Hubble–Lemaître law

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The Hubble-Lemaître law discovered in the 20th century by Edwin Hubble exactly in 1929, previously called Hubble's law, is a law of physics that establishes that the redshift of a galaxy is proportional to its distance, which is the same as expressing that the further a galaxy is from another, the faster it appears to be receding from it. observational evidence for the paradigm of the expansion of the universe and currently serves as one of the most cited pieces of evidence supporting the Big Bang.^{[citation required]}

According to this law, a measure of the inertia of the expansion of the universe is given by the Hubble constant. From this observational relationship, it can be inferred that galaxies are receding from each other at a rate proportional to their distance, a more general relationship known as the velocity-distance relationship and sometimes confused with Hubble's law. Don't misunderstand the speed-distance relationship either. It is not that the further away a galaxy is, the faster it is moving away from us. According to this, as the galaxy recedes, it would increase in speed, since it is further away than before. It is not like this. The speed-distance relationship, derived from Hubble's law, says that the further away a galaxy is now, the faster it is now moving away from us. Even if all galaxies were gradually reducing their speed of departure (currently, it seems that the opposite is the case), it would continue to be true that the speed of a distant galaxy is greater than that of a nearby one, always maintaining a speed-distance proportionality.^{[citation required]}

The Hubble-Lemaître law says that at each moment in the history of the Universe there is a proportionality between the redshift and the distance (consequently, also between speed and distance) but it does not say, in itself, how the universe evolves. Universe. It does not say whether the expansion is accelerating, slowing down, or remaining constant. The most recent calculations of the constant, using data from the WMAP satellite, began in 2003 and allowed us to give the value of 71 ± 4(km/s)/Mpc for this constant, which means that the Universe is 13,781 years old.,306 million years. In 2006, the new data provided by this satellite gave the value of 70 (km/s)/Mpc, +2.4/-3.2, so the Universe would have an age of 13,978.182 million years. Both measures are close to 14 billion, so it is that ballpark figure that is often given. In August 2006, a less precise measurement was obtained independently using data from NASA's orbiting Chandra X-ray Observatory: 77 ± 15%(km/s)/Mpc.

1 Mpc (1 Megaparsec) = 3.2616 million light years = 3.0857118 × 10^22 m.

At present, a galaxy 3.26 million light-years away would be receding at a speed of about 70 km/s (ignoring the peculiar proper motions of galaxies caused by the gravity of other galaxies within its cluster and its supercluster).^{[citation needed]}

Background

A decade before Edwin Hubble made his observations, several physicists and mathematicians had established a consistent theory of the relationship between space and time using Einstein's field equations of general relativity. Applying the general principles to the nature of the Universe, a dynamic solution was produced that clashed with the then prevailing notion of a static Universe.^{[citation needed]}

In 1922, Alexander Friedmann found his equations from Einstein's field equations, showing that the Universe can expand at a rate calculable by the equations. The parameter used by Friedman is now known as the scale factor with which it can be considered a scale-invariant form of the constant of proportionality of Hubble's law. Georges Lemaître independently found a similar solution in 1927. The Friedmann equations are obtained by inserting the metric of a homogeneous and isotropic Universe into the Einstein field equations for a fluid with a given density and pressure. This idea of expanding space-time would eventually lead to the Big Bang and Steady State theories of cosmology.^{[citation needed]}

Before the advent of modern cosmology, there was a lot of discussion about the size and shape of the Universe. In 1920, the famous Shapley-Curtis debate took place between Harlow Shapley and Heber D. Curtis on the subject. Shapley supported the idea of a small Universe the size of the Milky Way, and Curtis argued that the Universe was much larger. The subject of the debate ended up being resolved in the following decade, with the improved observations of Hubble.

Edwin Hubble spent much of his professional work in observational astronomy at Mount Wilson Observatory, the most powerful telescope in the world 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 found to be at distances that placed them outside the Milky Way. Nebulae were first described as "islands of universes" and only after that discovery did they begin to be described as galaxies.

In the 1920s, Hubble combined these measurements of galaxy distances with the Vesto Slipher measurements from the redshift, due to the relative receding or receding of each other according to the Doppler effect. Hubble discovered a linear relationship between both magnitudes, that is, the further away a galaxy is, the greater its redshift. The coefficient of proportionality is called Hubble's constant, H₀ Although there was considerable scatter (now known to be due to peculiar velocity), Hubble was able to draw a linear trend of 46 galaxies that he had studied, and obtained 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). In 1958, the first large estimate of H₀, 75 km/s/Mpc, was obtained and published by Allan Sandage.^{[citation needed]}

This relationship was interpreted as proof that the Universe was expanding, although Hubble personally doubted this interpretation. Subsequently, theoretical cosmological models based on Albert Einstein's theory of general relativity made it possible to explain this expansion, since which arises naturally from the field equations of the theory. Einstein himself, who initially believed in a static Universe, artificially introduced an extra term to these equations, called the cosmological constant, to avoid the phenomenon of expansion. Following the results published by Hubble, Einstein backed down and retired this term, which he called "the biggest mistake of my career." Einstein would famously make a trip to Mount Wilson in 1931 to thank Hubble for providing the observational foundation for modern cosmology.^{[citation needed]}

The value of the Hubble constant and the age of the universe

During the 20th century, one of the priorities of cosmology was the calculation of the Hubble constant. The first calculations made by Hubble were based on the redshift data of 46 galaxies, and gave a value of about 500 km/s/Mpc, according to which the universe would be only 2,000 million years old, an insufficient value already at that time. time, because from the isotopes of the rocks it was known that the age of the Earth was about 4,500 million years. In 1956, Allan Sandage determined the value to be 180 km/s/Mpc. Two years later, Sandage himself published an article with the value of 75 (km/s)/Mpc, very close to the current value. However, in the early 1970s the estimated value of H₀ varied from 50 km/s/Mpc to 100 km/s/Mpc, depending on the method used. Based on these data, the estimated age of the universe ranged from about 10 billion years to 20 billion years.

Obviously, this was excessive uncertainty that needed to be corrected. Errors in the estimate of H₀ were mainly due to instrumental limitations, so when the Hubble Space Telescope was launched, one of its priorities was the determination of H₀, within the framework of the so-called Hubble Space Telescope Key Project, taking advantage of the exceptional capabilities of this instrument. In 2001, the results of this project were published after several years of study, which yielded a value for H₀ of 72±8 km/s/Mpc, according to which the age of the universe should be about 10 billion years, insufficient to account for the oldest stars in globular clusters, with an age of about 14 billion years. At the same time, however, observations of distant supernovae revealed that there is some other factor driving the expansion of the universe that has been called dark energy. Specifically, the expansion of the universe is accelerating due to the action of dark energy, so the age of the Universe taking this acceleration into account is close to 14 billion years, which is in agreement with the age of the oldest stars.

In 2001, the WMAP satellite was launched for the study of microwave background radiation. This radiation provides data about the early universe, including the value of H₀, so when studying it, cosmologists have a second alternative method to the redshift of galaxies for calculating H₀. In 2003, the first WMAP results were published, giving a value of 71±4 (km/s)/Mpc for H₀. In 2006, some more detailed analyzes of the data have allowed H₀ to be estimated at 70 (km/s)/Mpc, +2.4/-3.2, and this is the largest measurement of the Hubble constant. precision obtained to date. Dr. Adolfo Moran, of the World Physics Society, found the quantity of 96.8 km/s/Mpsec to be the most accurate value of the Hubble constant, which would give an age of the Universe of just over ten billion years.

Also in 2006 the Chandra X-ray space telescope calculated H₀ by another independent method, and obtained the value of 77 km/s/Mpc.

On May 5, 2009, a team led by Adam Riess, using the Hubble telescope, announced a measurement that yielded a value for the constant of 74.2 +/-3.6 km/s/megaparsec. This measurement has a margin of error of less than 5%.

On July 25, 2011, Florian Beutler, a PhD student at the International Center for Radio Astronomy Research (ICRAR) in Australia, after analyzing more than 125,000 galaxies, achieved a new measurement, 67.0 ± 3.2 km/s/megaparsec.

Finally, in March 2014 the Planck space mission published what is currently the best value available, this being H₀ = 67.3 ± 1.2 (km/s)/Mpc, thanks to the study of microwave background radiation.

In 2017, with the detection of gravitational waves and corresponding optical counterparts from the source of GW170817, by fusion of two neutron stars, a value of ${displaystyle H_{0}=70_{-8}^{+12}}$ (km/s)/Mpc (at 68% LL), compatible with the rest of the measures and of great value by not using any other source of distances used for the rest of the measures.

In 2018, the study of a new independent calculation of Hubble Constant was published from the gravitational lens effect that caused the appearance of the 5th image of the Refsdal SN. The value obtained is ${displaystyle H_{0}=64_{-11}^{+9}}$ (km/s)/Mpc compatible with the values published by Planck Collaboration in 2015.

The value of the Hubble constant in the wave theory of the universe

The theory of the wave universe says that our universe is a 3D wave that has been produced on a 4D brane due to a disturbance, a collision between branes. Just like a stone falling on the surface of a pond (2D) generates a wave (1D), in the Omniverse there was a 4D brane and there was a disturbance of some kind that caused a 3D wave.

Our universe is that wave. Not the interior of the wave, what is left behind, but the wave front itself. This being the case, it is very easy to calculate the value of the Hubble constant at any time in history. The problem is the same as calculating how fast the length of a circular wave increases between any two points on it.

If the wave was born in a disturbance that occurred 13.7 giga years ago and moves at the speed of light, the current size of the wave would be 13.7 * 2 * PI = 86 Giga Light Years.

The furthest point of our position on the wave is at our antipodes, at 43 Gal.

As the wave continues to advance, the maximum length of the Universe continues to grow and the distance between any two points in the Universe will increase at a rate determined by the original distance between the two points.

For two bodies located at any distance, the distance will increase to:

H = c/r = 300,000 km/s / 13,700 Mega light years = 21.9 (km/s) / Mega light year

This quantity, 21.9, is the Hubble constant expressed in (km/s)/Mal. If we want to translate it to (km/s)/Mega Parsec, we have to multiply it by 3.26, giving us a total of 71.39 (km/s)/Mpc, more like the units commonly used by astronomers.

If the increment per Mega Light Year or per Mega Parsec is used, the Hubble constant is the same although, as it is easy to verify, the Hubble constant is NOT constant, but varies with the radius of the Universe, and therefore both with his age. To calculate the constant H at any time in the Universe, one only has to calculate c/r.

Mathematical expression of Hubble's law

The ultimate destiny of the Universe and the age of the Universe can be obtained by measuring the current Hubble constant and extrapolating with the observed value of the deceleration parameter, characterized uniquely by density parameters values (

Omega

). A "closed unit" (

1}" xmlns="http://www.w3.org/1998/Math/MathML">Ω Ω ▪1{displaystyle Omega 한1}1}" aria-hidden="true" class="mwe-math-fallback-image-inline" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1fe249a7fd5fd9ab45447fd949e63ca3805c2aa1" style="vertical-align: -0.338ex; width:5.939ex; height:2.176ex;"/>

) goes towards a Big Crunch end and is considerably younger than its Hubble age. An "open universe"

{displaystyle Omega =1}

) expands forever and has an age that is close to your Hubble age. For the accelerating Universe in which we live, the age of the Universe is coincidentally close to the age of Hubble.

Hubble's law can be expressed as follows:

${displaystyle z={frac {lambda _{1}-lambda _{2}}{lambda _{2}}}={frac {H_{0}}{c}}D}$

being

z,

, the corrimiento to the red, a dimensional ratio of wavelengths at the emission and reception point.

D,

the current distance to the galaxy (in Mega parasec Mpc).

H_{0},

Hubble constant at the time of observation

c,

, speed of light.

And the speed-distance relationship —more general and often confused with Hubble's law— can be formulated as follows:

${displaystyle v=H_{0}cdot D}$

being

v

the speed of recession due to the expansion of the universe (usually in km/s).

The velocity-distance relationship can be derived by assuming that the Universe is homogeneous (observations made from all points are the same) and is expanding (or contracting).

Strictly speaking, $v$ and $D$ in the formula are directly observable, because from the moment the light was issued until the time of observation the Universe has changed in size. For relatively close galaxies (with $z$ much lower than the unit), $v$ and $D$ They won't have changed much, and $v$ can be estimated using the formula ${displaystyle v=zc}$ Where $c$ It's the speed of light. This is in fact the empirical relationship found by Hubble. For distant galaxies, $v$ (o) $D$ ) cannot be calculated from $z$ without specifying a detailed model of how it changes $H$ with time. The shift to red is not directly related to the speed of recession at the time the light came out, but has a simple interpretation: ${displaystyle (1+z)}$ is the factor by which the Universe has expanded while the photon was traveling to the observer.

If Hubble's law is used to determine distances, the speed due to the expansion of the Universe can only be used. Since galaxies gravitationally intersect relatively move with each other regardless of the expansion of the Universe, these relative speeds, called peculiar speeds, they would need to be taken into account to apply Hubble's law correctly. If the peculiar speed of a galaxy is $V$ , then the speed-distance relationship should be expressed as follows:

{displaystyle v=Hcdot D+V}

Additional Notes

The distance $D$ to nearby galaxies can be estimated for example by comparing its apparent brightness with its absolute theoretical brilliance.

In any case, $D$ must be the current distance to the galaxy, not the one that existed when the galaxy issued the light we received today. This distance is actually impossible to observe directly. It is deduced from the theoretical models and from the observation of the apparent brightness of the galaxy or the light curve of type Ia supernovas that are observed in that galaxy.

Speed $v$ defined as the distance variation rate $D$ with time.

The speed-distance ratio is strictly valid for any distance while Hubble's law is a valid approximation for relatively close galaxies where the speed can be determined by the red (z) correction using the formula ${displaystyle vapprox zc}$ ; being $c$ the speed of light. However, only the speed due to the expansion of the Universe must be considered, apart from other relative movements of galaxies (the peculiar movement).

Systems with gravitational constraints, such as galaxies or the Solar System, also suffer the effects of cosmological expansion.

Hubble's constant

Hubble's constant is the constant of proportionality that appears in the mathematical form of Hubble's law. Although in the original formulation, this parameter appeared as a number with a fixed value, the relativistic cosmological models on which the Big Bang are based suggested that the Hubble parameter was not really a constant but a parameter that varied slowly over time, which is why many authors nowadays refer to the "Hubble constant" more properly the Hubble parameter.

Using the equations of the theory of general relativity specialized to the models of metric expansion of space with metric of metric FLRW it can be proved that the age of the universe is related to the Hubble constant and also the radius of the observable universe (if the age of the universe is known).

Temporal variation

Hubble parameter value changes over time by increasing or decreasing depending on the deceleration parameter sign $q$ which is defined by:

${displaystyle q=-H^{-2}left({{;dH} over {;dt}}+H^{2}right)}$

Podemos definir la "edad de Hubble" (también conocido como el "tiempo de Hubble" o el "periodo de Hubble") del universo como 1/H₀, o 978.000 millones de años/[H₀/(km/s/Mpc)]. La edad de Hubble es de 14 000 millones de años para H₀=70 km/s/Mpc, o 13800 millones de años para H₀=71 km/s/Mpc. La distancia a una galaxia es aproximadamente zc/H₀ para pequeños desplazamientos al rojo z y expresando c como 1 año luz por año, esta distancia puede expresarse simplemente como z veces 13800 millones de años luz.

For a long time q was thought to be positive, indicating that the expansion was slowing down due to gravitational pull. This would imply an age of the universe less than 1/H (which is about 14 billion years). For example, a value of q of 1/2 (considered by many theorists) would give an age of the universe of 2/(3H). The discovery in 1998 that q is apparently negative means that the universe could actually be older than 1/H. In fact, estimates of the age of the universe are precisely very close to 1/H.

Measurement of the Hubble constant

For many people in the second half of the centuryXX. value $H_0$ is estimated to be between 50 and 90 (km/s)/Mpc. The value of Hubble's constant was the theme of a long and rather incarnated dispute between Gérard de Vaucouleurs that claimed a value around 100 and Allan Sandage that claimed a value of about 50. In 1996, a moderate debate by John Bahcall between Gustav Tammann and Sidney van den Bergh was held in the same way as the previous debate between Shapley and Curtis on these two competing values. This difference was partially resolved with the introduction of the Lambda-CDM Model of the universe in the late 1990s. With the observations of this model of the high-corranced clusters to the red at microwave wavelengths using the Siunyáiev-Zeldóvich effect, the measurements of the anthropologies of the cosmic microwave background and all optical expeditions gave a value of around 70 for the constant. In particular the Hubble Space Telescope (driven by Dr. Wendy L. Freedman of the Carnegie Observatory) gave the most accurate optical resolution in May 2001 with its final estimate of 72±8 (km/s)/Mpc, consisting of a measure of $H_0$ based on the observations of the Siunyáiev-Zeldóvich effect of many galactic groups having a similar accuracy. The highest accuracy in the resolution of the cosmic microwave fund has been 71±4 (km/s)/Mpc, by the WMAP in 2003 and 70(+2.4,-3.2) (km/s)/Mpc, for the measurements of 2006. In August 2006, using NASA's Chandra X-ray Observatory, a Marshall Space Flight Center team found that Hubble's constant was 77 (km/s)/Mpc, with uncertainty of approximately 15%. The consistency of the measures of all these methods is provided to support the measured value of $H_0$ and the Lambda-CDM model. In the metric decimal system, $H_0$ is about 2.3×10^-18 s^-1, this should not be written on Hz as the amount is not a frequency.

The value of the deceleration parameter $q$ measured from the observations of supernova Type Ia, one of the standard candles, which in 1998 was found to be negative, surprised the entire astronomical world because this implied that the expansion of the universe is "accelerating" for about 6 billion years (although Hubble's parameter continues to decrease over time).

Measurements by Adam Riess et al.

Measurements by Adam Riess et al. in 2018 they have provided a value of H₀ = 73.52±1.62 km/s/Mpc, which differs by almost 9% (8.7%) from the H_{value 0} = 67.4±0.5 km/s/Mpc as measured by the Planck Collaboration et al. This discrepancy between the current values is what in current cosmology is called the "Hubble voltage". According to the assessment made by Kenworthy et al., the value proposed by A. Riess et al., is the most accurate to date, April 24, 2019 (Kenworthy, Scolnic, & Riess, 2019).

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