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3 questions on Physical Cosmology 
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#1
Sep308, 07:36 AM

P: 80

First question:
According to Hubble's Law, the redshift observed by distant galaxies are proportional to their distance. This is what I already know: It says on wikipedia that Hubble observed cepheid variable stars in a spiral nebulae to calculate their distance, cepheid variable stars are cosmological candles, meaning they emit a consistent light signature. Q: How did Hubble calculate distances using cephied stars in spiral nebulae? 


#2
Sep308, 08:04 AM

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Cepheids have a relationship between their period and luminosity. So basically you have to measure the period of the Cepheid and the luminosity. You can use the period luminosity relation to tell you what the luminosity should be and the inverse square law of light to calculate the distance.



#3
Sep308, 12:52 PM

P: 80

Thanks Kurdt,
I see, the star is emitting light homogeneously in all directions, so since the total luminosity (the luminosity emitted in all directions) is exclusively determined by the relation to the Cepheid's period, then you can treat the total luminosity of the star a known quantity and thereby calculate the distance by the observed luminosity, because the observed luminosity is a proportion of how large the telescope's surface area is to the area of the spherical shell (with radius r) around the Cepheid. What I know; according to Hubble's Law Redshift is a function of distance. The Doppler Effect is the phenominon in which waveemitting bodies which are moving toward an observer will be percieved by that observer to be of a lower frequency (a function of the relative velocity) and wave emitting bodies which are moving away will have a lower frequency According to the Expanding Space Paradigm, this observed redshift as a function of distance is the result of the stars moving away from us. Q2:So by this, is it right to assume that stars are moving away from each other at an exponential rate with time? (because after a time period has elapsed the space in between will be greater and therefore the redshift will be greater and therefore the recession velocity will too.) 


#4
Sep408, 06:40 PM

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3 questions on Physical Cosmology
I'm not really sure under what circumstances (if any) it would be safe to assume exponential rate of recession. The difficulty arises because the Hubble parameter is a function of time. A resident cosmologist will be able to provide a more in depth answer.



#5
Sep408, 08:22 PM

P: 38

WCOLtd,
I'm more of an astrophysicist, but here's my answer anyway. How fast things are moving away from each other (due to expansion of space) depends on a variety of properties of the massenergy density in the universe. As it turns out, we think the universe is accelerating due to some energy density in the universe (dark energy) that somehow remains constant in time (it might change, but not nearly as fast as the energy density of matter). As this dark energy begins to dominate, then the stars (unless they are gravitationally bound in a galaxy or group of galaxies) will be moving away from each other exponentially. You do get exponential expansion if the Hubble constant were really constant, which is probably why you asked that question. In reality, the proportionality constant between proper distance and recessional velocity is not a constant. This "not a constant" is known as the Hubble parameter and is written as H(t). The Hubble parameter evaluated now, at t ~ 14 Gyr is known as the Hubble constant [itex]H_0[/itex]. However, in a dark energy dominated universe, the Hubble parameter will be constant in time, giving us exponential expansion. (Incidentally, during inflation the universe underwent exponential expansion also.) 


#6
Sep508, 12:49 PM

P: 80

Neutralseer,
Thank you for that post, albeit I am a little confused. Let me rephrase, the Hubble constant is a measure of the recession velocity as a function of distance. Gravity works in the opposite direction, it's the measure of directed velocity as a function of mass and distance. So, the distribution of mass effects the observed expansion. However, I would think that this would lead to clusterings of mass, beyond a certain distance, the recession velocity by Dark Energy will exceed the directed velocity by gravity. Once bodies of mass move beyond this threshold, they begin to move apart from eachother, so the larger the distances, the more the recession velocity should approach the value predicted by the Hubble constant, because the Gravitational effects will become negligable at greater distances. Am I correct so far? 


#7
Sep508, 01:40 PM

P: 38

WCOLtd,
Here's few comments. It's not that Dark Energy will take over at some point, just expansion will take over. Dark energy is just one of the things that affects expansion in certain ways. If there were no Dark Energy, expansion would still take over at some point. You have very good intuition about this stuff. Keep up the good questions. 


#8
Sep608, 12:19 AM

P: 80

I was describing it in terms of inertia of the body in free fall, I felt as though it was more correct to say it is a directed velocity than a directed force. Because body does not experience a force when it's in free fall or freely passing through a gravitational field, it experiences a change in velocity over time. It is as if the body is moving at a constant velocity in space and the space it's moving in is being sucked up by the mass. Kind of like a stick in a whirlpool or something. Which makes me wonder  because at some distance that has to be true  is there an edge to our observable universe? do stars ever fade away completely from our view or do they dim asymptotically? This question makes me wonder about light, and whether, by Hubble's constant, is only capable of traveling a certain distance until it becomes entirely redshifted. What would that mean? I wonder if dark energy should even be considered energy, because if it's constantly growing, wouldn't that violate conservation? Does dark energy contain with it any observational signatures other than the expansion itself? Why not just say it's an attribute of 'empty' space rather than calling it energy? What does the term "energy" signify in the case of dark energy? 


#9
Sep608, 11:48 PM

P: 38

WCOLtd,
Once again, let me warn you, I'm neither a cosmologist nor a general relativity expert. I do astrophysics which (in my case) only requires me to have a peripheral knowledge of such fields. I don't think your right about the earth expanding, etc. Also, about the directed velocity: in general relativity a light objectsay a satellite moving under Earth's influence is actually just moving in a straight line, it's just the mass of the Earth is warping spacetime, which means that the straight line for the satellite is straight in the curved spacetime. This produces what appears to us to be Newton's law of gravitation in a flat spacetime. Don't think about the total amount of dark energy since space is (probably) infinite, in this case talking about the total amount of anything doesn't make much sense. It's all about energy densities (Amount of energy per volume of space). In fact, in general relativity, talking about energy conservation in the universe is a very tricky business. You're right that people could call dark energy an attribute of space itself. Sometimes people just call it the cosmological constant or vacuum energy (vacuum refers to empty space). The term energy in this case, just refers to fact that, in the absence of this stuff/thing/propertyofspace, the motion of galaxies wouldn't be accelerating. In general relativity, only energy can affect space time (in this case causing the expansion of space to accelerate). Great questions. 


#10
Sep808, 10:04 PM

P: 80

To Neutralseer,
I appreciate all your answers, I can say that I have learned more than I ever thought I would. Does light going around the event horizon of a black hole redshift with time just as if it were traveling across the universe? Empty space has properties like "dark energy" but does it posess any form of comparable properties? Meaning, does there exist an energy to (expanding) distance equivalency? For instance, if you have a mass of 10 kg and you were able to convert all that restmass energy into pure distance, what volume of empty space would it constitute? I thought that maybe entirely redshifted light (light of zero frequency) actually contains energy. Is that what "dark energy" is insinuating? 


#11
Sep1008, 09:34 PM

P: 80

Imagine two circles seperated by a distance of r, according to one theory, the distance between the two circles measured in terms of the size of the circle increases with time.
That would be analgous to saying that the distance r remains constant and the sizes of the circles shrink with time. Could that same concept be applyed to the universal expansion model to explain the expansion of the universe? in terms of a relative shrinkage of the observers? is light only an interaction between masses? Or does it travel into the depths of space indefinitely? In other words, does baryonic matter in the universe decrease with time as a function of emitted light? (Since that light is ultimately being created by the restmass energy of the star and since that light never gets reabsorbed into restmass?) 


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