Return to cosmology Is inflation in trouble? Are we cycling back to cycles? And then what happens to the 2 nd law?
We saw inflation correctly predict: 1. Flatness of universe 2. Homogeneity of universe 3. Absence of magnetic monopoles 4. Many details of the microwave background If you just granted it: 1. The right general sort of scalar potential 2. Fine-tuned so that the end of the rapid inflationary roll is gentle, not a huge energy dumping crash. Fine-Tuning Inflation
Inflation Issues Old issue: Parameters have to be fine-tuned to get the sort of Goldilocks universe in which something could live. Can we use anthropic selection to account for that? Where do we get the ensemble to select from? Birth of new inflating bubbles from old cold flat empty universes? Eternal inflation? (see below) A problem shared by all such anthropic pictures: Our universe is much larger and more homogeneous than needed (so far as we know) to form life. It seems there should be much more net volume of livable space in smaller universes or smaller livable pockets. Why aren t we there? Have we Missed something needed for anthropic selection? Missed something major in cosmology? This problem was already present for Boltzmann s anthropic ideas about the origin of the Second Law (initial low entropy). Why over such a big volume?
A Special Problem for Inflation The 1960 s inflationary predictions were confirmed in amazing detail. They described what would happen to a typical patch of space, if the inflationary form was tuned to give a soft landing. But these predictions were not correct theoretically! (according to Steinhardt, Turok,..) The fate of a typical starting patch of space is not the typical condition for a resulting patch, Because certain atypical patches inflate much more! And quantum fluctuations guarantee that the starting conditions include those atypical possibilities.
Why the smooth distribution of matter? Unless the inflation parameters are tuned just right, a much lumpier distribution comes out. What s wrong with that? Still plenty of galaxies. So why don t we see a universe like that?
Anthropic Answers?.the anthropic principle assumes we live in a very atypical island with just the minimal conditions needed to support life. The claim is that the conditions in more typical islands are incompatible with galaxies or stars or some other prerequisite for life as we know it. Even though the typical islands occupy more space than ones like ours, they can be ignored because we are interested only in regions that humans could potentially inhabit. Unfortunately for this idea, the conditions in our universe are not minimal the universe is flatter, smoother and more precisely scale-invariant than it had to be to support life. (Steinhardt) Is the highly even distribution required for there to be observers (thus reducing to previous case, with possible anthropic solution)? Not for any known reason. On the surface, more lumpiness leads to more galaxies and more chance for life. Are we missing something about the conditions for life to exist? Or is there actually a very different explanation for the homogeneity of the universe?
Does Inflation Even Help? Second issue: Penrose claims it requires much less fine-tuning to get here without inflation! Although it s basically a one-parameter tuning for inflation (instead of many parameters for many temperature in different region), the tuning of that one is exceedingly fine.
Eternal Inflation: Feature or Bug? Third issue: Inflation predicts an infinite collection of postinflation bubbles. What are the predictions for them? Every physical possibility is realizedan infinite number of times. So much for the denominator in calculating the probability of life starting! What do we mean by fraction of universes with property. What fraction of the integers are even? How do we calculate what to expect?
An Alternative Cosmology? Ekpyrotic Models Basic claim: there are flattening processes other than inflation, occurring during a shrinking stage of the universe. In these processes the atypical lumpy parts shrink more instead of grow more. So you re mostly left with smooth parts. Requires some sort of cyclic picture. Current version: colliding 3-branes in a higher dimensional space. Cold flat branes collide, giving a hot flat universe with quantum fluctuations, similar but not identical to the post-inflation stage.
Is this testable? Phys. Rev. Lett. 100, 171302 (2008) Non-Gaussianities in New Ekpyrotic Cosmology Evgeny I. Buchbinder 1, Justin Khoury 1, and Burt A. Ovrut 2 The new ekpyrotic model is an alternative scenario of the early Universe which relies on a phase of slow contraction before the big bang. We calculate the 3-point and 4-point correlation functions of primordial density perturbations and find a generically large non- Gaussian signal, just below the current sensitivity level of cosmic microwave background experiments. This is in contrast with slow-roll inflation, which predicts negligible non-gaussianity. The model is also distinguishable from alternative inflationary scenarios that can yield large non-gaussianity, such as Dirac-Born-Infeld inflation and the simplest curvatonlike models, through the shape dependence of the correlation functions. Non-Gaussianity therefore provides a distinguishing and testable prediction of New Ekpyrotic Cosmology From 2012: The data are currently being gathered by the Planck satellite.
Is this testable? PHYSICAL REVIEW D 76, 123503 (2007) New ekpyrotic cosmology Evgeny I. Buchbinder,1 Justin Khoury,1 and Burt A. Ovrut2 At the level of a cosmological scenario, new ekpyrotic cosmology provides a consistent alternative paradigm to inflationary cosmology. The two scenarios make distinctive predictions for the gravitational wave spectrum: the inflationary spectrum is nearly scale invariant, whereas that of ekpyrotic cosmology is very blue and, therefore, unobservable on large scales [8]. Moreover, the generic prediction of the simplest inflationary models is a significant gravity wave amplitude, just below the current sensitivity levels of microwave background experiments [6]. Ekpyrosis, on the other hand, predicts an unobservably small amplitude. Thus the failure to detect B-mode polarization in upcoming experiments would place inflation in an uncomfortable corner [6], while lending support to the ekpyrotic paradigm. From 2012: The data are currently being gathered by the Planck satellite.
Some Planck Results Are In! arxiv:1303.5084v1 [astro-ph.co] 20 Mar 2013 Planck 2013 results. XXIV. Constraints on primordial non-gaussianity So inflation- the standard version, wins this round! We re waiting for the gravity wave results.
Cycles and Entropy? How can any cyclic picture be reconciled with the Second Law? Extrapolation of the Second Law to an infinite universe is problematic. E.g. in Carroll s rough picture. The birth of baby universes from big flat ones increases entropy. But each baby universe is born with very low entropy. Those that happen to be inflatable become like ours. The rest of the high-entropy multiverse is not directly visible. Net entropy keeps increasing, but observable entropy starts over from scratch on each round. If this picture turns out to be consistent with full quantum gravity!
Putting together GR, QM, and entropy Hawking and beyond The entropy of a black hole is known from classical thermodynamics, plus the rule that whatever comes out doesn't depend on the details of what went in. The object falling in never quite forms a black hole, due to the gravitational timeslowing near the (almost) horizon. Instead, it is thought to form a tangle of stringsand the entropy of those strings can be calculated via standard techniques: the log of the number of possible string states which have the right total mass. It comes out to be the same entropy which classical thermodynamics attributed to that much mass disappearing into the black hole! This turns out to be generic for quantum gravity, not a specific string result. In the long run the stuff evaporates into (mainly) electromagnetic radiation, almost the same as the ideal thermal radiation predicted by Hawking for quantum radiation from a fully-formed black hole. However, the detailed evolution from falling-in to radiating-out obeys the Liouville theorem, i.e. no entropy production in principle. In practice, the input is thoroughly scrambled.
But here's a problem From 2012 notes: In the reference frame of the guy falling in, he crosses the horizon and loses contact with the outside universe, before disappearing in the singularity. Far in the outside future includes his Hawking-evaporated self. Is it uniquely determined by his current self (as in the outside frame) or is it genuinely random (as per Hawking)? Is all this even self-consistent? A paradox? I ll try to get some answers from the experts. Since then the experts have weighed in.
The Black Hole Information Paradox We try to put together 3 basic principles 1. Nothing special happens as you cross the horizon Since the curvature there isn t very big the Equivalence Principle should hold. 2. The universe far from the black hole is described by quantum field theory (QFT) 3. The overall time evolution is still just a rotation in the space of quantum states ( unitary ) and thus obeys the quantum Liouville theorem. One state one state Follows from a mathematical correspondence between a QFT in D-1 dimensions and a QFT+gravity in D dimensions (more later) So no global entropy is made or lost. It turns out these aren t consistent!
The outline of the argument A particle decays into two particles: They re entangled (spins, momentum, ) (Not quite to scale) Hawking radiation is entangled with the black hole. Just like any two-particle decay. So what if one of the particles is much bigger? After most of the BH entropy has been radiated away, the remaining radiation is pretty much determined by the previous radiation, i.e. strongly entangled with it. So it s entangled both with the earlier radiation and the leftover BH But a fundamental property of QM is that entanglement is monogamous. Whoops. So it looks like (at least) one of our three assumptions must be wrong.
Aaronson s Take on Firewalls http://www.scottaaronson.com/blog/?p=1508 As I understand it, the issue is actually pretty simple. Do you agree that (1) the Hawking evaporation process should be unitary, and (2) the laws of physics should describe the experiences of an infalling observer, not just those of an observer who stays outside the horizon? If so, then you seem forced to accept (3) the interior degrees of freedom should just be some sort of scrambled re-encoding of the exterior degrees, rather than living in a separate subfactor of Hilbert space (since otherwise we d violate unitarity). But then we get (4) by applying a suitable unitary transformation to the Hawking radiation of an old enough black hole before you jump into it, someone ought to be able, in principle, to completely modify what you experience when you do jump in. Moreover, that person could be far away from you an apparent gross violation of locality. Susskind goes with (4): The black hole and the remote entangled radiation are not really separate objects. And suggests that all entangled objects are maybe connected by spacetime wormholes, which can t transmit information.