Expert: Patrick Weiler - 1/26/2012

Question
QUESTION: How accurate is the rate of calculated expansion of the universe?

Has the concept been explored that ‘light from distant stars undergoing continual gravitational bending back and forth on its journey from there to here takes longer to reach us than it would be if the light were travelling in a straight line’?

I imagine this would extend the perceived distance of the star to be much greater than it actually was, increasing exponentially with distance the light travels, affecting calculations for speed of expansion of the universe.

If so, how is it factored into equations deducing the speed of expansion of the universe, as surely the myriad of gravitational influences the light would be subjected to (i.e. any point of mass in the universe) on its gargantuan journey would be impossible to calculate?

ANSWER: In your question you're actually asking about "gravitational redshift" which describes how gravity's effect on spacetime changes the wavelength of light moving through that spacetime. The classic example of the gravitational redshift has been observed on the earth; if you shine a light up to a tower and measure its wavelength when it is received as compared to its wavelength when emitted, you find that the wavelength has increased, and this is due to the fact that the gravitational field of the earth is stronger the closer you get to its surface, causing time to pass slower - or, if you like, to be "stretched" - near the surface and thereby affecting the frequency and hence the wavelength of the light.

The expansion of the universe is *not* based on gravitational redshift but rather "cosmological redshift."  

Practically speaking, the difference between the two (Doppler redshift and cosmological redshift) is this: in the case of a Doppler shift, the only thing that matters is the relative velocity of the emitting object when the light is emitted compared to that of the receiving object when the light is received. After the light is emitted, it doesn't matter what happens to the emitting object - it won't affect the wavelength of the light that is received. In the case of the cosmological redshift, however, the emitting object is expanding along with the rest of the universe, and if the rate of expansion changes between the time the light is emitted and the time it is received, that will affect the received wavelength. Basically, the cosmological redshift is a measure of the total "stretching" that the universe has undergone between the time the light was emitted and the time it was received.

---------- FOLLOW-UP ----------

QUESTION: Thanks for getting back to me so quickly and with clarity.

I think rather than redshift (though I may well be wrong!) I was theoretically comparing the light from two points equidistant from here, one of which was influenced by gravitational forces en route e.g. black holes, galaxies (in the extreme) and the other which the light had a fairly uneventful journey through 'empty' space, avoiding large gravitational forces.

I was assuming with the first light source its route would be longer as it would be bent (lensed?) around these gravity sources and therefore the light source would seem further away.

This perceived increase in distance of the light source would also increase with more distant light sources, as they would be influenced by more gravity sources.

Maybe it still sounds like a redshift issue and I need more understanding.

Answer
Hello again...
Perhaps if we talked about the so-called Hubble Constant, which in reality isn't all that "constant"; it's been adjusted and revised countless times. Right now, the value of the Hubble Constant is ≈73.8 km/sec per megaparsec (1 megaparsec = 3,261,688.071 light years)All this means is that for every additional megaparsec farther away some galaxy is, its velocity will be ≈73.8 km/sec faster than some nearer galaxy. You can probably see that if we can determine the recessional velocity of a galaxy we can find its distance from us. Of course that critical recessional velocity is found via measuring the subject's redshift. On to the main point of all this --

Obviously we can't measure the redshift of all galaxies. What we do is sample numerous regions of space. Imagine that in one region there are 1,000 galaxies. We measure their redshift values and establish an average. Some of the redshifts will be significantly outside that average. We ascribe that difference to gravitational redshift, or even to extremely dense intervening "walls" of gas/dust clouds. Such anomalies aren't figured into the overall average redshift. Repeat this sampling technique enough times and we arrive at ≈73.8 km/sec/Mpc.

Even though I suspect that your question hasn't been completely answered, I'm afraid this is about the best I can do.