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I have recently learnt about Hubble's Law and this is my understanding of it:

Galaxies move away from us at a rate that is proportional to their distance from us. So, considering an arbitrary unit of distance d, if a galaxy at a distance d from us is moving away from us with a velocity v, then a galaxy at a distance 2d is moving away from us with a velocity 2v. This proves that the universe is expanding.

But the part that I can't quite visualize is the fact that it doesn't matter where you are in the universe. Regardless at what point in space we are standing, it will look like the galaxies are moving away from us. How is this possible? Are the galaxies moving *outward*? Should I visualize this as the galaxies being on the surface of a sphere whose radius is increasing?

How do I gain intuition about this and better visualize this?

Think about it as if you were baking bread (or cake, whatever you prefer). When you bake a bread with raisins, it rises in all directions (due to the yeast). Every raisin in a rising loaf of raisin bread will see every other raisin expanding away from it. Now suppose the raisins as galaxies and the yeast as the Hubble constant.

An illustration from Hyperphysics (Georgia State University) to illustrate this further:

When you now suppose you are the raisin at the edge, from your perspective, you are standing still and the other raisins are receding away. It is all about the perspective, the body which you take as a reference (like with relativity).

another way to think about this is to imagine what some magic observer expanding with the universe would see

they see galaxies as (mostly) fixed in place - with some small individual random motion - but those galaxies, and everything within them, appears to be getting smaller

this frame of reference is what we call the *comoving frame* and we use it a lot in the mathematics of an expanding universe - like a rotating frame it is arguably aphysical (it introduces extra forces to account for the transformation, and no being following the laws of physics could inhabit it) and thus we rarely talk about observers in it

but, if we did, we'd have an observer who sees a mostly stationary universe in which the physical constants are changing such as to shrink down every bound system - effectively changing the units of measurement

if our magic comoving observer peered into a galaxy and saw a rapidly shrinking physical observer they would agree that the measured distance between galaxies is increasing, but not because they're moving apart - because the meter-long stick used to measure the constant distance keeps shrinking

Here are some galaxies (in the first line), and the same galaxies a bit later (in the second line)

If you are in the red galaxy (the one in the middle), galaxies that used to be one space away are now two spaces away, so they are moving away with a speed of one space per unit time. Galaxies that used to be two spaces away are now four spaces away, so they are moving away with a speed of two spaces per unit time. All of the galaxies seem to be moving away, and the further away they are, the faster they go.

If you are in the purple galaxy (second from the left), the red galaxy (in the middle) is moving away with a speed of one space per unit time. The turquoise galaxy (fourth from the left) is moving away with a speed of two spaces per unit time. So you also see all the galaxies moving away from you, and the further they are, the faster they go.

Whichever galaxy you are in, you see all the other galaxies getting further and further.

I don't know how colorblind friendly this drawing is. If you have a hard time distinguishing two colors, say so in the comments, I'll try to do better.

## 54 Hubble’s Law

Two years later, in 1929, Hubble confirmed the Universe is expanding. Hubble also was able to infer the recessional velocities of a number of objects from the spectral redshifts he observed.

Hubble’s Law states that an object’s recessional velocity is proportional to the distance from the observer. In equation form, Hubble’s Law is described by:

**v &equals H _{o} d**

*v*is the velocity of the object, in km/s*d*is the distance to the object, in megaparsecs, Mpc, where 1 Mpc &equals 1 million parsecs and- H
_{o}, the Hubble constant or Hubble parameter, a proportionality between*d*and*v*also known as the rate of expansion, in (km/s)/Mpc or simply km/s/Mpc.

Different space telescopes have been used to determine the Hubble Constant, H _{o} . Each of these space telescopes — Hubble, Spitzer — WMAP, and Planck — look at the universe in different parts of the electromagnetic spectrum. Even though the H _{o} ranges for each space telescope vary, the data is more-in agreement than it was 10 years ago. Recent Hubble’s Constant Values by Primefac is licensed under CC BY-SA 3.0

What does the km/s/Mpc unit mean? The km/s is a velocity, kilometers per second. Most of us are used to speeds in miles per hour, or mi/hr. A km/s velocity is much faster velocity than we are used to 1 km/s is approximately 2,237 mi/hr. A megaparsec, Mpc, is a specific distance, about 3.26 million light years, 30.86 × 10 18 kilometers, or 1.92 × 10 19 miles. The km/s/Mpc is a unit of velocity per distance, velocity per megaparsec or about 3.26 million light years.

The Hubble’s Law equation can be rearranged to solve for an object’s distance:

**v &equals H _{o} d**

**d &equals v/H _{o}**

With Hubble’s Law arranged in this form, one can determine the distance to an object like a distant galaxy or quasar by determining the object’s recessional velocity from the object’s spectral red shift and knowing the Hubble parameter.

A red-shifted absorption line spectrum, indicating the object is moving away from the observer (us here on Earth) Redshift horizontal by Georg Wiora is licensed under CC BY 2.5 / A derivative from the original work

With an understanding of the relationship between an object’s redshift, its receding velocity, and distance, the work turned to determining the Hubble parameter value, H _{o} . A correct, or at least close, Hubble parameter would lead astronomers and cosmologists to not only determining the distances to these galaxies, but the age of the observable Universe itself. Hubble’s Law applies to galaxies and objects that are extremely far away specifically, more than 10 megaparsecs from the observer.

## The Hubble–Lemaître Law

Lemaître had no trouble at all seeing how faith — divine creation out of nothing — and the Big Bang, which seems to look just like that, were compatible.

Monsignor Georges Lemaïtre

& Albert Einstein, 1933

Thanks to the Hubble telescope, even those unfamiliar with astronomy have heard the name of Edwin Hubble. Those more familiar with the subject will know of Hubble's Law, which is about to be renamed the "Hubble–Lemaître Law," overdue recognition for the astronomer and Belgian priest, Monsignor Georges Lemaître, the father of the Big Bang theory.

Father Lemaître's recognition is a good occasion to remember not to mix up astronomy with philosophy, physics with metaphysics. When elementary Greek philosophy was taught in high school, as it was in the time of Hubble and Lemaître a century ago, the different disciplines were rarely confused or conflated. Today, a great many scientists do just that, and would find it hard to understand a figure like Father Lemaître, a Catholic priest and one of the century's leading astronomers.

The International Astronomical Union vote to rename the law was announced this week after a worldwide consultation with its members. The "Hubble-Lemaître" law describes the speed at which objects move in an expanding universe. The specifics are beyond a newspaper column — and this columnist. But general principles are accessible to lay interest.

By the 1920s astronomy had reached a widespread consensus that the universe was in a perpetual "steady state," that it had always existed. That working consensus avoided having to conjure with the physics of how something so enormous could be assembled, as it were, and where it would come from.

Lemaître, a mathematician who read astronomy after his theological studies, argued that the universe began at a distinct moment, with all of its mass in an unimaginably dense quantum. He then likened that first moment to fireworks, with the resulting galaxies like the trails of burning embers that are launched away from the central burst.

So the universe had a beginning, after which time and space made sense, as there was now change and motion. When did the universe begin? Lemaître, who had a facility for expression, referred to it as "a day without yesterday."

The astronomy guild did not appreciate its consensus being disturbed, and what we now call the "Big Bang" theory was coined by a critic and intended as derogatory. Yes, everything just went "bang" in the beginning, and unfolded from there! Ridiculous.

Despite later disagreements, Albert Einstein greatly admired Lemaître's work, with the two of them travelling to California in 1933 for a series of seminars on their respective work.

"This is the most beautiful and satisfactory explanation of creation to which I have ever listened," said Einstein of Lemaître's theories on their joint trip.

Einstein did not by "creation" mean the biblical account of a personal God who creates out of love, but Lemaître had no trouble at all seeing how faith — divine creation out of nothing — and the Big Bang, which seems to look just like that, were compatible.

The Big Bang theory, which now meets with wide acceptance, requires that there be something to go "bang" in the first place. And where did that come from? What was there before there something to go bang? Nothing?

The prior consensus on the cosmos was reluctant to accept the idea of a "beginning." It sounded rather too much like the first words of the Hebrew bible: "In the beginning, God created . "

And if nothing, how could something come from it? That's metaphysics now, of which astronomy can tell us nothing. Astronomy, like all branches of physics, requires there be something to observe before it can do its work.

The Big Bang, despite being used by scientists weak in metaphysics to "explain" that the origins of the universe exclude divine creation, actually points — suggestively, but not definitively — to a complementarity between astronomy and biblical revelation, righty understood.

The prior consensus on the cosmos was reluctant to accept the idea of a "beginning." It sounded rather too much like the first words of the Hebrew bible: "In the beginning, God created …"

So an alternative "steady state" was proposed, in which the emissions from the Big Bang accelerated away from the central burst, but at a decreasing rate of acceleration due to gravitational force. Eventually the force of gravity would overcome the initial momentum from the Big Bang, and the universe would slow down until the expansion was reversed, and gravity pulled the mass of the universe back toward the centre, leading to everything disappearing in a "big crunch." Thereupon would follow another Big Bang and so on it would go, the universe constantly creating and destroying itself, expanding and contracting, banging and crunching.

Lemaître did not follow that line, likely influenced by the biblical idea of creation being a singular event, not an infinitely iterative process. But wherever Lemaître's intuition came from, it would be evidence that would determine the truth. In 1998, astronomers observing supernovas — exploding stars — found that the rate of acceleration were increasing, not decreasing. Bang but no crunch.

Lemaître's work, now vindicated, has long been overlooked in favour of other astronomers to which he was equal or superior. That was due, in part, to anti-religious prejudice. Scientists think of themselves as being without prejudices, another widely believed proposition for which there is a lack of evidence.

Father Raymond J. de Souza, "The Hubble–Lemaître Law." *National Post*, (Canada) November 3, 2018.

Reprinted with permission of the *National Post* and Fr. de Souza.

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## Edwin Hubble

**Edwin Powell Hubble (1889 - 1953)**

Edwin was an American astronomer, inspired by the science fiction books he read as a child. He graduated from Oxford University with a degree in law philosophy, before returning to university (this time the University of Chicago) to study astronomy. Not long later, he was recruited by California's Mount Wilson Observatory to aid in the construction of their new telescope. However, before accepting the job, he completed a doctorate in astronomy, enlisted in the US Army, and served a tour of duty in World War I.

Whilst working at Mount Wilson, Edwin used the observatory's telescope to prove that other galaxies existed outside of the Milky Way. To do this, he compared the various degrees of luminosity among Cepheid variable stars. He was able to estimate that the Andromeda 'nebula' was nearly 900,000 lightyears away from the Milky Way, and therefore it must be its own galaxy. Renamed the Andromeda galaxy, it was later shown to be much more distant, at nearly 2.48 million lightyears away.

In the early 1920s, Edwin began to study the spectral lines of galaxies, and in particular their spectral shifts. Working alongside the astronomer Milton Humason, they published their work together in 1929. The work theorised that the redshift of the emission from a galaxy (which showed that all galaxies are moving away from one another, and the Universe is expanding) is directly related to the distance of the galaxy from Earth. Put another way, the recessional velocity of a galaxy increases with its distance from Earth. This simple relation became known as Hubble's Law.

## 12.3: Hubble’s Law

Two years later, in 1929, Hubble confirmed the Universe is expanding. Hubble also was able to infer the recessional velocities of a number of objects from the spectral redshifts he observed.

Hubble&rsquos Law states that an object&rsquos recessional velocity is proportional to the distance from the observer. In equation form, Hubble&rsquos Law is described by:

**v &equals H _{o} d**

*v*is the velocity of the object, in km/s*d*is the distance to the object, in megaparsecs, Mpc, where 1 Mpc &equals 1 million parsecs and- H
_{o}, the Hubble constant or Hubble parameter, a proportionality between*d*and*v*also known as the rate of expansion, in (km/s)/Mpc or simply km/s/Mpc.

What does the km/s/Mpc unit mean? The km/s is a velocity, kilometers per second. Most of us are used to speeds in miles per hour, or mi/hr. A km/s velocity is much faster velocity than we are used to 1 km/s is approximately 2,237 mi/hr. A megaparsec, Mpc, is a specific distance, about 3.26 million light years, 30.86 × 10 18 kilometers, or 1.92 × 10 19 miles. The km/s/Mpc is a unit of velocity per distance, velocity per megaparsec or about 3.26 million light years.

The Hubble&rsquos Law equation can be rearranged to solve for an object&rsquos distance:

**v &equals H _{o} d**

**d &equals v/H _{o}**

With Hubble&rsquos Law arranged in this form, one can determine the distance to an object like a distant galaxy or quasar by determining the object&rsquos recessional velocity from the object&rsquos spectral red shift and knowing the Hubble parameter.

With an understanding of the relationship between an object&rsquos redshift, its receding velocity, and distance, the work turned to determining the Hubble parameter value, H _{o} . A correct, or at least close, Hubble parameter would lead astronomers and cosmologists to not only determining the distances to these galaxies, but the age of the observable Universe itself. Hubble&rsquos Law applies to galaxies and objects that are extremely far away specifically, more than 10 megaparsecs from the observer.

## Contents

A decade before Hubble made his observations, a number of physicists and mathematicians had established a consistent theory of an expanding universe by using Einstein's field equations of general relativity. Applying the most general principles to the nature of the universe yielded a dynamic solution that conflicted with the then-prevalent notion of a static universe.

### Slipher's observations Edit

In 1912, Vesto Slipher measured the first Doppler shift of a "spiral nebula" (the obsolete term for spiral galaxies) and soon discovered that almost all such nebulae were receding from Earth. He did not grasp the cosmological implications of this fact, and indeed at the time it was highly controversial whether or not these nebulae were "island universes" outside our Milky Way. [19] [20]

### FLRW equations Edit

In 1922, Alexander Friedmann derived his Friedmann equations from Einstein's field equations, showing that the universe might expand at a rate calculable by the equations. [21] The parameter used by Friedmann is known today as the scale factor and can be considered as a scale invariant form of the proportionality constant of Hubble's law. Georges Lemaître independently found a similar solution in his 1927 paper discussed in the following section. The Friedmann equations are derived by inserting the metric for a homogeneous and isotropic universe into Einstein's field equations for a fluid with a given density and pressure. This idea of an expanding spacetime would eventually lead to the Big Bang and Steady State theories of cosmology.

### Lemaître's equation Edit

In 1927, two years before Hubble published his own article, the Belgian priest and astronomer Georges Lemaître was the first to publish research deriving what is now known as Hubble's law. According to the Canadian astronomer Sidney van den Bergh, "the 1927 discovery of the expansion of the universe by Lemaître was published in French in a low-impact journal. In the 1931 high-impact English translation of this article, a critical equation was changed by omitting reference to what is now known as the Hubble constant." [22] It is now known that the alterations in the translated paper were carried out by Lemaître himself. [10] [23]

### Shape of the universe Edit

Before the advent of modern cosmology, there was considerable talk about the size and shape of the universe. In 1920, the Shapley–Curtis debate took place between Harlow Shapley and Heber D. Curtis over this issue. Shapley argued for a small universe the size of the Milky Way galaxy, and Curtis argued that the universe was much larger. The issue was resolved in the coming decade with Hubble's improved observations.

### Cepheid variable stars outside the Milky Way Edit

Edwin Hubble did most of his professional astronomical observing work at Mount Wilson Observatory, [24] home to the world's most powerful telescope at the time. His observations of Cepheid variable stars in "spiral nebulae" enabled him to calculate the distances to these objects. Surprisingly, these objects were discovered to be at distances which placed them well outside the Milky Way. They continued to be called *nebulae*, and it was only gradually that the term *galaxies* replaced it.

### Combining redshifts with distance measurements Edit

The parameters that appear in Hubble's law, velocities and distances, are not directly measured. In reality we determine, say, a supernova brightness, which provides information about its distance, and the redshift *z* = ∆*λ*/*λ* of its spectrum of radiation. Hubble correlated brightness and parameter *z*.

Combining his measurements of galaxy distances with Vesto Slipher and Milton Humason's measurements of the redshifts associated with the galaxies, Hubble discovered a rough proportionality between redshift of an object and its distance. Though there was considerable scatter (now known to be caused by peculiar velocities—the 'Hubble flow' is used to refer to the region of space far enough out that the recession velocity is larger than local peculiar velocities), Hubble was able to plot a trend line from the 46 galaxies he studied and obtain a value for the Hubble constant of 500 km/s/Mpc (much higher than the currently accepted value due to errors in his distance calibrations see cosmic distance ladder for details).

At the time of discovery and development of Hubble's law, it was acceptable to explain redshift phenomenon as a Doppler shift in the context of special relativity, and use the Doppler formula to associate redshift *z* with velocity. Today, in the context of general relativity, velocity between distant objects depends on the choice of coordinates used, and therefore, the redshift can be equally described as a Doppler shift or a cosmological shift (or gravitational) due to the expanding space, or some combination of the two. [28]

#### Hubble diagram Edit

Hubble's law can be easily depicted in a "Hubble diagram" in which the velocity (assumed approximately proportional to the redshift) of an object is plotted with respect to its distance from the observer. [29] A straight line of positive slope on this diagram is the visual depiction of Hubble's law.

### Cosmological constant abandoned Edit

After Hubble's discovery was published, Albert Einstein abandoned his work on the cosmological constant, which he had designed to modify his equations of general relativity to allow them to produce a static solution, which he thought was the correct state of the universe. The Einstein equations in their simplest form model generated either an expanding or contracting universe, so Einstein's cosmological constant was artificially created to counter the expansion or contraction to get a perfect static and flat universe. [30] After Hubble's discovery that the universe was, in fact, expanding, Einstein called his faulty assumption that the universe is static his "biggest mistake". [30] On its own, general relativity could predict the expansion of the universe, which (through observations such as the bending of light by large masses, or the precession of the orbit of Mercury) could be experimentally observed and compared to his theoretical calculations using particular solutions of the equations he had originally formulated.

In 1931, Einstein made a trip to Mount Wilson Observatory to thank Hubble for providing the observational basis for modern cosmology. [31]

The cosmological constant has regained attention in recent decades as a hypothesis for dark energy. [32]

The discovery of the linear relationship between redshift and distance, coupled with a supposed linear relation between recessional velocity and redshift, yields a straightforward mathematical expression for Hubble's law as follows:

- v
is the recessional velocity, typically expressed in km/s. *H*_{0}is Hubble's constant and corresponds to the value of H(often termed the **Hubble parameter**which is a value that is time dependent and which can be expressed in terms of the scale factor) in the Friedmann equations taken at the time of observation denoted by the subscript*0*. This value is the same throughout the universe for a given comoving time.- D
is the proper distance (which can change over time, unlike the comoving distance, which is constant) from the galaxy to the observer, measured in megaparsecs (Mpc), in the 3-space defined by given cosmological time. (Recession velocity is just *v*=*dD/dt*).

Hubble's law is considered a fundamental relation between recessional velocity and distance. However, the relation between recessional velocity and redshift depends on the cosmological model adopted and is not established except for small redshifts.

For distances *D* larger than the radius of the Hubble sphere *r*_{HS} , objects recede at a rate faster than the speed of light (*See* Uses of the proper distance for a discussion of the significance of this):

Since the Hubble "constant" is a constant only in space, not in time, the radius of the Hubble sphere may increase or decrease over various time intervals. The subscript '0' indicates the value of the Hubble constant today. [25] Current evidence suggests that the expansion of the universe is accelerating (*see* Accelerating universe), meaning that for any given galaxy, the recession velocity dD/dt is increasing over time as the galaxy moves to greater and greater distances however, the Hubble parameter is actually thought to be decreasing with time, meaning that if we were to look at some *fixed* distance D and watch a series of different galaxies pass that distance, later galaxies would pass that distance at a smaller velocity than earlier ones. [34]

### Redshift velocity and recessional velocity Edit

Redshift can be measured by determining the wavelength of a known transition, such as hydrogen α-lines for distant quasars, and finding the fractional shift compared to a stationary reference. Thus redshift is a quantity unambiguous for experimental observation. The relation of redshift to recessional velocity is another matter. For an extensive discussion, see Harrison. [35]

#### Redshift velocity Edit

The redshift *z* is often described as a *redshift velocity*, which is the recessional velocity that would produce the same redshift *if* it were caused by a linear Doppler effect (which, however, is not the case, as the shift is caused in part by a cosmological expansion of space, and because the velocities involved are too large to use a non-relativistic formula for Doppler shift). This redshift velocity can easily exceed the speed of light. [36] In other words, to determine the redshift velocity *v _{rs}*, the relation:

is used. [37] [38] That is, there is *no fundamental difference* between redshift velocity and redshift: they are rigidly proportional, and not related by any theoretical reasoning. The motivation behind the "redshift velocity" terminology is that the redshift velocity agrees with the velocity from a low-velocity simplification of the so-called Fizeau-Doppler formula. [39]

Here, *λ _{o}*,

*λ*are the observed and emitted wavelengths respectively. The "redshift velocity"

_{e}*v*is not so simply related to real velocity at larger velocities, however, and this terminology leads to confusion if interpreted as a real velocity. Next, the connection between redshift or redshift velocity and recessional velocity is discussed. This discussion is based on Sartori. [40]

_{rs}#### Recessional velocity Edit

Suppose *R(t)* is called the *scale factor* of the universe, and increases as the universe expands in a manner that depends upon the cosmological model selected. Its meaning is that all measured proper distances *D(t)* between co-moving points increase proportionally to *R*. (The co-moving points are not moving relative to each other except as a result of the expansion of space.) In other words:

where *t*_{0} is some reference time. If light is emitted from a galaxy at time *t _{e}* and received by us at

*t*

_{0}, it is redshifted due to the expansion of space, and this redshift

*z*is simply:

Suppose a galaxy is at distance *D*, and this distance changes with time at a rate *d _{t}D*. We call this rate of recession the "recession velocity"

*v*:

_{r}We now define the Hubble constant as

and discover the Hubble law:

From this perspective, Hubble's law is a fundamental relation between (i) the recessional velocity contributed by the expansion of space and (ii) the distance to an object the connection between redshift and distance is a crutch used to connect Hubble's law with observations. This law can be related to redshift *z* approximately by making a Taylor series expansion:

If the distance is not too large, all other complications of the model become small corrections, and the time interval is simply the distance divided by the speed of light:

According to this approach, the relation *cz* = *v _{r}* is an approximation valid at low redshifts, to be replaced by a relation at large redshifts that is model-dependent. See velocity-redshift figure.

### Observability of parameters Edit

Strictly speaking, neither *v* nor *D* in the formula are directly observable, because they are properties *now* of a galaxy, whereas our observations refer to the galaxy in the past, at the time that the light we currently see left it.

For relatively nearby galaxies (redshift *z* much less than unity), *v* and *D* will not have changed much, and *v* can be estimated using the formula v = z c *c* is the speed of light. This gives the empirical relation found by Hubble.

For distant galaxies, *v* (or *D*) cannot be calculated from *z* without specifying a detailed model for how *H* changes with time. The redshift is not even directly related to the recession velocity at the time the light set out, but it does have a simple interpretation: *(1+z)* is the factor by which the universe has expanded while the photon was travelling towards the observer.

### Expansion velocity vs. relative velocity Edit

In using Hubble's law to determine distances, only the velocity due to the expansion of the universe can be used. Since gravitationally interacting galaxies move relative to each other independent of the expansion of the universe, [42] these relative velocities, called peculiar velocities, need to be accounted for in the application of Hubble's law.

The Finger of God effect is one result of this phenomenon. In systems that are gravitationally bound, such as galaxies or our planetary system, the expansion of space is a much weaker effect than the attractive force of gravity.

### Time-dependence of Hubble parameter Edit

On defining the dimensionless deceleration parameter

From this it is seen that the Hubble parameter is decreasing with time, unless q < − 1

### Idealized Hubble's law Edit

The mathematical derivation of an idealized Hubble's law for a uniformly expanding universe is a fairly elementary theorem of geometry in 3-dimensional Cartesian/Newtonian coordinate space, which, considered as a metric space, is entirely homogeneous and isotropic (properties do not vary with location or direction). Simply stated the theorem is this:

Any two points which are moving away from the origin, each along straight lines and with speed proportional to distance from the origin, will be moving away from each other with a speed proportional to their distance apart.

In fact this applies to non-Cartesian spaces as long as they are locally homogeneous and isotropic, specifically to the negatively and positively curved spaces frequently considered as cosmological models (see shape of the universe).

An observation stemming from this theorem is that seeing objects recede from us on Earth is not an indication that Earth is near to a center from which the expansion is occurring, but rather that *every* observer in an expanding universe will see objects receding from them.

### Ultimate fate and age of the universe Edit

The value of the Hubble parameter changes over time, either increasing or decreasing depending on the value of the so-called deceleration parameter q

In a universe with a deceleration parameter equal to zero, it follows that *H* = 1/*t*, where *t* is the time since the Big Bang. A non-zero, time-dependent value of q

It was long thought that *q* was positive, indicating that the expansion is slowing down due to gravitational attraction. This would imply an age of the universe less than 1/*H* (which is about 14 billion years). For instance, a value for *q* of 1/2 (once favoured by most theorists) would give the age of the universe as 2/(3*H*). The discovery in 1998 that *q* is apparently negative means that the universe could actually be older than 1/*H*. However, estimates of the age of the universe are very close to 1/*H*.

### Olbers' paradox Edit

The expansion of space summarized by the Big Bang interpretation of Hubble's law is relevant to the old conundrum known as Olbers' paradox: If the universe were infinite in size, static, and filled with a uniform distribution of stars, then every line of sight in the sky would end on a star, and the sky would be as bright as the surface of a star. However, the night sky is largely dark. [43] [44]

Since the 17th century, astronomers and other thinkers have proposed many possible ways to resolve this paradox, but the currently accepted resolution depends in part on the Big Bang theory, and in part on the Hubble expansion: In a universe that exists for a finite amount of time, only the light of a finite number of stars has had enough time to reach us, and the paradox is resolved. Additionally, in an expanding universe, distant objects recede from us, which causes the light emanated from them to be redshifted and diminished in brightness by the time we see it. [43] [44]

### Dimensionless Hubble constant Edit

Instead of working with Hubble's constant, a common practice is to introduce the **dimensionless Hubble constant**, usually denoted by *h*, and to write Hubble's constant *H*_{0} as *h* × 100 km s −1 Mpc −1 , all the relative uncertainty of the true value of *H*_{0} being then relegated to *h*. [45] The dimensionless Hubble constant is often used when giving distances that are calculated from redshift *z* using the formula *d* ≈ *c* / *H _{0}* ×

*z*. Since

*H*is not precisely known, the distance is expressed as:

_{0}In other words, one calculates 2998×z and one gives the units as Mpc h − 1

Occasionally a reference value other than 100 may be chosen, in which case a subscript is presented after *h* to avoid confusion e.g. h_{70} denotes H 0 = 70 h 70

This should not be confused with the dimensionless value of Hubble's constant, usually expressed in terms of Planck units, obtained by multiplying *H*_{0} by 1.75 × 10 −63 (from definitions of parsec and *t*_{P}), for example for *H*_{0}=70, a Planck unit version of 1.2 × 10 −61 is obtained.

The value of the Hubble constant is estimated by measuring the redshift of distant galaxies and then determining the distances to them by some other method than Hubble's law. This approach forms part of the cosmic distance ladder for measuring distances to extragalactic objects. Uncertainties in the physical assumptions used to determine these distances have caused varying estimates of the Hubble constant. [2]

The observations of astronomer Walter Baade led him to define distinct "populations" for stars (Population I and Population II). The same observations led him to discover that there are two types of Cepheid variable stars. Using this discovery he recalculated the size of the known universe, doubling the previous calculation made by Hubble in 1929. [47] [48] [49] He announced this finding to considerable astonishment at the 1952 meeting of the International Astronomical Union in Rome.

In October 2018, scientists presented a new third way (two earlier methods, one based on redshifts and another on the cosmic distance ladder, gave results that do not agree), using information from gravitational wave events (especially those involving the merger of neutron stars, like GW170817), of determining the Hubble constant. [50] [51]

In July 2019, astronomers reported that a new method to determine the Hubble constant, and resolve the discrepancy of earlier methods, has been proposed based on the mergers of pairs of neutron stars, following the detection of the neutron star merger of GW170817, an event known as a dark siren. [52] [53] Their measurement of the Hubble constant is 73.3 +5.3

−5.0 (km/s)/Mpc. [54]

Also in July 2019, astronomers reported another new method, using data from the Hubble Space Telescope and based on distances to red giant stars calculated using the tip of the red-giant branch (TRGB) distance indicator. Their measurement of the Hubble constant is 69.8 +1.9

−1.9 (km/s)/Mpc. [55] [56] [57]

### Earlier measurement and discussion approaches Edit

For most of the second half of the 20th century, the value of H 0

The value of the Hubble constant was the topic of a long and rather bitter controversy between Gérard de Vaucouleurs, who claimed the value was around 100, and Allan Sandage, who claimed the value was near 50. [58] In 1996, a debate moderated by John Bahcall between Sidney van den Bergh and Gustav Tammann was held in similar fashion to the earlier Shapley–Curtis debate over these two competing values.

This previously wide variance in estimates was partially resolved with the introduction of the ΛCDM model of the universe in the late 1990s. With the ΛCDM model observations of high-redshift clusters at X-ray and microwave wavelengths using the Sunyaev–Zel'dovich effect, measurements of anisotropies in the cosmic microwave background radiation, and optical surveys all gave a value of around 70 for the constant. [* citation needed *]

More recent measurements from the Planck mission published in 2018 indicate a lower value of 67.66 ± 0.42 , although, even more recently, in March 2019, a higher value of 74.03 ± 1.42 has been determined using an improved procedure involving the Hubble Space Telescope. [59] The two measurements disagree at the 4.4σ level, beyond a plausible level of chance. [60] The resolution to this disagreement is an ongoing area of research. [61]

*See table of measurements below for many recent and older measurements.*

### Acceleration of the expansion Edit

A value for q

### Matter-dominated universe (with a cosmological constant) Edit

### Matter- and dark energy-dominated universe Edit

If the universe is both matter-dominated and dark energy-dominated, then the above equation for the Hubble parameter will also be a function of the equation of state of dark energy. So now:

If *w* is constant, then

If dark energy does not have a constant equation-of-state w, then

Other ingredients have been formulated recently. [64] [65] [66]

### Hubble time Edit

This is slightly different from the age of the universe which is approximately 13.8 billion years. The Hubble time is the age it would have had if the expansion had been linear, and it is different from the real age of the universe because the expansion is not linear they are related by a dimensionless factor which depends on the mass-energy content of the universe, which is around 0.96 in the standard ΛCDM model.

We currently appear to be approaching a period where the expansion of the universe is exponential due to the increasing dominance of vacuum energy. In this regime, the Hubble parameter is constant, and the universe grows by a factor *e* each Hubble time:

Likewise, the generally accepted value of 2.27 Es −1 means that (at the current rate) the universe would grow by a factor of e 2.27

Over long periods of time, the dynamics are complicated by general relativity, dark energy, inflation, etc., as explained above.

### Hubble length Edit

### Hubble volume Edit

Multiple methods have been used to determine the Hubble constant. "Late universe" measurements using calibrated distance ladder techniques have converged on a value of approximately 73 km/s/Mpc . Since 2000, "early universe" techniques based on measurements of the cosmic microwave background have become available, and these agree on a value near 67.7 km/s/Mpc . (This is accounting for the change in the expansion rate since the early universe, so is comparable to the first number.) As techniques have improved, the estimated measurement uncertainties have shrunk, but the range of measured values has not, to the point that the disagreement is now statistically significant. This discrepancy is called the **Hubble tension**. [68] [69] [70]

As of 2020 [update] , the cause of the discrepancy is not understood. In April 2019, astronomers reported further substantial discrepancies across different measurement methods in Hubble constant values, possibly suggesting the existence of a new realm of physics not currently well understood. [60] [71] [72] [73] [74] By November 2019, this tension had grown so far that some physicists like Joseph Silk had come to refer to it as a "possible crisis for cosmology", as the observed properties of the universe appear to be mutually inconsistent. [75] In February 2020, the Megamaser Cosmology Project published independent results that confirmed the distance ladder results and differed from the early-universe results at a statistical significance level of 95%. [76] In July 2020, measurements of the cosmic background radiation by the Atacama Cosmology Telescope predict that the Universe should be expanding more slowly than is currently observed. [77]

## Hubble’s Law

We need to be fair here: Edwin Hubble‘s discoveries were indipendently found by Georges Lemaître too. So the law should be called Hubble-Lemaître law. But still, in the scientific community, everybody recalls Hubble’s name only. That is why we wanted to put a feature image above that portraits both scientists. We ask forgiveness to Lemaître, but we shall follow the universal terminology.

Hubble’s law gave the birth to modern cosmology because it has found evidence of a striking fact about our observable universe: the universe is expanding.

This lecture will illustrate the path to the discovery of such an outstanding fact and will also give the mathematical rule of such discovery.

We have learnt from the Nature of Light lecture that light is an EM radiation, and we can obtain the spectrum of all EM radiations, practically the “*fingerprint*” of the examined EM radiation. So, as all the astronomers do, Edwing Hubble had a natural inclination to attach a spectrograph to his telescope for any observations. To his great astonishment, he found out that several nebulae appeared to be completely different objects, much farther than expected. They were entire galaxies, not nebulae, distant islands of stars, most of them presenting an overwhelming feature: a red shift of their spectra. In other words, given a single element in the spectrum, its absortion lines were shifted towards the longer wavelenghts. According to the Doppler Effect this could only mean that the objects observed were all moving away from the Earth.

By observing the apparent brightness and pulsation periods of Cepheid variables in several galaxies, he calculated the distance of those objects realizing that these objects were much farther away than expected, outside our own galaxy itself.

We will talk about Cepheid variables, but for now let’s say that those variable stars can be used as standard candles and by calculating their pulsating period and directly relate it to their luminosity, we obtain their distance.

Several galaxies were observed in the same fashion, and Hubble (and Lemaître, to be fair) obtained a direct relation between distance and Doppler Shift (in this case, a red shift). We have learnt this in the lecture about the Doppler effect:

So he managed to calculate the velocity at which the objects were moving away. Putting all things together, he issued this chart in 1929:

You can see that there is a direct relation between the recession velocity of a galaxy and its distance from the Earth. This relation H_{o} has been calculated as: 71 km/s/Mpc:

It is obviously noted from the chart above that this direct relation (H_{o}) is not really precise: the positions of the galaxies in the chart are almost consistent to a straight diagonal line, but there are few difficulties: the exact determination of their distance. As the observations become more precise, the Hubble constant H_{o} has been more and more refined, and the charts related to it appeared more and more precise:

However, observations of Hubble Space Telescope to Cepheid variables and galaxies as far away as 30 Mpc (100 million ly) have lead the value of H_{o} to 73/km/s/Mpc. So, because the value of H_{o} is still somewhat uncertain, astronomers often prefer to express the distance of remote galaxies in terms of red shift z (which can be measured very accurately), thus creating a Hubble law chart like this:

Where the value of z is on the x-axis against the value of Δm on the y-axis.

The cosmological implications of such a discovery is that, at very large scales, the universe is expanding, inflating. That concept has lead scientists to the idea of an inflationary universe which started its expansion immediately after the Big Bang. This was a revolution that lead Einstein himself to abandon the idea of a *cosmological constant*, a factor in the equation to preserve a stationary idea of the universe.

Not all the galaxies show a red shift, though. There are many of them, in our Local Group, that show a blue shift (approaching). Cosmically speaking, these galaxies are part of a neighbourhood of galaxies (including M31 Andromeda Galaxy) who are moving towards us due to gravitational effects.

But what does an expanding universe exactly mean?

Well, there is no exact explanation for that, because we enter the realm of out-of-ordinary experience for us human beings. For a start, the universe is NOT expanding inside a container, because there is no container in the first place. Therefore, it is already quite difficult for our limited minds to understand in depth the concept of an expanding universe. However, we can describe the general characteristics of such an expansion. How? With a raisin bread inflating from the action of yeast!

It is important to point out that each of the raisin moves away from each other, but there is really no center of inflation: If we were onboard another raisin we would see all the other raisin moving away from us. Likewise, our Milky Way is not at the center of the universe, but every single galaxy is moving away from the other, except the ones who are moving towards another due to gravitational effects (Andromeda Galaxy towards the Milky Way).

How much the remote objects move away one another? We saw that it does depend on their distance. For example, quasar 3C273 in Virgo constellation, moves at 51,000 km/s away from us, as we see in this example. And the more it moves away, the more recession speed it will have.

Such a speed it is quite remarkable, but if we look back at the origins of our universe, something really astonishing comes up: the initial expansion of the universe, at the very early stages after the Big Bang, was faster than the speed of light itself!

Of course you know that nothing can be faster than the speed of light **c**. But this is true INSIDE our universe, in other words, inside the container of all the laws of physics that we know. However, the container itself expanded faster than c and this does not break any known law of physics.

As a matter of fact, there are objects that are so distant that their recession speeds go beyond the speed of light, but this cannot be assessed by the Doppler effect. We will talk about this when we will cover the concept of **Cosmological Shift**.

## Contents

He was born in La Crosse, Wisconsin to D. D. MacMillan, who was in the lumber business, and Mary Jane McCrea. His brother, John H. MacMillan, headed the Cargill Corporation from 1909 to 1936. MacMillan graduated from La Crosse High School in 1888. In 1889 he attended Lake Forest College, then entered the University of Virginia. Later in 1898 he earned an A.B. degree from Fort Worth University, which was then a Methodist university in Texas. He performed his graduate work at the University of Chicago, earning a master's degree in 1906 and a PhD in 1908. In 1907, prior to completing his PhD, he joined the staff of the University of Chicago as a research assistant in geology. In 1908 he became an associate in mathematics, then in 1909 he began instruction in astronomy at the same institution. His career as a professor began in 1912 when he became an assistant professor. In 1917 the U.S. declared war on Germany, and Dr. MacMillan served as a major in the U.S. army's ordnance department during World War I. Following the war he became associate professor in 1919, then full professor in 1924. MacMillan retired in 1936. [1] [3] [4]

In a 1958 paper about MacMillan's work on cosmology, Richard Schlegel introduced MacMillan as "best known to physicists for his three-volume *Classical Mechanics*" that remained in print for decades after MacMillan's 1936 retirement. [1] MacMillan published extensively on the mathematics of the orbits of planets and stars. In the 1920s, MacMillan developed a cosmology that presumed an unchanging, steady-state model of the universe. This was uncontroversial at the time, and indeed in 1918 Albert Einstein had also sought to adapt his relativity theories to the model using a cosmological constant. [5] MacMillan accepted that the radiance of stars came from then unknown processes that converted their mass into radiant energy. This perspective suggested that individual stars and the universe itself would ultimately go dark, which was called the "heat death" of the universe. MacMillan avoided the conclusion about the universe through a mechanism later known as the "tired-light hypothesis". He speculated that the light emitted by stars might re-create matter in its travels through space. [2]

MacMillan's work on cosmology lost influence in the 1930s after Hubble's Law became accepted. Edwin Hubble's 1929 publication, and earlier work by Georges Lemaître, reported on observations of entire galaxies far from the earth and its galaxy. The further away a galaxy is, the faster it is apparently moving *away* from the earth. Hubble's Law strongly suggested that universe is expanding. In 1948, a new version of a steady-state cosmology was proposed by Bondi, Gold, and Hoyle that was consistent with the measurements on distant galaxies. While the authors were apparently not aware of MacMillan's earlier work, there were substantial similarities. [1] [2] With the observation of the cosmic microwave background (CMB) in 1965, steady-state models of the universe have been rejected by most astronomers and physicists. The CMB is a prediction of the Big Bang model of an expanding universe.

MacMillan also had a distaste for Einstein's relativity theories. In a published debate in 1927, Macmillan invoked "postulates of normal intuition" to argue against them. He objected to the theories' inconsistency with an absolute scale of time. Einstein's theories predict that an observer will see that rapidly moving clocks tick more slowly than the observer's own clock. Later experiments amply confirmed this "time dilation" prediction of relativity theory. [6]

In an Associated Press report Dr. MacMillan speculated on the nature of interstellar civilizations, believing that they would be vastly more advanced than our own. "Out in the heavens, perhaps, are civilizations as far above ours as we are above the single cell, since they are so much older than ours." [* citation needed *]

## Hubble law

In 1929 Edwin Hubble published his landmark discovery that distant spiral "nebulae" are receding from us at speeds proportional to their distances, implying that the Universe is expanding at a constant rate.

The linear relationship between the distance of a galaxy (D) and its cosmological recessional velocity (V) V = HxD, where H is Hubble's constant.

**Hubble law** - the principle that a distant galaxy's recessional velocity is proportional to its distance from Earth .

Now let's return to the discussion of the astronomer Hubble. Hubble, you will recall, determined the distance to the Andromeda galaxy by finding a Cepheid variable star there. This settled the question as to whether or not the spiral nebula were galaxies.

Binney, J. and Tremaine, S. Galactic Dynamics. Princeton, NJ: Princeton University Press, 1987.

- (n.)

The linear relation between the velocity of recession of a distant object and its distance from us, v = H0d.

human genome project - (n.) .

27.1 Quasars, 29.1 The Age of the Universe

Hubble Space Telescope6.2 Telescopes Today, 6.5 Observations outside Earth's Atmosphere, 6.5 Observations outside Earth's Atmosphere, 27.1 Quasars, 27.2 Supermassive Black Holes: What Quasars Really Are

Hubble time29.1 The Age of the Universe .

Law proposed by Edwin hubble in his landmark paper of 1929 claiming a linear relation between the distance of galaxies from us and their velocity of recession, deduced from the redshift in their spectra. The law can be stated as:

v = H0d .

with time variable Hubble parameter is satisfied exactly at all times by the metric radial distance D(t) which is the spatial separation at the common time t, so

"velocity" = dD/dt = H(t)D(t).

such an important discovery?

What does the value of the Hubble Constant tell us?

What methods do astronomers use to determine the mass of galaxies, and what are the limitations of those methods?

What is the significance of the Mass-to-Luminosity ratio?

This relationship is known as the

and the constant of proportionality H is the Hubble Constant. (See Figure 1.)

Figure 1

The Hubble Relationship and Law (Hubble 1929).

Bulk motions of distant galaxies deviating from the Hubble flow. see

HUBBLE CONSTANT: The constant of proportionality (designated H) between recession velocity and distance in the

. It is a constant of proportionality but not a constant in time, because it can change over the history of the universe.

Hubble constant The proportionality constant relating velocity and distance in the

the value, now around 75 km/s/Mpc, changes with time as the Universe expands. Hubble time Numerically the inverse of the Hubble constant it represents, in order of magnitude, the age of the universe.

According to this law, known as the

, the greater the distance of a galaxy, the faster it recedes. Derived from theoretical considerations and confirmed by observations, the velocity-distance law has made secure the concept of an expanding universe.

(with our adopted value of the Hubble constant H0 = 65 km/s/Mpc), we obtain distances of 660 Mpc for 3C 273 and 1340 Mpc for 3C 48. (More Precisely 25-1 discusses in more detail how these distances are determined and what they mean).

Hubble constant - the proportionality constant that arises from the

, the relationship between a galaxy's expansion velocity and the distance to that galaxy. An accurate value of the Hubble constant is required to know the critical density of the universe, as well as the age of the universe.

It should be noted that, on very large scales, Einstein's theory predicts departures from a strictly linear

. The amount of departure, and the type, depends on the value of the total mass of the universe. In this way a plot of recession velocity (or redshift) vs.

Not only does this background radiation demonstrate that such a big bang occurred, the speed of the galaxies increase with increasing distance from us (also called the

). With the age of the Universe at 13.7 billion years, we now have one variable solved when we run computer simulations of our Universe.

The premise of the method lies in the "

" which states that due to the general expansion of the universe, the velocity at which a galaxy is receding is proportional to the distance of that galaxy from us. Galaxies having the same redshift are thought to reside at the same distance from earth.

This motion can cause confusion when looking at a solar or galactic spectrum, because the expected redshift based on the simple

To do this, they must be moving very fast. This is exactly what the

shows! Furthermore, aliens living in other galaxies observed the exact same pattern from their galaxies. No matter where you stand, the rest of the Universe appears to be moving smoothly away from your position.

Q: Will the recommendation to rename the

to the Hubble-Lemaître law lead to other renamings?

In 1929, American astronomer Edwin Hubble matched up redshifts with distance estimates to the galaxies and uncovered something remarkable: the farther away a galaxy, the faster it's receding. This relation, the

, was renamed in 2018 by the International Astronomical Union to the Hubble-Lemaître law.