Inflation

The theory of cosmic or cosmological inflation is related to Big Bang theory. It’s been around now for the thick end of forty years. Or more. By 1980 a lot of cosmologists were happy that the universe was expanding, and that it wasn’t a steady-state universe. A lot of cosmologists also thought of the initial expansion of the universe as something fairly steady. However inflation introduced the idea that the initial expansion was very rapid:

Image from Rod Nave’s hyperphysics

As for how it all began, see the 2014 New Scientist article big bang breakthrough: who is the father of inflation? It’s by Stuart Clark, who says Alexei Starobinsky published his theory of inflation in December 1979. Starobinsky’s paper was Spectrum of relict gravitational radiation and the early state of the universe. Whilst only four pages long it’s rather technical and it doesn’t use the word inflation. So it’s not surprising that it didn’t get much attention. As to whether Starobinsky was the first, see the 1991 Inflation for astronomers by Jayant Narlikar and Thanu Padmanabhan. They refer to William McCrea’s 1951 paper Relativity theory and the creation of matter. And to Demosthenes Kazanas’ 1980 paper Dynamics of the universe and spontaneous symmetry breaking. There’s more on Philip Cole’s blog entry the early stages of cosmic inflation where you can also see John Peacock saying the first inflation paper was by Erast Gliner in 1965. You can soon find a guest post on Luboš Motl’s blog by Phil Gibbs. It’s called Who should get the Nobel Prize for cosmic inflation? There’s a comment and a link to a Reddit page which says Andrei Linde ascribes the inflation idea to Gliner, and which links to the paper itself: algebraic properties of the energy-momentum tensor and vacuum like states of matter. Again it didn’t get much attention.

Guth gets tenure

Instead Alan Guth did. See his Wikipedia article for some history, and his 2007 paper Eternal inflation and its implications. He was an insecure postdoc who’d worked on grand unification theories. He knew that GUTs predict magnetic monopoles, and he knew about the monopole problem. He also attended a lecture by Robert Dicke on the flatness problem and a lecture by Steven Weinberg about GUTs and the early universe. Guth worked with his colleague Henry Tye on phase transition and supercooling and the expansion of the universe. Then he heard colleagues talking about the horizon problem, and came up with “his historic inflation breakthrough”. After his SLAC seminar of January 1980 entitled 10−35 seconds after the Big Bang, he had job offers galore. See his 1997 book The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. He gives an account on page 186: “I began the seminar by recounting the standard big bang theory and the magnetic monopole problem, reviewing Preskill’s arguments that indicated a large excess of monopole production. Then I described the work by Henry and me, showing how the monopole problem can be evaded by extreme supercooling. Finally I presented the inflationary theory, showing how it would solve not only the monopole problem, but also the flatness and horizon problems as well. The seminar went smoothly, although it ran one and a half hours, a half hour longer than scheduled”. Tye was in China for six weeks when this happened, hence Tye is the most important cosmologist you’ve never heard of. Guth is said to have said that if Tye had not gone to China for six weeks, in December 1979, he would have been a co-author on the first inflation paper. Interesting stuff.

Guth’s first inflation paper

Guth’s first inflation paper dates from August 1980. It was Inflationary universe: A possible solution to the horizon and flatness problems. He gave an overview of the horizon and flatness problems and talked about the standard model of cosmology, saying the universe is assumed to be homogeneous and isotropic and described by the Robertson-Walker metric. He also said the evolution of the scale factor R(t) is governed by the Einstein equations, he referred to conservation of energy, and he said “one also assumes the expansion is adiabatic”. He said the above equations must be supplemented by an equation of state for matter which can be approximated to an ideal quantum gas of massless particles. Then he said the horizon problem and the flatness problem could disappear “if the assumption of adiabaticity were grossly incorrect”, and instead one had a cooling universe where “bubbles of the low-temperature phase nucleate and grow”. He also talked about supercooling which leads to the release of latent heat, and said “in order for this scenario to work it is necessary for the universe to be essentially devoid of any strictly conserved quantities”.

Inflationary bubbles image attributed to Cosmology.com, see PhysOrg

Later on he said the assumption of a homogeneous isotropic universe means it would be senseless to talk about solving the horizon problem, because homogeneity was assumed at the outset. He also talked about grand unified models which tend to provide phase transitions which could lead to an inflationary scenario, and which include monopoles in their particle spectrum. He described these monopoles as “topologically stable knots in the Higgs field expectation value”. He finished with an appendix where he said some physicists are skeptical that there was a flatness problem, saying “to these physicists I point out that the universe is certainly not described exactly by a Robertson-Walker metric”. I would too. Particularly after reading Guth’s last sentence: “However, I am also sure that many physicists agree with me that the flatness of the universe is a peculiar situation which at some point will admit a physical explanation”.

Guth’s model didn’t work

I say that because another peculiar situation was that Guth’s model didn’t work, but nobody cared. He had bubbles forming in a supercooled environment which is the opposite of boiling, he was treating space like a liquid instead of a ghostly elastic solid, and he had nothing to curtail the exponential expansion. See the 2005 Symmetry magazine article the growth of inflation by Davide Castelvecchi. He quotes Michael Turner saying “one of the striking things about [Guth’s] paper was that he said ‘Look, guys, the model I am putting forward does not work. I can prove it doesn’t work. But I think the basic idea is really important’”.

GUT image from Symmetry magazine, see A GUT feeling about physics, artwork by Sandbox studio Chicago

Also see the Wikipedia eternal inflation article. It talks about false vacuum decaying into empty bubbles of true vacuum expanding at the speed of light, but in a universe expanding faster than light. Hence the bubbles couldn’t coalesce to reheat the universe. It goes on to describe how this “graceful exit problem” was solved by Andrei Linde, and by Andreas Albrecht and Paul Steinhardt.

Linde puts in a fix

Whilst Guth’s model didn’t work, that didn’t stop inflation. It was as if Guth had struck gold when he killed three problems with one blow, and the rush was on. First off the blocks was Andrei Linde with a new inflationary universe scenario in October 1981. Linde referred to Guth’s paper and said this: “Unfortunately, however, this scenario in the form suggested in ref. [12] leads to some unacceptable consequences, recognized by Guth himself and by other authors”. He talked about the energy of the bubbles becoming concentrated in their walls and thermalization occurring only after the collision of the bubble walls. He said for the flatness problem to be solved, the critical temperature should be 1028 times smaller than the temperature at which exponential expansion starts, but that no GUTs with such a fantastically small critical temperature have been suggested.

Fair use excerpt from Andrei Linde’s 1981 paper a new inflationary universe scenario 

He also said the bubble wall collisions would result in an inhomogeneous and anisotropic universe, contradicting cosmological data. Then he said he’d like to suggest an improved scenario employing the Coleman-Weinberg symmetry-breaking mechanism. This was proposed in 1973 by Sidney Coleman and Erick Weinberg in Radiative Corrections as the Origin of Spontaneous Symmetry Breaking. Linde’s crucial point or should I say fix, was that “the whole observable part of the universe is contained inside one bubble, so we see no inhomogeneities caused by the wall collisions”. However there’s a hint of handwaving when he said “one may argue that it is not very good to obtain an absolutely homogeneous universe, since in that case it would be difficult to understand the origin of galaxies”. And a puff of smoke and mirrors when he said “It is clear, however, that the baryon asymmetry generated by the decay of the Higgs mesons may be generated by the decay of the classical Higgs field vacuum”. Plus a whiff of ingratiation in “One may ask e.g. whether it is possible for the universe to be in a state with temperature Tc smaller than the Hawking temperature”. He ended up proposing an “improved” Coleman-Weinberg theory “in de Sitter space with the curvature R determined by the vacuum energy density”. Overall it all feels very abstract, and very very speculative. Especially when you know about lepton asymmetry and the mystery of missing antimatter.

Albrecht and Steinhardt get in the game

Andreas Albrecht and Paul Steinhardt finished their paper in January 1982. It was Cosmology for grand unified theories with radiatively induced symmetry breaking. They too referred to Coleman-Weinberg symmetry-breaking. They too talked about supercooling and bubbles. They said The decay of a metastable phase to a stable phase has been compared to a classical nucleation process. At T < TGUT there is a rate per unit time per unit volume, Γ(f), for producing finite sized fluctuations containing stable phase – bubbles – within the metastable system. Once produced, the bubbles grow, coalesce and convert the system to the stable phase”. They too talked about issues with Guth’s scenario, wherein the bubbles never coalesce. Then they said our universe would have to lie within a single rare bubble, whereupon it’s difficult to understand how its high entropy could have been generated. But they went on to say the homogeneity puzzle is solved along with the flatness puzzle, and there’s no reason to expect to find any monopoles. It’s similar to what Linde said and did, it was a fix. We now had “new inflation”, but it definitely feels like they were sweeping the problems under the carpet. Especially since there was no inhomogeneity left to account for the galaxies.

Another fix

But that was fixed too. Linde came up with a lot more papers, including one in May 1982 entitled Coleman-Weinberg theory and the new inflationary universe scenario. It’s just over four pages long, plus references, and now we’re seeing “small inhomogeneities, which are necessary for the galaxy formation”, and the “improved” Coleman-Weinberg theory. Linde also wrote a 44-page paper for the three-week June/July 1982 Nuffield workshop in Cambridge on the very early universe. Check out the Wikipedia inflation article and note the effects of asymmetries section: “the fluctuations were calculated by four groups working separately over the course of the workshop: Stephen Hawking; Starobinsky; Guth and So-Young Pi; and Bardeen, Steinhardt and Turner”. Hawking’s paper was the development of irregularities in a single bubble inflationary universe, and was just over two pages long. There are no calculations, just assertions. Like the universe is homogeneous because it’s all one fluctuation, but there are galaxies because of fluctuations. Only that doesn’t match the almost-uniform microwave background, hence “what is needed is a potential of a different form” and “such a potential might arise in a supersymmetric theory”. It’s clear that the physics has now turned into whack-a-mole. Regardless of what’s wrong with inflation, there’s always another fix, and the bandwagon rumbles on.

Eternal inflation

The inflation story continued with eternal inflation. That was proposed by Paul Steinhardt at the 1982 Nuffield workshop in a paper called Natural Inflation. He started by saying unlike the case for ordinary GUTs the Coleman and Weinberg models “result in enormous exponential expansion of the universe during the GUT phase transition without preventing the phase transition from being completed and homogenizing the universe”. He ended up talking about regenerative meta-cosmology: The resulting bubble inflates to a size much larger than our observed Universe. The interior is perfectly Robertson-Walker. Observers inside the bubble can never observe the bubble wall because the bubble expands at nearly the speed of light”. That’s a handy way to explain why there’s no observable evidence to support a hypothesis:

Multiverse artwork by Detlev Van Ravenswaay

There’s more along the same lines: “When a new bubble is formed, it regenerates a new Universe which can never contact our own. New Universes are regenerated forever because the Universe is only percolated (fractally) as time approaches infinity. (See Albrecht et al., 1982b for more elaborate discussions.) The regenerative scenario is probably the most surprising and radical cosmological possibility”. Steinhardt had invented the inflationary multiverse.

Chaos ensues

In 1983 Steinhardt along with James Bardeen and Michael Turner wrote Spontaneous creation of almost scale-free density perturbations in an inflationary universe. They said much of the work was done at the 1982 Nuffield workshop, and that the simplest model of “new inflation”, based on an SU(5) GUT with Coleman-Weinberg spontaneous symmetry breaking, is in obvious conflict with the large-scale isotropy of the microwave background. So, old inflation didn’t work, and nor did new inflation. Whack. They later said O’Raifertaigh-Witten-type supersymmetric potentials might yield the right kind of inflation, and the geometric hierarchy model of Dimopoulis and Raby is a potentially viable candidate for an ultimate model. The word inflaton was coined in 1983 in After primordial inflation by Dimitri Nanopoulos, Keith Olive, and Mark Srednicki. Also in 1983 Linde came up with chaotic inflation. He said the original problem of obtaining a sufficiently large inflation in the context of some natural theory of elementary particles does not seem to be a problem any more. Whack. He said classical field ϕ could have any “chaotic” value, but expansion means the universe becomes divided into many exponentially large domains containing an almost homogeneous field ϕ. He talked about an infinite open universe containing an infinite number of mini-universes in which life might exist:

Self-reproducing inflationary universe image from Andrei Linde’s inflation and string cosmology lecture 1, slide 31

He also said the chaotic inflation is different in that it wasn’t based on high-temperature phase transitions in the early universe. What it was based on escaped me. As did his reason for saying “This suggests that inflation is not a peculiar phenomenon which is desirable for a number of well-known reasons, but that it is a natural and may be even inevitable consequence of the chaotic initial conditions in the very early universe”. His inflation papers came thick and fast after that. They include Eternally Existing Self-Reproducing Chaotic Inflationary Universe from 1986. It’s more of the same, describing a universe without a beginning or end where inflation is continually occurring in one region or another. But it lacks any connection to real physics. What is this field? Why does it cause the rapid expansion of space? It’s turtles all the way down, but as John Gribbin says in Inflation for Beginners, it is the standard version of inflation today, and can be regarded as an example of the kind of reasoning associated with the anthropic principle”. That’s not just any multiverse. That’s Andrei Linde’s Goldilocks multiverse. But there is no physical explanation for any of it, and no predictions either.

A chaotic landscape of inflation theories

Instead we now have a chaotic landscape of inflation theories that collectively predict anything. Take a look at an introduction to cosmological inflation by Andrew Liddle dating from 1999. He says a great number of inflationary models have been devised, and “I will discuss a very small subset of the models which have been introduced, just to give you a flavour of the variety”. He tells us about chaotic inflation models, which are standard, about multi-field theories including hybrid inflation, about beyond general relativity models, and about open inflation. There’s also secondary inflation, and more. See The Best Inflationary Models After Planck by Jerome Martin, Christophe Ringeval, Roberto Trotta, and Vincent Vennin. It dates from 2014. They say this: “We compute the Bayesian evidence and complexity of 193 slow-roll single-field models of inflation using the Planck 2013 Cosmic Microwave Background data”. Also check out classification of inflationary models and constraints on fundamental physics by Mauro Pieroni dating from 2016. It was his PhD thesis. In chapter 6 he says “we are still far from the definition of a realistic model of inflation that is consistent with our knowledge of the fundamental interactions”. But there have been an awful lot of papers on inflation. Search the arXiv for papers with inflation in the title for the past year, and there’s 320 hits. That’s nearly one a day. Inflation is a moveable feast, able to postdict everything, and predict anything. It can cover all the bases. No wonder Steinhardt has grown dissatisfied and is rocking the boat.

The Theory of Anything

Take a look at Linde’s Inflationary Cosmology after Planck 2013 dating from 2014. On page 66 he says “Some people do not like eternal inflation, multiverse and the anthropic principle. In particular, according to Steinhardt, the emergence of the concept of the inflationary multiverse is the failure of two favorite theoretical ideas – inflationary cosmology and string theory”. He was referring to Steinhardt’s contribution to the 2014 Edge question what scientific idea is ready for retirement? It was Theories of Anything. That’s where Steinhardt lays into the multiverse and quotes Guth saying “anything that can happen will happen – and it will happen infinitely many times”. Steinhardt talks about a Theory of Anything that cannot be falsified and so lies beyond the bounds of normal science. He says the latest measurements show our observable universe to be remarkably simple, and a simple outcome calls for a simple explanation, so why consider a Theory of Anything that allows any possibility, including complicated ones? He complains of physicists moving the goalposts. He says a Theory of Anything is useless and worthless, and it’s getting in the way of scientific progress. I think that’s commendable. All the more so because he’s the man who came up with eternal inflation in 1982. Compare and contrast with Sean Carroll’s essay, where he said he’d like to retire falsifiability.

Pop goes the universe

I’m with Steinhardt, because I’ve read A Critical Look at Inflationary Cosmology by John Earman and Jesus Mosterin dating from 1999. Hence I watch the debate with interest. See John Horgan’s SciAm blog physicist slams cosmic theory he helped conceive. It dates from December 2014. Also see Pop Goes the Universe which featured in SciAm in February 2017. The latter was written by Steinhardt along with Anna Ijjas and Abraham Loeb, as was their paper Inflationary Schism after Planck 2013. SciAm later published a response letter called A Cosmic Controversy. It was written by Alan Guth, Andrei Linde, David Kaiser, and Yasunori Nomura, and endorsed by 29 signatories including Michael Turner, Stephen Hawking, Steven Weinberg, Sean Carroll, Martin Rees, Frank Wilczek, and many others. Guth and Linde et al say there are now more than 14,000 inflation papers written by over 9,000 scientists. They say the standard inflationary models predict that the universe should be flat, even though inflation was invented to explain the flatness problem. They say inflation predicts the CMB ripples and polarization, even though the CMB is uniform to one part in 100,000, and it was all postdiction. Peter Woit talks about it on his not even wrong blog. He says “the political campaign for the multiverse continues today with a piece by Amanda Gefter at Nautilus. It’s a full-throated salvo from the Linde-Guth side of the multiverse propaganda war they are now waging”. He also refers to the Princeton website where Steinhardt Ijjas and Loeb state their case. They say their opponents claim four successful predictions of inflation, namely critical mass density, nearly scale-invariant perturbations, adiabatic, and Gaussian. But they also say some of their opponents wrote papers making the opposite predictions, and they give plenty of examples.

BICEP2

I think they make a good case. Particularly because I remember BICEP2. The announcement of March 17th 2014 came with considerable hype. See Ross Anderson’s account of events on the Aeon website. Also see Dennis Overbye’s New York Times articles of 17th  and 24th March 2014. It was front page news, a seven-sigma discovery, and the “smoking gun” evidence for inflation. There was talk of Nobel prizes. We all saw the video where Chao-Lin Kuo knocked on Linde’s door and told him the good news. We all heard about the million-dollar Kavli prize shared by Guth, Linde, and Starobinsky. And then we all heard how the smoking gun turned to dust. See A Joint Analysis of BICEP2/Keck Array and Planck Data. And Ron Cowen’s January 2015 Nature article Gravitational waves discovery now officially dead. The curlicue pattern in the CMB polarization was caused by dust. Not inflation. How could it be? The early universe was a maelstrom. The CMB dates from circa 400,000 years after the big bang. Expecting to see polarization patterns due to inflation is like tapping a jelly on a plate with a spoon to make it wobble, then putting the jelly in a blender for 400,000 years and expecting to still detect the wobble. So when BICEP2 bit the dust, the evidence for inflation bit the dust too. Guth and Linde et al were making sweeping claims they couldn’t back up, and Steinhardt et al burst their bubble:

Pop goes the universe image copyright Nature/Scientific American

I’m confident of that, because of what I know about the fundamental physics. I know about electromagnetism and monopoles. and gravity and black holes and mass. I also know that little misunderstandings can have big consequences. See for example what Linde said in his Edge essay about retiring Uniformity and Uniqueness of The Universe.

Fundamental physics

He said “the electron mass is the same everywhere in the observable part of the universe”. Only it isn’t. When you lift your electron you do work on it. You add energy to it. That energy is in the electron, not anywhere else. Then when you drop your electron, gravity converts gravitational potential energy into kinetic energy. When the electron hits the ground the kinetic energy gets radiated away, and you’re left with a mass deficit. Because the mass of a body is a measure of its energy content. Because gravitational potential energy is mass-energy. Because the electron’s mass varies in the room you’re in. For another example look at Guth’s book The Inflationary Universe. On page 13 Guth said the large positive energy of the masses in the universe can be counter-balanced by a corresponding amount of negative energy in the form of the gravitational field. Only it can’t. Gravitational field energy is positive. Hence as Einstein said, “the energy of the gravitational field shall act gravitationally in the same way as any other kind of energy”. Guth’s appendix A is incorrect. When you extract energy via ropes on the descending pieces attached to generators, that energy comes from the mass deficit. Not from the gravitational field.

Magnetic charge is misguided

Also note Guth’s repeated references to electric and magnetic fields. Such as on pages 47, 60, 116, 139, 156, and 170. It’s as if Guth doesn’t know that Maxwell unified electricity and magnetism a hundred and fifty years ago.  That doesn’t auger too well for Guth’s interest in monopoles. Grand Unified Theories predict monopoles, and inflation is said to explain why we don’t see them. But as Martin Rees said, skeptics “might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical”. Particularly when the electron doesn’t have an electric field and a magnetic field. It has an electromagnetic field, and it takes two to tango. Electromagnetic field interactions result in linear force and rotational force. When we only see linear force we talk of an electric field, and when we only see rotational force we talk of a magnetic field. But you cannot take the magnetic aspect away from the electron’s electromagnetic field to leave it with an electric field only. Or vice versa. So electric charge is a misnomer. So magnetic charge is misguided. So the monopole problem is no problem at all.

Inflation is a solution to problems that do not exist

It gets worse, because as Stephen Hawking said, the universe is like a black hole in reverse. A black hole is a place where the “coordinate” speed of light is zero and space is homogeneous. Since the speed of light does not vary in this frozen-star thing, it’s a place where spacetime is flat. And since nothing can move faster than the speed of light, nothing moves, so there is no heat. All in all the monopole problem misses the point that the electron has an electromagnetic field, the flatness problem misses the point that homogeneous space is space without a gravitational field, and the horizon problem misses the point that the universe may have started with no temperature at all. It means inflation is a solution to problems that do not exist. It means Big Bang cosmology never needed inflation in the first place. It also means what it always needed was the subject of Einstein’s greatest blunder. Einstein talked about it in 1930 when he said space remains the sole medium of reality”. He was talking about that quintessential thing which is perhaps not constant, and is nowadays known as dark energy.

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