki/Georges_Lemaître