Inflationary Cosmology

By Amanda Gefter
New Scientist, June 30, 2012

Edited by Andy Ross

Paul Steinhardt: "We thought that inflation predicted a smooth, flat universe. Instead, it predicts every possibility an infinite number of times. We're back to square one."

Max Tegmark: "Inflation has destroyed itself. It logically self-destructed."

Sean Carroll: "Inflation is still the dominant paradigm. But we've become a lot less convinced that it's obviously true."

Alan Guth proposed inflation in 1980. Some 12 Ts after the big bang, the cosmos had expanded and cooled enough for the first atoms to form and photons to fly free. Now, 13.8 Gy later, we see them as a CMB with an almost uniform temperature of 2.7 K.

You can measure the CMB 10 Gy away in one direction and 10 Gy in the other and still observe that uniformity. But that uniformity is a suspicious coincidence. Also, the universe is extremely flat, with a nearly Euclidean geometry, which is also unlikely, given that gravity warps space.

The inflationary story is that in the beginning was a quantum field called the inflaton. It was in an unstable false vacuum energy state. A quantum jiggle collapsed it to the true vacuum and repulsive gravity inflated space superluminally. In far less than a yoctosecond, the observable universe ballooned over 20 orders of magnitude in size. Inflation solved the horizon problem and the flatness problem. And by inflating tiny density fluctuations to astronomical size, it seeded the galaxies we see today.

But inflation is hard to stop. Quantum jiggles gave the inflaton field different energies in different places. Each collapse kicks off the inflation of a different region of space. These regions bud off to form an infinite multiverse, where there are no definite predictions, only probabilities. Any value of anything appears an infinite number of times in the infinity of universes. The odds of observing any particular value are infinity divided by infinity.

Cosmologists hoped to take a snapshot of the multiverse and then extrapolate the relative probabilities of various observations out to ever later times and ever more universes. But relativity says there is an infinite number of slicing time into snapshots, each giving different probabilities. This is the measure problem.

In 2001, Paul Steinhardt, Justin Khoury, Burt Ovrut, and Neil Turok put the big bang into a cyclic history inspired by string theory. If our cosmos sits in a brane, a 4D object floating in a 5D space, maybe two neighboring branes collide every few Ty or so. The fifth dimension briefly goes pop and reappears as the branes bounce apart. Our 4D brane gets a huge hit we call the big bang.

This cyclic model does much of what the inflationary big bang was invented to do. The branes are flat and hit all at once, solving the flatness problem and creating a nearly uniform cosmos. Quantum fluctuations are enough to seed galaxies. No multiverse, no measure problem, but still a lot to explain.

In quantum physics, when a particle travels from A to B it goes all possible ways at once. To find out which path we are most likely to observe, we add together the wave functions for each possible path, working out how they cancel and amplify each other. The total wave function codes everything we need to know about the particle at B.

Stephen Hawking and James Hartle argued that a similar approach could be applied to the universe as a whole. Point B is the universe we see today. Looking back toward its origin, we can trace many valid histories of its expansion back to point A where semiclassical physics breaks down and quantum spacetime foams up. Point A is a timeless zone where a superposition of all possible universes pops into existence. This was the no-boundary proposal.

Adding up all the possible histories of a universe with no boundary, we get a universe with multiple histories. Its wave function gets rid of the measure problem, as it encodes a unique set of probabilities for anything we might observe. The horizon and flatness observations are inputs to the theory.

Inflation crops up naturally along many paths the universe could have taken to get here. Thomas Hertog: "You can calculate the probability that inflation occurred, and it turns out that probability is very high."

The holographic principle says that 4D physics with gravity is mathematically equivalent to the physics on its 3D boundary without gravity. The world is a holographic projection of information from the edge of reality. This duality appears both in string theory and in most approaches to unifying relativity and quantum theory.

The no-boundary proposal says the universe has a direct connection with string theory, as Hawking, Hartle, and Hertog showed in a recent arXiv paper.

Brian Greene on inflation, dark energy, strings, and the multiverse

Alan Lightman on the contingency of the anthropic string multiverse

Sean Carroll on an idea to merge the multiverse with quantum branching

Stephen Hawking, Roger Penrose, and Jeremy Bernstein on cosmology

Infinitary Cosmology

By Amanda Gefter
New Scientist, August 17, 2013

Edited by Andy Ross

The standard model of particle physics was long beset by pathological infinities. Decades of work banished most of them, but gravity resists unification.

Cosmic inflation creates an infinite multiverse where everything that can happen will happen an infinite number of times. This is the measure problem.

Max Tegmark: "Inflation is saying .. our problems with .. the measure problem come immediately from our assumption of the infinite."

Doron Zeilberger wants to do away with infinity by setting a largest number. Count from 1 and eventually you reach a limit he calls N0. If you try to add 1 to N0, you get either an overflow error or a reset to 0. We can redo mathematics with N0 and make it circular.

Seth Lloyd: "We have no evidence that the universe behaves as if it were a classical computer, and plenty of evidence that it behaves like a quantum computer .. If you really wanted to specify the full state of one qubit, it would require an infinite amount of information."

Tegmark: "I think .. we'll see that continuous quantum mechanics is itself just an approximation to some deeper theory, which is totally finite."

Quantum Cosmology

By Natalie Wolchover
Quanta Magazine, June 6, 2019

Edited by Andy Ross

In 1983, Stephen Hawking and James Hartle (HH) proposed the universe might have no boundary and derived a wave function of the universe that encompasses the entire past, present, and future at once.

HH saw the cosmos as having the shape of a shuttlecock, with a diameter smoothly expanding from a point of zero size. Each moment in the universe becomes a cross-section of the shuttlecock. Entropy increases from the cork to the feathers, defining an emergent arrow of time. Near the bottom, time ceases and is replaced by pure space.

In 2017, Job Feldbrugge, Jean-Luc Lehners, and Neil Turok (FLT) called the HH proposal into question. The proposal is only viable if a universe that curves out of a point can grow into a universe like ours. HH said universes with no boundaries will tend to be huge, smooth, flat, and expanding, just like ours. FLT claimed such a universe is forbidden by quantum mechanics.

HH said the universe began as pure space. They used an approach invented by Richard Feynman: The HH wave function sums all possible ways the universe might have expanded smoothly from a point. They hoped the sum of all histories would yield a wave function giving a high probability to a huge, smooth, flat universe like ours.

The path integral over all possible expansion histories is impossible to calculate, so HH took the path integral over all possible toy universes in the set of all universes with a single energy field to power cosmic inflation. Even their "minisuperspace" calculation is hard to solve exactly.

Two possible histories dominate the calculation. These are classical histories where, after inflating from size zero, the universe expands according to general relativity. One resembles our universe. The other is nothing like it: Density variations form an inverted bell curve, where differences between regions approach infinity.

FLT looked at the expansion histories leading to the second dominant solution that had real values for a variable called lapse, which is not quite our usual notion of time. Summing over universes with real values of lapse leads to the wildly fluctuating solution.

Jonathan Halliwell and others say only contours that pick up the good expansion history make sense, as a wildly fluctuating universe is not normalizable. They say the critics are invoking a false notion of causality in demanding that lapse be real.

John Wheeler and Bryce DeWitt said the wave function of the universe cannot depend on time, since there is no external clock to measure it, and also the total energy of the universe must be zero. The HH wave function satisfies the Wheeler−DeWitt equation for minisuperspace.

Latham Boyle, Kieran Finn, and Neil Turok (BFT) are developing a new cosmic model that instead of one shuttlecock has two, set cork to cork with time flowing in both directions. The twin lobes realize CPT symmetry, but they meet at a singularity.

Alexander Vilenkin and Andrei Linde propose casting the birth of the universe as a quantum tunneling event. Questions abound about how the various proposals intersect with anthropic reasoning and the multiverse idea.


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