# Fact or Fiction?

## Place a dot by the number of each true statement below

• ### there is a rest frame in cosmology (see below for complete statement)

Votes: 6 60.0%
• ### there is an idea of the present moment (simultaneity, see below)

Votes: 4 40.0%
• ### the distance in the Hubble law is current distance

Votes: 3 30.0%
• ### the current radius of the observable U is 40 billion LY

Votes: 2 20.0%
• ### some objects in the observable universe are currently receding faster than light

Votes: 4 40.0%
• ### the CMB has lost all but a thousandth of its energy

Votes: 4 40.0%
• ### gravity can be mild near the event horizon of a black hole

Votes: 7 70.0%
• ### the cosmological horizon is receding at an estimated 3c

Votes: 3 30.0%
• ### "light travel time" distance does not work in the Hubble law

Votes: 3 30.0%
• ### the Einstein equation relates curvature to energy density (and like) terms

Votes: 7 70.0%

• Total voters
10
Science Advisor
Gold Member
Dearly Missed
Put a dot by the true statements. Let's see what PF people think about these statements.

1. there is a rest frame in cosmology defined by the expansion

2. this gives us a notion of simultaneity. In principle, observers at rest all over the universe could agree on what is meant by the present moment

3. the basic Hubble law distance (that goes into v = H0 D) is the current distance to objects as measured by observers at rest---sometimes called the "comoving distance"
because it is seen by observers comoving with the expansion

4. the current radius of the observable universe is estimated to be around 40 billion lightyears----this includes all the stuff whose light is reaching us so we can observe it.

5. much of the stuff in the observable universe is currently receding at speeds greater than c. General relativity does not forbid this---indeed it encourages it

6. the expansion of space has chilled down the CMB by a factor of 1000 (more accurately an estimated 1100). That energy is gone. General Relativity does not have a global energy conservation theorem or a consensus as to where that energy may have gone.

7. an observer suspended near the event horizon of a black hole does not see the event horizon rushing at him and (depending on the size of the BH) does not necessarily feel any extreme force of gravity. Gravity near the horizon can be similar to that at the surface of the Earth if the BH is large enough.

8. the boundary of the observable universe is currently receding at an estimated speed of around 3c.

9. cosmologists tend not to use the "light travel time" distance for technical work---this distance does not work in the Hubble law---however popularized accounts do use the "light travel time" index of distance.

10. Gmu,nu = 8pi Tmu,nu relates curvature to energy density-----the units on the lefthand side are reciprocal-area units of curvature and the units on the righthand are those of energy-density (formally equivalent to pressure)

## Answers and Replies

Science Advisor
Gold Member
Dearly Missed
Eric Linder's 18-page cosmic overview

Eric Linder of UC Berkeley has a concise overview of
cosmology online at

http://panisse.lbl.gov/~evlinder/lcos.pdf

It is 18 pages and called "Cosmology Overview---Whence Cosmology?, Dynamics of the Universe, Fate of the Universe"

This is in the form of lecture notes, so it leaves out some qualifications and details, but it is a useful thumbnail sketch.

Linder is the author of an introductory textbook on cosmology
and, if I remember correctly, participated in the famous 1998 discovery of accelerated expansion---implying dark energy.
I think he was one of a team that found evidence of that in
the form of a bunch of Type Ia supernovas.

This thing of Linder's is a good addition to Ned Wright's Cosmology Tutorial.

Recently at PF meteor was asking about metrics----Linder has a brief treatment of metrics, here is an exerpt:

[[Isotropy and homogeneity immediately give specific form to the metric ga,b which determines the spacetime geometry and physics of the universe. This is Robertson-Walker form. Distance interval ds is simple; in some common coordinate choices:

Table 3.1: Forms of the Robertson-Walker Metric

...]] and so on.

This is a clear mainstream treatment that will assure anyone who may be in doubt that the standard metric in cosm. is RW (also FRW, for Friedmann-Robertson-Walker) which takes several forms including what he calls the "comoving" and "standard" forms
both of which reduce to the same form in the spatially flat case

ds2 = - dt2 + a2 (t) [dr2 + r2 d&omega;2 ]

This is the metric used in defining what Wright calls the "Hubble law" distance, or comoving distance, in terms of which the current distance to an object and its current recession speed can be measured.

Wright's tutorial is in certain ways less confusing and more accessible----more pictorial in places. Wright has probably taught more courses of cosmology to undergraduates than Linder has, I would guess from the style, and knows where people get hung up. But both complement each other.

Linder's general audience FAQ is not so good, I advise staying away from it. He glosses over too much and gives wrong impressions on some matters apparently in the interest of communicating to laymen.

If everybody at PF who wants to ask questions and discuss cosmology would read over these 18 pages (not the general audience Linder stuff! this 18-page overview of the real subject) we would have more of a shared perspective. If you want to do this----dont get bogged down in his formulas: read for content, skip over formulas you find too hard and ask about them later.

I don't have Linder's "Introduction to Cosmology" hardcopy textbook so I can't say what I think about it, but it also might be helpful----with more explanation than this condensed overview can give.

Science Advisor
Gold Member
Dearly Missed
another unintuitive fact or two

cosmology has some unintuitive facts and I think it helps develop understanding to try to assimilate them, maybe a bit at a time though.

its bad enough, in some sense, that there are objects in the universe receding from us at speeds greater than c
I mean stationary objects just going along with the general expansion of space

and on top of that, some of these objects belong to our observable universe----we see them now as they were in the past---although today they may be receding faster than light

somehow you may find that is acceptable---and that the presentday distance of the farthest observable objects is around 40 billion LY----this is the real physical distance or the best cosmologists have to offer along those lines (there is also "angular-size-distance", "light-travel-time-distance", and "luminosity distance" but the alternatives have problems---Ned Wright's tutorial discusses the alternatives as well.

but, horror of horrors, it is also true (in seeming defiance of all intuition) that an object today can be receding faster than light
and can today emit some light which (!) will eventually reach us.

George Dishman was discussing related matters on a Usenet thread in sci.astro. I found it by searching with keywords [light cone expansion] in Google groups. He was saying "If you tell laymen this it will just confuse them." I thought this kind of
droll----"shhhhh don't tell anybody..." I was wondering how other people felt about it. Here is the scandalous fact:

It is possible for light aimed at us, and which is going to eventually make it here, to begin by actually being carried away from us by the expansion of space. This is clear pictorially from the pear-shape lightcones in Wright's tutorial, but one rarely hears it expressed because so contrary to prejudice.