From the deceleration parameter q=−(a¨a/(a˙)2) ---------(1)
where a is the scale factor.
Hubble's parameter H=a˙/a ------------(2)
Substituting equation (2) in (1),
q=−(a¨/Ha˙) ---------------(3)
Making a¨ the subject in equation (3),
a¨= −(qHa˙)
This clearly shows that there is a link between the magnitude of the Hubble's constant and the acceleration value of the Observable Universe.
The present day value of q is approximately −0.55.
Is my proposal correct?
Max,
Q1: Is the acceleration value of the expansion ...
A1: There is no compelling reason to think that this hypothesis is true.
Furthermore, if the postulated dark energy is indeed acting as a negative pressure then the acceleration will not be uniform (as your hypothesis suggests). If my understanding is correct.
Max, it would avoid a lot of confusion if you used the standard symbols for the parameters. The letter a is usually the scale factor, q is used for deceleration and c is the speed of light.
ME: Is the acceleration value of the expansion of the Observable Universe the product of Hubble's constant and the speed of light?
No, it is defined as the product of the scale factor and its second derivative divided by the square of the first derivative. See the first link.
ME: From Hubble's constant being equal to the second divided by the first derivative of the scale factor ...
No, the Hubble parameter is the first derivative divided by the scale factor, see the second link.
ME: C is the speed of the farthest galaxies in our Hubble volume which move at light speed.
All sources beyond roughly z=1.6 are receding at more than the speed of light. The farthest known galaxy is at z=11.09 and the CMBR comes from z=1089.
https://en.wikipedia.org/wiki/Deceleration_parameter
https://en.wikipedia.org/wiki/Scale_factor_%28cosmology%29
In a general sense the Hubble's constant relates velocity of recession with distance. Now in the special case of a FRW universe H=ȧ/a (that is a-dot by a) where a(t) is a parameter entering in the expression of Robertson Walker metric. It appears as [a(t)]2 in the space part and along the diagonal. I guess either you are using a different metric or your starting definition is wrong.
James,
in this case the acceleration value is not fixed it diminishes with Hubble's constant.
ME: .. it diminishes with Hubble's constant.
No, Hubble's constant gets smaller with time but the deceleration parameter was initially positive but changed sign to be negative around 9 billion years ago and the acceleration (negative deceleration) is getting larger.
The scale factor function contains the hubble constant H:
In case of spatially flat LambdaCDM model it is:
a(t)=(OM/OL)^(1/3)*(sinh(1.5*sqrt(OL)*H*t)^(2/3),
where approximately OM = 0.3 and OL = 0.7 (mass density parameter and dark energy parameter)
In de Sitters universe (no matter) it is a(t)=A*exp(sqrt(OL)*H*t). Only in this case the Function H(t)=da/a*dt is a constant
Max, now that you've rewritten the equations, your algebra is correct. H and q are just defined combinations of the scale factor and its derivatives so of course they are closely related.
Max sir, you just change the form of the equation.. As observational evidence shows the universe accelerating , therefore in this relation the a¨>0, H>0, and a˙>0. so q
In standard FRW as well as lambda CMD Model which is a generalised FRW Model, Hubble constant vary over scale factor. In the past its value was less. So naturally there is a link in betwee
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