The early universe

colinr

I am struggling to come to terms with the theory of inflation. The figures I've been presented with mean that the Universe for a very short time expanded at a speed much greater than the speed of light.

Is that possible?

marcus

sure, much of the universe around us is, at this moment, receding at several times the speed of light

this is the content of the Hubble Law

v = H d

where H is the current value of the Hubble parameter (71 km/s per Mpc)
and d is the current distance of some point in space and
v is the speed that point is currently receding

Ned Wright discusses this in his Cosmology Tutorial (google Ned Wright)

colinr

how can that be possible, how can you measure the speed or distance of something you can't observe.

I'm assuming you can't observe something travelling faster than the speed of light.

marcus

the speed limit everyone is familiar with exists in the context of Special Relativity (1905)

cosmology, the universe, black holes, dark energy, expansion, and all that are part of a different theory, 1915 General Relativity.

In gen rel space can expand faster than c. indeed 100s of times faster, no problemo. It does not have to obey the special rel speed limit. Indeed it CAN not. It would be logically or mathematically awkward for the expansion of space to try obey the old 1905 speed limit. I dont think anyone has ever tried to see if it could be done---it would presumably be very ugly and unnatural looking, if not simply impossible.

the Hubble Law is a nice uniform simple linear proportion between speed and distance and it says that any point that is more than around 14 billion lightyears away at this moment MUST be receding faster than light.

there is widespread confusion about superluminal recession speeds and two New Zealanders have written a tutorial article to help clear it up.
the article is by Charles Lineweaver and Tamara Davis and it is called
"Expanding Confusion..."

maybe it would help. I will see if I can find the link

colinr

you're a star, thank you

marcus

my pleasure, thanks for the question!

most of the galaxies in the observable universe have redshift z greater than 2.

indeed galaxies with redshift z greater than 6 have been observed

in the case of an object with z = 2 or greater, which we are now observing, that object was receding away from us faster than light AT THE VERY MOMENT when it emitted the light, and it is receding even faster now.

naturally when an object emits light in our direction and is receding away from us FTL it makes it hard for the light

at first the light is actually swept back by the expansion

but it eventually makes its way to us, by stubborn swimming-upstream persistence, and the proof is that we see all these galaxies which emitted the light now arriving to us at a time when they were receding FTL

Lineweaver and Davis try to explain this in layman's terms

marcus

these calculators may help:
two good online cosmology calculators:

Ned Wright's
http://www.astro.ucla.edu/~wright/CosmoCalc.html

Siobahn Morgan's
http://www.earth.uni.edu/~morgan/ajj...gy/cosmos.html

homepage for Siobahn in case you want to see who she is
http://www.earth.uni.edu/smm.html
homepage for Ned in case you want to see who he is
http://www.astro.ucla.edu/~wright/intro.html


In Siobahn's calculator put in H = 71, and Omega = 0.27, and Lambda = 0.73

then put z = 2 and it will tell you about a galaxy that we are now observing with redshift = 2, it will tell you the "speed then" when it emitted the light we are receiving, and it will tell you the "speed now"

the 0.27 is the prevailing estimate of the matter fraction (dark matter + ordinary) and the 0.73 is the prevailing estimate of the cos. const. or dark energy. so those are just standard settings which she wants her students to know to put in when they use the calculator.

marcus

here is the pedagogical article by Davis and Lineweaver
------------------------
http://arxiv.org./abs/astro-ph/0310808

Davis and Lineweaver
"Expanding Confusion:common misconceptions of cosmological horizons and the superluminal expansion of the Universe"

Lineweaver and Davis are at the University of New South Wales.
Lineweaver was one of the leaders of the COBE project (satellite
mapping the cosmic microwave background in the 1990s)
and Davis is a recent PhD working for him
----------------------------

Chronos

Marcus has already answered your question. I just wanted to add a footnote. Theoretically, it is impossible to see anything before the universe was about 300,000 years old. The redshift of such an object would be around z=1000. From a practical / technological standpoint, it would be enormously difficult to detect such a hugely redshifted object.

Nereid

[NITPICK]If we ever get to being able to detect relict neutrinos, we will be able to 'see' back to the time when neutrinos decoupled from the rest of the matter in the universe - i.e. (crudely) the time when the inverse beta 'decay' process ceased to be in equilibrium with the beta decay process.[/nitpick]

Chronos

Dang neutrinos are always getting me in trouble. Agreed, neutrino decoupling occured much earlier than photon decoupling [around 1 second after the big event as I recall].

marcus

still it is clear that you (as well as nereid obv.) are up on this so next time an "early universe" question or "ftl expansion" question comes up I will
duck and let it go to you. should not hog podium! just a question of not answering immediately kneejerkwise and waiting to see of Chronos or someone else jumps in

Mike2

Two questions.

1) Can the Hubble constant be derived from the equations of Gen Rel?

2) If we can see all the way back to the CMBR, then doesn't that mean we should be able to see anything younger than this, namely everything?

Thanks.

Chronos

Hi Mike2
1] No, the Hubble constant was derived from observation. I am not aware of any relatavistic predictions.
2] Seeing back even as far as the relic CMBR is problematic. We definitely cannot see back before recombination... in the EM spectrum [curtsey to Nereid].

chronon

If you could look further back in time then you get to see more and more of the early universe. You would get to see all of it were it not for the fact that GR predicts that the expansion of the universe is infinitely fast at t=0, i.e. the graph of scale factor against time is vertical (athough it never seems to be shown that way). This leads to particle horizons, which means that you don't get to see everything (see Wald Section 5.3 for the details)

mijoon

This is true. There are several important constants who's value we know from experiment but for which we have no strong theoretical explanation as to why they have their particular value. The speed of light, the gravitational constant, etc. etc. fall into this catagory.

I think we should make it clear to the younger people reading this board, that much important work remains to be done and many important discoveries remain to be made.

Do not for a moment think that science is merely learning the theories of men who died before you were born.

In spite of all the wonderful advances made in the last century or so, the young scientists of today are still challenged by a universe in which the most profound truths and beauties remain to be revealed.

The sacrifices a scientist must make are great, but for those who dare, the Golden age lies before you.

Chronos

Science is not for the faint of heart. Everytime we open another door, we find a room with multiple other exits. The body of historical scientific knowledge is merely a map showing which doors lead to dead ends and which ones lead further into the unknown.