What is Hubble parameter: Definition and 26 Discussions

Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from the Earth at speeds proportional to their distance. In other words, the farther they are the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the spectrum.
Hubble's law is considered the first observational basis for the expansion of the universe, and today it serves as one of the pieces of evidence most often cited in support of the Big Bang model.
The motion of astronomical objects due solely to this expansion is known as the Hubble flow. It is described by the equation v = H0D, with H0 the constant of proportionality—Hubble constant—between the "proper distance" D to a galaxy, which can change over time, unlike the comoving distance, and its speed of separation v, i.e. the derivative of proper distance with respect to cosmological time coordinate. (See "Uses of the proper distance" for some discussion of the subtleties of this definition of "velocity".)
Hubble constant is most frequently quoted in (km/s)/Mpc, thus giving the speed in km/s of a galaxy 1 megaparsec (3.09×1019 km) away, and its value is about 70 (km/s)/Mpc. However, the SI unit of H0 is simply s−1, and the SI unit for the reciprocal of H0 is simply the second. The reciprocal of H0 is known as the Hubble time. The Hubble constant can also be interpreted as the relative rate of expansion. In this form H0 = 7%/Gyr, meaning that at the current rate of expansion it takes a billion years for an unbound structure to grow by 7%.
Although widely attributed to Edwin Hubble, the notion of the universe expanding at a calculable rate was first derived from general relativity equations in 1922 by Alexander Friedmann. Friedmann published a set of equations, now known as the Friedmann equations, showing that the universe might expand, and presenting the expansion speed if that were the case. Then Georges Lemaître, in a 1927 article, independently derived that the universe might be expanding, observed the proportionality between recessional velocity of, and distance to, distant bodies, and suggested an estimated value for the proportionality constant; this constant, when Edwin Hubble confirmed the existence of cosmic expansion and determined a more accurate value for it two years later, came to be known by his name as the Hubble constant. Hubble inferred the recession velocity of the objects from their redshifts, many of which were earlier measured and related to velocity by Vesto Slipher in 1917. Though the Hubble constant H0 is roughly constant in the velocity-distance space at any given moment in time, the Hubble parameter H, which the Hubble constant is the current value of, varies with time, so the term constant is sometimes thought of as somewhat of a misnomer.

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  1. T

    I Hubble Parameter as function of time in universe models

    This graph shows ##H## as a function of time related to the L-CDM model. Do we (@Jorrie) have similar graphs e.g. for ##\Lambda=0##; ##k=-1## critical, ##\Lambda=0##; ##k=0## open, ##\Lambda=0##; ##k=+1## closed? That would be great, thanks in advance.
  2. W

    I New measurement of the Hubble Parameter

    I just saw a new paper on measuring the Hubble Parameter : https://arxiv.org/pdf/1908.06060.pdf It seems they are agreeing with Planck which I understand would speak largely against the idea of new physics from the Hubble tension. However it says +14 and -7 next to the estimate. I presume...
  3. Vick

    A Anisotropic Universe and Friedmann Equations

    The Friedman Equations is based on the cosmological principle, which states that the universe at sufficiently large scale is homogeneous and isotropic. But what if, as an hypothesis, the universe was anisotropic and the clustering of masses are aligned to an arbitrary axis (axial pole), how...
  4. Arman777

    I What is the Hubble Parameter over time and how can I calculate it?

    How can I calculate the Hubble Parameter in time. I know that it decreases in time and approaches to some constant value but I am not sure to what value, Is there any graph for that ?
  5. S

    I The error bars of redshift drift

    Dear all, I am reading the paper "Cosmic dynamics in the era of Extremely Large Telescopes " by Liske et al. about redshift. I get the physical meaning of redshift drift, but when it comes to the error bars, I am confused. - Aren't the error bars given in equation (15) ? - Isn't this function...
  6. S

    I Radial BAO size method and Hubble parameter

    Hi! Can anyone tell me what the radial BAO size method is? how do people use it to get to the H(z)? I am reading the paper "Constraints on the Dark Side of the Universe and Observational Hubble Parameter Data " by Zhang et al. and I think I am lost! Can anyone tell me very simple, how they do...
  7. M

    B Relationship Between Density and the Hubble parameter

    I'm just looking for conceptual clarification re: the relationship between matter density and the Hubble parameter in the Friedmann equation. Just for quick reference, the equation I'm looking at is H2 = 8πGρ/3 - ka-2 (I'm working through Liddle's Intro text, and for now we're ignoring the...
  8. K

    I How Does the Hubble Parameter Relate to Galaxy Movement?

    This is the time derivative to calculate the speed which a galaxy moves away from another galaxy. I don't understand how they get from da/dt (xi − x1) to (∙a)/a a(t). (xi − x1). Could anyone explain this? vi(t) = d/dt (ri(t) − r1(t)) = d/dt a(t)(xi − x1) = da/dt (xi − x1)...
  9. Elnur Hajiyev

    A Hubble parameter vs Scale factor's derivative

    How does Hubble parameter and scale factor's derivative differ geometrically? I am reading S. Caroll's GR book. But I cannot get the full representation of these two parameters. On the book, it says How can \dot{H} and \ddot{a} be opposite of each other on the same instance if both are...
  10. F

    I Hubble parameter in terms of the scale factor

    From Introduction to Cosmology by Matt Roos, he wanted to derive the Hubble parameter in terms of the scale factor. From the Friedmann's equation, ##\frac{R'^2 + kc^2}{R^2} = \frac{8πG}{3}ρ## The density parameter is ##~Ω(a) = \frac{8πG}{3H_o^2}ρ(a)~## and let ##~Ω_k = \frac{-kc^2}{H_o^2}##...
  11. S

    F(R) gravity and the Hubble parameter

    Dear all, Considering Einstein Hilbert lagrangian, by using Einstein field equations one can get the form of Friedman equations and consequently the Hubble parameter. I know that in f(R) models, Einstein equations get modified. However, what happens to the Friedman equation and the Hubble...
  12. Garth

    Utility of observational Hubble parameter data on DE

    Another paper in Friday's physics arXiv on using the H(z) v z plot to investigate any possible evolution of DE: Utility of observational Hubble parameter data on dark energy evolution. From that eprint: As discussed in the Marginal evidence for cosmic acceleration from Type Ia SNe, this paper...
  13. A

    Prove evolution of Hubble parameter

    Homework Statement Prove that Homework Equations [/B]The Attempt at a Solution Without cosmological constant, one finds that where w is the ratio between pressure and density.[/B]
  14. 2

    What exactly is the Hubble parameter?

    I'm looking at general relativity and particularly considering what happens at the Big Bang. I think the Friedman equation is H^2=\frac{8\pi G}{3}\rho so I see that as the matter density goes to infinity, H goes to infinity. According to this video (around 10:10), this is where the problem lies...
  15. L

    Time derivative of Hubble parameter

    Is rather a question of calculus skills, but how do I get the time derivative of the Hubble parameter here in [1]? Is it the Leibnitz rule, the chain rule, some clever re-arrangement? thank you
  16. H

    Is the Critical Density Related to the Friedmann Equation?

    Homework Statement For a κ=0 universe with no cosmological constant, show that H(z)=H0(1+z)3/2 Homework Equations Friedmann equation: H2=\frac{8*\pi*g}{3c^2}-\frac{κc^2}{r^2}*\frac{1}{a(t)^2} The Attempt at a Solution I know that R(z)=R0/(1+z) but I do not know where this comes...
  17. C

    Using Hubble parameter defn to change integration variable from t to a

    Homework Statement r1 = t∫t1 1/a(t) dt Use the Hubble parameter definition to change from t to a, if a(t) = a and a(t1) = 1 Homework Equations Hubble parameter H = a' / a where a' = da/dt The Attempt at a Solution Start with Hubble parameter definition, and rearrange to find dt aH =...
  18. K

    Why the Hubble Parameter Decreases to .85 of Today's Value

    Why will the Hubble parameter only decrease to .85 of today's Hubble parameter?
  19. J

    Constant Hubble parameter -> accelerating Universe?

    Hi, Let us assume that Hubble's Constant H is really constant. Therefore: a' / a = H where a is the scale factor. The solution to this equation is: a(t) = exp(H t) This equation describes an accelerating universe with deceleration parameter q given by: q = - a'' a / a'^2 =...
  20. marcus

    Maximum value of Hubble parameter (near start of expansion)

    An estimate of 0.94/tPlanck for the maximum reached by the Hubble parameter was given by Ashtekar and Sloan here (based on Loop qc): http://arxiv.org/abs/0912.4093 Loop quantum cosmology and slow roll inflation Abhay Ashtekar, David Sloan (Submitted on 21 Dec 2009) "In loop quantum cosmology...
  21. apeiron

    Initial value for hubble parameter

    Simple question hopefully. What was the initial value for the Hubble parameter immediately following the big bang (or ending of inflationary epoch)? I presume the initial velocity of expansion was lightspeed and started slowing from there.
  22. T

    Some slight confusion regarding the dimensionless Hubble parameter h.

    Hi, I am just writing up my MSc thesis and want to explain the dimensionless Hubble parameter that I have been using through my work. I understand that you take the valuefor the Hubble "constant" and then divide by 100km/sec/Mpc to leave get a value which has no units. There seems to be...
  23. K

    Value of Hubble Parameter in Decelerating Universe

    what was the value of the Hubble parameter when the universe was decelerating?
  24. Z

    Hubble parameter in early universe

    If the Hubble parameter is always decreasing for very early stages of Big Expansion of manifold (i.e. Big Bang), then what was it decreasing from?
  25. U

    Cepheid Stars & the Hubble Parameter: What is Their Role?

    What is the role of Cepheid stars in determining the Hubble parameter?
  26. S

    Hubble Parameter & acc. Universe

    Hubble "Parameter"& acc. Universe I am a senior high student. And I am studying on SnIa. I recently read that SOME(maybe most) theory said that hubble's constant is not a CONSTANT, it's changing by time. But I wonder if there are something influent the data. (like "slection effect" .etc)...