Evolving Potentials

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Mark at 7:58 am, June 15th, 2008

An important event of the early summer was the graduation of my most senior graduate student - Alessandra Silvestri - who successfully defended her thesis on May 15th, and who is leaving the nest at the end of the summer to take up a postdoc in the Physics Department and the Kavli Institute for Astrophysics and Space Research at MIT. Congratulations to Alessandra!

Alessandra’s thesis - Modified Gravity: Cosmic Acceleration and the Large Scale Structure of the Universe - contains, among other things, results obtained in a series of papers in which she, with collaborators, studied how one might search for an observational signature of modified gravity as the origin of cosmic acceleration, as compared to dark energy, or a cosmological constant.

While it is relatively easy to obtain the correct expansion history of the universe - how its size changes over the course of time - from all kinds of cosmic acceleration models, differences typically manifest themselves in the details of how structure grows, and how that structure influences the cosmic microwave background radiation (CMB). There are a number of different important effects, but one that is particularly interesting, and unusually easy to explain, is the Integrated Sachs-Wolfe (ISW) effect.

Here’s how it works. In the early universe, expansion ultimately stretches the wavelengths of photons enough that their energies are too low to ionize hydrogen atoms. This is called decoupling, and after this point the universe is electrically neutral, light essentially ceases to interact with matter, and the leftover photons stream through the universe. Today they form the CMB.

During the photons’ journey across the universe (ultimately to our detectors) they pass through overdense regions of matter that are in the process of becoming more dense, due to the attractive nature of gravity. In passing through such a growing overdensity, the photons gain energy as they fall into the associated potential well, and lose energy as they climb out of it (this is general relativity after all, and gravity affects light just as it would affect massive particles). For a static potential well, these effects would, of course, cancel, just as a ball rolling from one side of a symmetrical bowl to the other will reach precisely the same height that it started at. However, in reality two competing effects occur - the well is growing due to gravitational attraction, and is becoming shallower due to the expanding background. Thus, there is the possibility of an overall change in the photon energy, depending on how the universe is expanding.

The collapse of an overdensity can be thought of as the evolution of a small matter dominated portion of the universe. If the background evolution is matter dominated, this is cancelled by the expansion rate and the overall effect is zero, as for a static potential. However, if the background evolution differs from matter domination then there is a net effect. This adds up as the photon traverses multiple wells, and is known as the ISW effect.

Since we now know that the late time evolution of the universe is not matter dominated, but rather is accelerating, the ISW effect provides one possible insight into the nature of this phenomenon. And since cosmic acceleration is occurring in the most recent epoch (and to distinguish the effect from a related one occurring at early times, during radiation domination), we refer to this incarnation of the effect as the late-time ISW effect (or Rees-Sciama effect). Because acceleration is so dominant, the net effect is that the potential decays while the photon traverses the well, meaning that the photon emerges with a slight net blueshift, compared to how it entered.

Now, because the details of how structure forms depend not only on the background evolution, but also on how the different energy components of the universe cluster, and on the equations obeyed by the overdensities themselves, the size and sign of the late-time ISW effect depends on the origin of cosmic acceleration. For example, modified gravity theories typically introduce a scale-dependence into the growth function that may be used to distinguish such models from dark energy or the cosmological constant model. Thus, in principle, the late-time ISW effect is a powerful tool.

In practice this is very difficult to carry out, since the dominant effect is on large scales in the universe, where cosmic variance (the statistical effect, not us) gets in the way of interpreting any possible signal. Nevertheless, by cross-correlating the microwave background measurements with data from large scale structure surveys, one can make progress.

Cosmic acceleration is a huge mystery, but modern cosmology also provides us with a remarkable set of tools with which to probe it, and to constrain our theoretical approaches. The late-time ISW effect is one of these tools, and is a nice example of how the CMB - an amazing discovery in its own right - is now being put to use in many different ways to explore the details of our cosmological models.

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24 Comments on “Evolving Potentials” rss feed

Flaming Pope on Jun 15th, 2008 at 9:28 am

Congrats- you know I would be surprised if you just copy and pasted her thesis on here, seems a bit short. How did she go about defending her thesis?

Well anyway, have a nice time at MIT
Aaron F. on Jun 15th, 2008 at 12:20 pm

Cool!
Fred on Jun 15th, 2008 at 3:27 pm

Has there been any work done on possible gravitational wave signatures from theories of modified gravity?
Sili on Jun 15th, 2008 at 3:33 pm

I’m really grateful for how good you are at explaining what must be a very complicated phenomenon.
Shantanu on Jun 15th, 2008 at 5:29 pm

Fred, there is a lot of literature on testing modified theories of gravity through gravitational
waves. See for a recent review
Also there have been gw based tests of modified theories of gravity which do away
with dark matter. See
this or here
for how ground based gw detectors could settle this issue.
johnmerryman on Jun 15th, 2008 at 6:13 pm

Wouldn’t the distribution of galaxies cause a curvature effect as well, since the further light travels, the greater number of gravity fields it passes through, so that closer light isn’t stretching faster, just passing through less dense regions?
Mark on Jun 15th, 2008 at 6:50 pm

Thanks Sili, and thanks Shantenu for the reply to Fred, although I think that there have ben very few studies of this in modified gravity models for cosmic acceleration. One thing is that the waves are usually caused by massive bodies moving, and most models are constructed to behave just like GR in that regime.

johnmerryman, the distribution of galaxies is taken into account in two ways here (this is very standard in cosmology): one is through averaging to get the background expansion and the other is through the influence of their potential wells, a small part of this I’ve described here.
John Merryman on Jun 15th, 2008 at 7:59 pm

Mark,

That’s my point. As you describe it, given an even distribution of galaxies across the universe, the further light travels, the more gravity fields it passes through, so if these blueshift the light somewhat, this cancels that much redshift, so the proportion of redshift for closer sources is greater.
Mark on Jun 15th, 2008 at 8:07 pm

This is nothing to do with sources John, I’m talking about the CMB, which comes from a single distance.
Shantanu on Jun 15th, 2008 at 8:27 pm

Mark, Obviously I am not familiar with all details of the models discussed in this post, but AFAIK , most models of f(R) gravity theories are similar to scalar tensor theories of gravity on which there is a lot of literature on testing with gws since the 70s. There is some discussion
on Page 39 of this in recent review on f(R)
gravity theories.
Another paper which discusses testing cosmic acceleration models of gravity through gw waves is
this and references there.
Mark on Jun 15th, 2008 at 8:34 pm

Thanks Shantenu! I also think these are good references. As you say, f(R) theories can be written as scalar tensor theories, but with a nonminimal, and universal coupling between the metric and matter. I honestly haven’t thought too much how this might affect the gravitational wave signal.

I guess the point I was making is that for a general scalar tensor theory, I think there may be many effects, but since those designed for cosmic acceleration are constructed to revert to GR where densities are high compared to the current cosmological one, there might be only a small effect for those.

Cheers,
Lab Lemming on Jun 15th, 2008 at 11:18 pm

How large is this effect?
For example, if our solar system got ejected from the galaxy (or local group) due to some unfortunate interstellar encounter, would would everything look noticeably redder as we floated through intergalactic space, or would the change in the visible wavelengths be fractions of a nanometer?
John Merryman on Jun 16th, 2008 at 5:36 am

Mark,

Pardon if I was not reading what you are saying correctly, but my understanding of the need for dark energy is based on explaining why standard candles appear to have a higher proportional redshift if they are closer, than those further away. As you seemed to be describing it, this effect seemed due to the redshift of the further candles being somewhat reduced by blueshifting caused by intervening gravity fields, rather than a recent acceleration of the expansion.

The cmb does come from a single distance, approximately 13.7 billion lightyears away. My problem with the basic model is that gravity apparently causes space to collapse, which is why Einstein added a cosmological constant in the first place. According to Hawking and the general consensus, as well as tests on the cmb, the effects of expansion and this contraction of space are in apparent balance, Omega=1. What I don’t understand is how can the entire universe be expanding, if the effect of the expansion of space is currently neutralized by the collapse of gravity? Yes, space is expanding, but it would seem to be flowing into these gravity wells at an equal rate.

Since the only light we can measure is what actually manages to traverse these enormous distances and not what is otherwise absorbed and blocked, it is greatly redshifted, but the actual pressure of expansion would seem to be released by gravitational contraction and photon absorption, including what falls into astronomers telescopes. Otherwise it would not appear to be flat space.

I digress somewhat in order to ask a further question; Since the CMB originates at the general point where visible light ends, could there be a horizon line cause by this redshift, over which the visible spectrum cannot travel, but black body radiation can?
Mark on Jun 16th, 2008 at 5:48 am

Lab Lemming. This is a tiny effect. What you describe wouldn’t so much affect this as it would affect the dipole of the CMB anisotropy spectrum. It would be a large effect there, but easily subtracted off, as we do already with the CMB dipole due to our peculiar velocity.

John, the ISW effect is in no way affecting the idea that we know acceleration is happening. It is a subtle effect on top of that (and very well understood). Einstein did not add a CC because gravity causes space to collapse - space can easily expand without one - but rather to allow a static solution. When you mention the balance in an Omega=1 universe, you are confusing a spatially flat universe (which we do seem to have) with a flat spacetime (which wouldn’t be expanding, but which we do not have). Omega=1 does not mean a flat spacetime.
Mark on Jun 16th, 2008 at 5:57 am

P.S. John. The need for dark energy comes not only from supernovae data, but from a set of other observations - the CMB, large scale structure, lensing, …, all of which indicate cosmic acceleration. The ISW effect isn’t one of our major pieces of evidence for it - it is a subtle effect we can try to use to get at the details of it.

I didn’t understand the question at the end at all.
Eugene on Jun 16th, 2008 at 2:21 pm

Congrats Alessandra! Have fun in Boston!
Lawrence B. Crowell on Jun 16th, 2008 at 7:53 pm

John Merryman on Jun 16th, 2008 at 5:36 am
Mark,

Pardon if I was not reading what you are saying correctly, but my understanding of the need for dark energy is based on explaining why standard candles appear to have a higher proportional redshift if they are closer, than those further away.

———————–

Think of the universe as made up of cells in space. Since on average a photon which enters a cell is equal in number and energy to those which leave we can think of these cells as perfectly reflecting boxes. In an expanding universe these boxes are growing in size. A resonance cavity with photons that expands in size will expand the wavelength of the photons inside. This has stretched out the wavelength of light which resulted after the deionization event to a microwave wavelength, which compose the CMB.

The physics here is to deduce how these boxes expanded in the past, particular prior to the deionization period. So reduce the problem of reflecting boxes or resonance cavities to one dimension. This is then a transmission line, or a string of them. If the couplers between each of these lines has “infinite” impedence then the model still holds. We can then consider the transmission line as adjusting the wavelength of a signal as it grows in length and remove the intermediate “couplers.” But these potentials introduce some impedence varations along the transmission line. So the observer measures an incoming wave and attempts to deduce its “history” by its structure. We know all about the “dark energy” accelerated expansion of the universe, but there might in addition be information in addition — analogous to these impedence variations or mismatches on the line due to these quirky potentials that vary in time and space.

Will this lead to modified gravity? Who knows!?

Lawrence B. Crowell
John Merryman on Jun 16th, 2008 at 9:22 pm

Lawrence,

In an expanding universe these boxes are growing in size. A resonance cavity with photons that expands in size will expand the wavelength of the photons inside.

I can certainly accept space that space can expand. As well as contract. Believe it or not, I tend to be a very credulous person. It’s easier that way. My problem has been that if space is expanding intergalactically and contracting intragalactically (or rather intragravitationally) and these two effects are in general equilibrium, how is it that the entire universe expands? I don’t want to go too far out on the limb of what seems to be my various hobby horses, since trying to explain how and why I differentiate between flat space and spacetime to Mark was deleted, but I do feel the basic foundation has some plastered over stress fractures running through it that those building on this foundation don’t seem able to explain away.
Inflation comes to mind.

But these potentials introduce some impedence varations along the transmission line. So the observer measures an incoming wave and attempts to deduce its “history” by its structure.

As with much of history, most of it doesn’t leave much evidence. Since photons of the same wave would seem as entangled as any such particles could be, is there any effect of those falling into gravity wells on those which continue their travels, such as incremental effects on their spectrum?
Mark on Jun 16th, 2008 at 9:38 pm

John. The physics of the expanding background spacetime in geeneral relativity, and its effect on propagating light is a completely understood and solved problem that is explained in detail at even the undergraduate level these days. There are no “plastered over stress fractures” at all. We have explained this many, many times, but for future information on this topic I would try, for example, Andrew Liddle’s undergraduate text:

http://www.amazon.com/Introduction-Modern-Cosmology-Andrew-Liddle/dp/0470848359/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1213670159&sr=8-1

I do not intend to be rude, but we don’t want to turn every thread about cosmology into the same set of well-understood questions about the foundations.
John Merryman on Jun 17th, 2008 at 5:48 am

Lawrence,

Thank you for your efforts, but I think I better give the subject a rest.
Theda on Jun 17th, 2008 at 8:03 am

Hi, Mark and everyone. Have y’all heard of Tinyurl.com? You can go to tinyurl.com, enter a long url such as the book url above, click the button, and instantly receive http://tinyurl.com/43c83e, a tiny url which navigates to the exact same page.
Mark on Jun 17th, 2008 at 8:36 am

Thanks Theda - useful!
Anisotropie on Jun 17th, 2008 at 4:06 pm

Hello Mark,
this is my first comment on Cosmic Variance; I do my compliments for this beautiful blog!

I wish to ask you if the ISW test is useful to make prediction on f(R) models, because the cross-correlation function with f(R) models is too much similar from the standard one, given the galaxy distribution uncertainties and the error bars in the correlation between CMB and LSS.

Thank you very much
Mark on Jun 17th, 2008 at 4:17 pm

Hi Anisotropie - thanks! It is indeed challenging with f(R) models, although one might hope that with future gains in the uncertainties and error bars one might have a chance.

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Evolving Potentials

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