# Density fluctuations that result after inflation

1. May 10, 2012

### robertjford80

This is from Krauss' A Universe from Nothing

How could Guth know what density fluctuations arise after inflation?

More context to better help a potential answerer:

2. May 10, 2012

### marcus

I have a suggestion. To get a constructive reasoned discussion focus on the question that interests you (suggested by your title) namely
And avoid dragging controversial mass-market books into the discussion. Pop-cosmology authors put their own spin on stuff (partly to make it sell). It can be a major waste of time for us to try to correct for commercial distortion.

What you are asking is a really interesting objective question and at least one of the regulars here has published technical research papers about it.
The question is about the statistics of the little hot and cold patches in the CMB map. How many there are of each size.

How many biggish patches compared with how many medium-size and how many tiny patches and so on. It is the face of the early universe, the face of the ancient light. One reason it is so beautiful is because the statistics of the bump-and-dimple counts are beautiful. So much information about the past written there! You know those blotchy blue and red oval maps of the whole microwave sky.

When people finally got good maps around say 2003, fine clear enough resolution to make the counts, they were surprised to learn that the statistics were just what you would expect from an episode of exponentially rapid expansion given the miniscule jitters that pervade all quantum reality.

The CMB temperature variation is only about one thousandth of one percent and the hills and valleys come in all sizes. It was, so to speak, a great magnified picture of the small percentage quantum fuzz that we know pervades the world at small scale. The very slight uncertainty about everything.

What were the quantum fluctuations IN? What were they fluctuations OF? Well people guess different technical things. For my part I think the HIGGS FIELD has always been there and could have been the jittery wavery culprit. But Heisenberg uncertainty, generalized, infects everything. It could have been whatever, whatever could infuse energy into what came after inflation was done.

Several people are expert in this and can correct me if I've made serious mistakes. My main point is that it is really work in progress. Nobody has final answers. It is still conjectures. But there is a lot of information in the map of the ancient light and answers are coming out, and the inflation hypothesis has been amazingly successful in explaining the statistics seen since, say, 2003.

So I would encourage you to stick to the question of how did inflation influence the distribution of hot and cold speckles on the map. Make people answer that one to your satisfaction.

It has to do with a fascinating process of "freezing" random chance fluctuations by stretching them out so far that one end is out of touch with the other and they can no longer "unfluctuate".

Other people can tell you about this. It's very interesting. We are talking more waves than particles but put in particle language it would be as if an electron and antielectron appeared (virtual fluctuations of the electron field) and then did NOT cancel each other immediately because they were pulled way apart from each other so fast they did not have time to annihilate each other. They would so to speak by "frozen" into real existence by the rapid expansion. But that is just an analogy. We are not talking about electrons and antielectrons. We aren't even sure what the field was that had the fluctuations (as far as I know.)

3. May 10, 2012

### Mark M

Robert,

The fluctuations after inflation, known as the primordial fluctuations, are represented by a power spectrum which defines the fluctuations as a function of spatial scale. The fractional energy density of said fluctuations is given by the following equation
$$\delta (\vec{x})=\frac{p(\vec{x})}{\bar{p}}-1=\int dk \delta _{k}e^{i \bar {k} \bar {x}}$$

Many inflationary models predict a power spectrum governed by

$$P_{s}(k)\propto k^{n_{s}-1}$$
As Krauss says, inflation's predictions of the primordial fluctuations have been confirmed to excellent accuracy by the seven year WMAP. Here are two papers on results from WMAP

Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters
http://lambda.gsfc.nasa.gov/product...powspectra/wmap_7yr_power_spectra_reprint.pdf

Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Are There Cosmic Microwave Background Anomalies?
http://lambda.gsfc.nasa.gov/product...year/anomalies/wmap_7yr_anomalies_reprint.pdf

4. May 11, 2012

### robertjford80

Marcus, thanks for the info. Do you know of any review of Krauss written by other cosmologists. I tried to find a good review of K's book but there were so many of them written by non scientists that I gave up looking for one.

I understand what you're said elsewhere, yes, I'm aware that the density fluctuations of the CMB are the same to one part in 100,000. I guess it will come more clear to me when I read up on quantum fluctuations.

Mark44, thanks for the equations.

5. May 11, 2012

### marcus

Sean Carroll is a cosmologist and has a blog called Cosmic Variance. I think he is a longtime buddy of Larry Krauss. He wrote something that was both sympathetic and critical as I recall.
http://blogs.discovermagazine.com/cosmicvariance/2012/04/28/a-universe-from-nothing/
I don't know if you'd call it a review of the Krauss' book or a balancing act in the storm of controversy occasioned by it. The short answer is no I don't know of a serious review by a cosmologist. I haven't read the book so can't evaluate the reviews, but judging from Sean's comments the most salient feature of the book seems to be that it expressed some fairly common cosmo speculations in a provocative way.

Peter Woit also posted about the controversy and got some rather funny comments:
http://www.math.columbia.edu/~woit/wordpress/?p=4623
The comments start here:

Maybe someone else can recommend

Last edited: May 11, 2012
6. May 11, 2012

### robertjford80

I saw that Carroll wrote a review but I didn't bother to read it because I thought he would be too biased towards K. I didn't know Woit wrote a review but I'm afraid he will be too biased against K but I will read it anyway.

7. May 11, 2012

### marcus

I looked back and couldn't find anything by Woit that I could call a review of K's book. He just seems to be reporting on the controversy and giving links. Sorry for the empty lead. I looked back at the Carroll review and my personal opinion is it's worthwhile. He makes sense of the issues, parses it all clearly (IMO) and doesn't seem overly biased in the book's favor. I'm not a Carroll fan but I give him good marks on this one.

If you don't mind saying, I'm curious what issues matter especially to you. What questions do you anticipate seeing resolved? What sparked your interest in cosmology, so that you are now working through a textbook (which is great, more power to you). My private suspicion is that cosmology, although endlessly fascinating in its own right, does not at this point have much to say about Ultimate Questions such as why does existence exist. Quantum cosmology may have proposals for modeling conditions immediately leading up to the start of expansion ("big bang") but then the start of expansion would not represent the beginning of time or existence. It would just be another event along the road.

8. May 11, 2012

### clamtrox

The density fluctuations that arise from inflation can be calculated if you know what's the "stuff" that makes inflation happen. This of course we have no idea of, but we can make educated guesses. The standard guess is to take a single scalar field, not unlike the famous Higgs field (there even is something called Higgs inflation, but that is a bit more technical).

Then if you assume that this single scalar field is the only thing that is relevant for the expansion of the universe during inflation, you can find the power spectrum of the fluctuations in terms of how the field interacts with itself (the potential of the field, if you know any quantum field theory). This is kind of cool, because being able to measure the power spectrum, you can effectively do particle physics in very very high energies. For example, after the measurements of the Planck satellite, we can probably tell (if inflation is true), whether the potential of the inflaton is a convex or a concave function, just by measuring the fluctuations.

Inflation also produces gravitational waves, and signatures of these can also be searched in the CMB. Finding some would be an indication that inflation happened at very high energies, close to Planck energy, while no gravitational waves means that the inflationary energy scale was lower.

So in short, no one knows what kind of fluctuations inflation produced, but by observing them, we can find stuff about inflation.

9. May 11, 2012

### bapowell

Minor correction: those should be $\rho$'s instead of $p$'s.

10. May 11, 2012

### Mark M

I thought so! Do you know what the LaTeX code for that is?

EDIT: Never mind, it's \rho. Thanks for pointing that out.

11. May 11, 2012

### bapowell

Good question, and I'll try to elaborate a little on the already excellent responses. There are some generic predictions of simple (technically single field, slow roll) inflation. These are that the inflaton fluctuations should be 1) Gaussian, 2) nearly scale invariant, and 3) adiabatic. Surprisingly, even just these three conditions impose rather nontrivial constraints on the possible form of the temperature anisotropies in the CMB. For example, in the early days people weren't sure if inflation or topological defects (e.g. cosmic strings) were the dominant source of structure formation. Unlike inflation, topological defects resulted in isocurvature, as opposed to adiabatic, fluctuations, with a resulting CMB spectrum that lacked its characteristic peaks and valleys. This was before my time, but this paper: http://arxiv.org/abs/astro-ph/0702223 has a nice plot of CMB spectra of the different models on pg. 2.

I can elaborate more on why the spectra should have these properties, based on our understanding of the inflationary mechanism, but I have to run now. More later.