# Thread: How is H(z) measured?

1. Established Member
Join Date
Nov 2005
Posts
458

## How is H(z) measured?

Hi can anyone answer a couple of questions about this...

In this paper https://arxiv.org/abs/1507.02517 ,page 2 there is a table of how Hubbles constant varies with redshift

1) How has H(z) been measured or deduced for a given z?

2) According to the table, generally with increasing z, looking further back into the past, H(z) increases. But if the expansion of the universe is meant to be accelerating. Shouldn't the highest value be nowadays at z = 0?

Thankyou.

2. I've moved this thread from Google Hangouts to Q&A, where it will more likely be addressed.

3. Originally Posted by john hunter
Hi can anyone answer a couple of questions about this...

In this paper https://arxiv.org/abs/1507.02517 ,page 2 there is a table of how Hubbles constant varies with redshift
The table shows how the Hubble parameter varies with redshift, not the Hubble Constant.

The distinction seems important, because of the discussion in your ATM thread.
1) How has H(z) been measured or deduced for a given z?

2) According to the table, generally with increasing z, looking further back into the past, H(z) increases. But if the expansion of the universe is meant to be accelerating. Shouldn't the highest value be nowadays at z = 0?

Thankyou.

4. Established Member
Join Date
Nov 2005
Posts
458
Ok, the expression 'Hubble constant' has been changed to 'the Hubble parameter'...

In this paper https://arxiv.org/abs/1507.02517 ,page 2 there is a table of how the Hubble parameter H(z) varies with redshift

1) How has H(z) been measured or deduced for a given z?

2) According to the table, generally with increasing z, looking further back into the past, H(z) increases. But if the expansion of the universe is meant to be accelerating. Shouldn't the highest value be nowadays at z = 0?

Thankyou.

5. A simplistic answer to 1. above how was it measured:
Astronomers measured the maximum brightness and red-shift of may distant objects that had reliable brightnesses (such as Type 1a Supernovae), and determined the distance the light had traveled to get here. This gave a good curve for the relationship between z and distance. The first derivative of that curve is H(z). That was a first effort, and refinements were made from other observations, such as the Planck data. The Euclid probe should give us many more data points to help refine the curves even more.

6. Order of Kilopi
Join Date
Mar 2010
Location
United Kingdom
Posts
6,673
Originally Posted by john hunter
2) According to the table, generally with increasing z, looking further back into the past, H(z) increases. But if the expansion of the universe is meant to be accelerating. Shouldn't the highest value be nowadays at z = 0?
You are misunderstanding what is meant by the Hubble parameter. In the simple linear model it is the product of the distance and the Hubble constant.

If expansion were not accelerating then we'd expect the plot of H(z) to be a straight line. That table is showing that H(z) is not a straight line because the absolute value of the rate of change of the Hubble parameter with z is not constant. And as you get closer to home that rate of change is increasing compared to intermediate distances.

7. The behavior is easier to visualize by plotting the scale factor (to a multiplicative constant, the distance n=between two objects each of which is at rest in the local cosmological environment) versus time (an example is in Ned Wright's online notes). Something that it took me a while to realize is that the separation between objects can increase faster than linearly with time (acceleration) while the Hubble "constant" (parameter) decreases, because we parametrize H using distance at each time (so we measure the expansion across regions that are progressively smaller fractions of any object separation we took as our starting distance).

8. Established Member
Join Date
Nov 2005
Posts
458
Originally Posted by Shaula
If expansion were not accelerating then we'd expect the plot of H(z) to be a straight line. That table is showing that H(z) is not a straight line because the absolute value of the rate of change of the Hubble parameter with z is not constant. And as you get closer to home that rate of change is increasing compared to intermediate distances.
Thanks everyone so far...Shaula, did you mean that if the universe were not accelerating the plot of H(z) against z would be a straight line? Would it be of the form H(z)=H(0)(1+z)?

Just wondering if the data shown figure 1 of https://arxiv.org/abs/1507.02517 rules the non-accelerating universe out, such a straight line might actually fit that data quite well?!
Last edited by john hunter; 2017-Jul-16 at 09:28 PM.

9. Order of Kilopi
Join Date
Mar 2010
Location
United Kingdom
Posts
6,673
Originally Posted by john hunter
Thanks everyone so far...Shaula, did you mean that if the universe were not accelerating the plot of H(z) against z would be a straight line? Would it be of the form H(z)=H(0)(1+z)?
Yup.

Originally Posted by john hunter
Just wondering if the data shown figure 1 of https://arxiv.org/abs/1507.02517 rules the non-accelerating universe out, such a straight line might actually fit that data quite well?!
Fitting lines by eye is fraught with danger. If you take the predicted relationships from the accelerating and non-accelerating models you find that the accelerating universe is a better fit. There are straight lines you can (just) fit to the data, but they are all statistically lower confidence than the curved line from the LCDM model. The differences between the two models are small and the data tends to have large uncertainties on it. So we can't rule out either case with 100% confidence. But we can say that the accelerating case is much more likely.

10. Established Member
Join Date
Nov 2005
Posts
458
Thankyou everyone,

The straight line has only one parameter H(0), whilst the LCDM has at least two H(0) and omega(m), but maybe it's a topic to be continued back on the ATM thread...

11. Order of Kilopi
Join Date
Aug 2008
Location
Wellington, New Zealand
Posts
3,688
Not right. H(0) is the value of the Hubble parameter at z = 0. The LCDM has H(z) and only 1 value of H(0). This is not the Hubble constant. There are 2 different ways of measuring the Hubble constant (cosmological and direct). The measurements give 2 close but different values.

ETA: If you want to see a derivation of H(z) then read the Wikipedia Hubble's law article, Derivation of the Hubble parameter section. Note that H(z) is not a straight line without dark energy except at low z (z << 1).
ETA2: Also see
Utility of observational Hubble parameter data on dark energy evolution equation 3 is H(z) for a flat universe as shown by independent measurements.
Last edited by Reality Check; 2017-Jul-19 at 10:33 PM.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•