The Newest Tool To Help Us Understand The Expansion History of the Universe: The DESI Project

 

Cosmic map generated by DESI 

Until relatively recently only about two million galaxies had ever been imaged via our astronomical telescopes.  That radically increased in April with up to 6 million now numbered in the galactic census.  This thanks to the Dark Energy Spectroscopic Instrument (DESI), an Observatory in Kitt Peak, AZ, funded by the U.S. Department of Energy.  The 3d map produced by DESI now offers much more elaborate clues to the behavior of dark energy, which I've written about before, e.g.

• Dark Energy - Evidence for a New Law of Physics?

Regarding dark energy , precision measurements of the cosmic microwave background (CMB), including data from the Wilkinson Microwave Anisotropy Probe (WMAP), have already provided solid evidence for it. The same is true of data from two extensive projects charting the large-scale distribution of galaxies - the Two-Degree Field (2DF) and Sloan Digital Sky Survey (SDSS).

The curves from other data - with corrected apparent magnitude v. redshift (z) -  give different combinations of   W _dark to  W _matter over the range. However, only one of the graph combinations bests fits the data:

W_dark = 0.65 and  W_matter = 0.35

These correspond to an expansion accelerating for the last 6 million years- with much more dark energy involved (0.65) than ordinary matter.

When the predictions of the different theoretical models are combined with the best measurements of the cosmic microwave background, galaxy clustering and supernova distances, we find that:

 0.62 < W _dark < 0.76, 

where W_dark = r _dark/ r_c, 

The energy density of dark energy is denoted in the numerator while the critical density is the denominator.

By way of update the DESI project has capped off the first seven months of its survey run by smashing through all previous records for three-dimensional galaxy surveys, creating the largest and most detailed map of the universe ever. Yet it’s only about 10% of the way through its five-year mission. Once completed, that phenomenally detailed 3D map will yield a better understanding of dark energy, and thereby give physicists and astronomers a better understanding of the past – and future – of the universe. Meanwhile, the impressive technical performance and literally cosmic achievements of the survey thus far are helping scientists reveal the secrets of the most powerful sources of light in the universe.  

DESI is an international science collaboration managed by the Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab) with primary funding for construction and operations from DOE’s Office of Science.  DESI scientists are presenting the performance of the instrument, and some early astrophysics results, this week at a Berkeley Lab-hosted webinar called CosmoPalooza

Which will also feature updates from other leading cosmology experiments.  In the words of Berkeley Lab scientist Julien Guy, one of the presenters:

“There is a lot of beauty to it. In the distribution of the galaxies in the 3D map, there are huge clusters, filaments, and voids. They’re the biggest structures in the universe. But within them, you find an imprint of the very early universe, and the history of its expansion since then.”

DESI has come a long way to reach this point. Originally proposed over a decade ago, construction on the instrument started in 2015. It was installed at the Nicholas U. Mayall 4-meter telescope at Kitt Peak National Observatory near Tucson, Arizona. Kitt Peak National Observatory is a program of the National Science Foundation’s (NSF) NOIRLab, which the Department of Energy contracts with to operate the Mayall Telescope for the DESI survey.

This  unique instrument saw its beginnings in late 2019. Alas, during its validation phase the coronavirus hit shutting down the telescope for several months. Then, by December 2020, DESI turned its eyes to the sky again, testing hardware and software. By May 2021 it was ready to start its science survey.

But work on DESI itself didn’t end once the survey started. In the words of physicist Klaus Honscheid of Ohio State University, co-Instrument Scientist on the project:

 “It’s constant work that goes on to make this instrument perform. The feedback I get from the night observers is that the shifts are boring, which I take as a compliment,”

In fact that monotonous productivity requires incredibly detailed control over each of the 5000 cutting-edge robots that position optical fibers on the DESI instrument, ensuring their positions are accurate to within 10 microns.  According to  Honscheid:

“Ten microns is tiny. It’s less than the thickness of a human hair. And you have to position each robot to collect the light from galaxies billions of light-years away. Every time I think about this system, I wonder how could we possibly pull that off? The success of DESI as an instrument is something to be very proud of.” 

That level of accuracy is needed to accomplish the primary task of the survey: collecting detailed color spectrum images of millions of galaxies across more than a third of the entire sky. By breaking down the light from each galaxy into its spectrum of colors, DESI can determine how much the light has been redshifted – stretched out toward the red end of the spectrum by the expansion of the universe during the billions of years it traveled before reaching Earth. It is those redshifts that let DESI see the depth of the sky.

The more redshifted a galaxy’s spectrum is, in general, the farther away it is. With a 3D map of the cosmos in hand, physicists can chart clusters and superclusters of galaxies. Those structures carry echoes of their initial formation, when they were just ripples in the infant cosmos. By teasing out those echoes, physicists can use DESI’s data to determine the expansion history of the universe.  In the words of another DESI Collaborator:

“Our science goal is to measure the imprint of waves in the primordial plasma. It’s astounding that we can actually detect the effect of these waves billions of years later, and so soon in our survey.”

Understanding the expansion history is crucial, with nothing less than the fate of the entire universe at stake. Today, about 70% of the content of the universe is dark energy, a mysterious form of energy driving the expansion of the universe ever faster. As the universe expands, more dark energy pops into existence, which speeds up the expansion more, in a cycle that is driving the fraction of dark energy in the universe ever upwards. Dark energy will ultimately determine the destiny of the universe:

See Also:

https://www.yahoo.com/news/mind-blowing-dark-energy-instrument-010001393.html?soc_src=social-sh&soc_trk=ma

And:

DESI Creates Largest 3D Map of Our Expanding Universe Ever | Sci.News

Revisiting Differential Geometry

 The basic core of differential geometry entails the application of differential calculus to what we call parametric curves, e.g.  y= x(t).  Consider the curve in 3-space (x,y,z) below:

 

Fig.1

Here the  position of P becomes a function if the arc length  as s  traverses from P 0  to P on the curve.  Then the vector:

  R =  i x  + j y + k z 

 is also a function of s.   Of particular interest will be the derivative:

dR/ ds =  i(dx/ds) + j(dy/ds) + k(dz/ds)

By taking the limit: dR/ ds =

It can be shown one obtains a unit vector tangent to the curve at P, say, and pointing in the direction in which arc length s increases along the curve.  One thereby arrives at the vector T: T = dR/ ds

But we first must become familiar with the basic laws of vector calculus as they apply to Euclidean space.   Thus, consider the scalar product of two vectors  A and B  (as seen in Ch. 2) also called the dot product because of the symbol used to denote it.   Thus, in general if  A,  B  are two arbitrary vectors where Θ  denotes the angle between A  and  B  as shown below: 

  Fig. 2

Hence we can write:  A ·B    =  |A| |B|  cos Θ,  

Or in the transformed system (Fig. 2):

 A ·B    = A1 B1   = |A| |B| cos Θ,                  

Thereby we see that two non-null vectors are orthogonal to each other (i.e. at 90 degrees) if and only if their scalar product vanishes.  This means we have:  

cos(Θ) = (A ·B)/ |A| |B|    =  0   

Meanwhile the vector product of two vectors, i.e.  V  =  A x B   is defined by:

V=  A x B  =

   [ e 1      e  2    e3 ]

   [  a 1      a  2    a3]

   [  b 1     b  2    b 3] 

Where e _i  denotes a unit vector having the positive direction of the ith coordinate axis of the Cartesian coordinate system in spaceR₃.                                                                                                              

This is a prelude to getting a handle on right-handed and left -handed orthogonal systems of coordinates, which we also need to proceed further. Such a right-handed system (in 3 dimensions) is shown below;

Fig. 3

    With orthogonal parallel coordinates (x₁ ,  x₂ , x₃) correspond to points: (1,0,0),  (0,1,0) and (0, 0, 1), respectively, so each have the distance '1' from the origin.  In general, a coordinate system is called right-handed if the axes assume the same sort of orientation as the thumb, index finger and middle finger of the right hand.

      A system is said to be left-handed if the axes assume the same sort of orientation - in their natural configuration - as the thumb, index finger and middle finger of the left hand.  In this case we will have the reference frame orientation (note axes directions!):

Fig. 4

   The use of the notation (x₁ , x₂ , x₃)  for the orthogonal coordinates is more convenient  than the familiar (x, y, z) since it enables the use of the more compact form x _i for the coordinates   of a point).   Then any other similar Cartesian coordinate system  e.g.  (x'₁ ,  x'₂ , x'₃)  will be related to the given one by a particular linear transformation of the form:

x' _i  =å ³ _b =1   a _ik  x _k  +  b _i

 

Whose coefficients satisfy the conditions: 

1)  å ³ _b =1   a _ik  a _il  =  d _kl   =   

                     {0    for  k ≠  1    

                      {1  for   k  =  1

2)   d _ik = a _ik   =

(1….0…..0)

(0….1…..0)

(0….0… ..1)

Where  d _ik   is the Kronecker  delta

    The transition from one Cartesian coordinate system to another can always be done by an appropriate rigid motion of the axis of the original system. Usually this entails a suitable translation and a suitable rotation. Any rigid motion which carries a Cartesian coordinate system into another Cartesian system is called a direct congruent transformation. 

 From the preceding we can also write:

A  =   a _ik     =  

   [ a ₁₁      a ₁₂   a₁₃]

   [ a ₁₂₁    a ₂₂   a₂₃]

   [ a ₃₁     a  ₃₂   a₃₃]

Which is a quadratic matrix. In general, we note that a system of   m · n   quantities arranged in a rectangular array of m horizontal rows and n vertical columns is called a matrix, and the quantities are the elements of the matrix.   If m equals n the matrix is called 'square'  and the number n is the order of the matrix. Thus, the coefficients  a _ik  for the preceding linear transformation equation form a quadratic matrix.  The corresponding determinant is then:

det (A)  =  det (a _ik )  

 If in particular A  equals the Kronecker delta (unit matrix) then the new Cartesian coordinate system is given by:

 

x'_{i =    x i  +   b i}             i=  1, 2, 3.....

Which is a translation of the coordinate system.  If, however,   _b i =  0  then we find: 

x'_{i =    x i} 

And the transformed coordinates are the same as the original ones.  Such a special transformation is called the identical transformation.  If _b i =  0  and the coordinates  a _ik   are arbitrary, but such that the two conditions (1) and (2)  are satisfied, then:

  

x' _i  = å ³ _b =1   a _ik  x _k  +  b _i  

 Corresponds to a rotation of the coordinate system with the origin (0,0,0 ) as center.  Such a rotation is called a direct orthogonal transformation.   Finally,  note that a transformation of the form:

x' _i  =å ³ _k =1   a _ik  x _{k  ,}    å ³ _i =1   a _ik  a _il  =  d _{kl  ,}     

 

det (a _ik ) =  -1   

Can be geometrically interpreted as a motion composed of a rotation about the origin and a reflection in the plane.  This type of transformation is called an opposite orthogonal transformation because it transforms a right-handed coordinate system into a left-handed one and vice versa.

 

 Suggested Problems:

1) Consider two vectors A, B spanning a subspace of   R ⁴   where: A = (1, 2, 1, 0) and B = (1, 2, 3, 1)  

Find:  A/ ‖A ‖    and:  B/ ‖A‖

2)  Given  x'_{i =    x i  +   b i}

And:  x _i   =

(2….1…..0)

(3….-5.….6)

(-7….0… .4)

Find the new coordinates x'_i   if :

  _b i  =

(1….2…..1)

(2….1.….3)

(3….2… .1)

Write out the matrix elements for  a _ik . 

The Real Culprits Responsible For Trump 2.0 ? The 10 Million Who Never Showed Up This Time (As They Did For Biden In 2020)

                                                                     

" The opening phase of President-elect Donald Trump’s second trip to the White House has been nothing like the first. What this portends for the coming four years is exactly what Trump pledged in the campaign: disruption and retribution." - Dan Balz, Washington Post, Trump Intends Disruption & Retribution

Robert Reich recently wrote (There Was No Mandate for Trump. There Was No Red Shift. There Was Only a Blue Abandonment, Substack)

"Trump is saying the election gave him a “very big mandate.” Rubbish. It wasn’t a mandate at all. It wasn’t even a “red shift” to Trump and the Republicans. It was a blue abandonment. We now know that nine million fewer votes were cast nationwide in 2024 than in 2020.

Trump got about a million more votes than he did in 2020 (700,000 of them in the seven battleground states). That’s no big deal.

The bigger news is that Harris got 10 million fewer votes than Biden did in 2020 (400,000 fewer in the battleground states). The biggest takeaway is that Biden’s 9 million votes disappeared.  Why?"

To echo a recent observation by David French (NY Times): 

"One of the most maddening aspects of the 2024 election was the extent to which so many voters viewed Trump as a mostly normal political candidate." 

 In other words, this lamo lot, either because they didn't follow serious news sources enough, or were too mesmerized by vicious Trump campaign ads and FOX News propaganda, "dropped the ball", failed to show up - and basically tossed our democracy into a veritable shithole.   As Mr. French goes on to write:

"One of the challenging realities of American politics is that while vast numbers of Americans participate in presidential elections, only small minorities of voters actually stay engaged. And the priorities of the two groups are not the same, far from it. The majority is focused on the things that directly affect their lives — prices, crime, peace. How much do concerns about democracy matter if people don’t feel safe on the streets? Or if they’re struggling to keep a roof over their heads? The minority, by contrast, follows politics closely and can focus on issues that can feel more abstract or niche to the majority."

Janice and I as well as our circle of friends, family, all have followed politics closely especially the Trump campaign over the last two years. Hence we are all fully aware that Trump is a piece of decayed snot who has no business running anything except maybe a porto-potty. This deeper and more intimate knowledge of the political process means we are the ones Jefferson referred to in his Notes on Virginia when he wrote:

"Every government degenerates when trusted to the rulers of the people alone. The people themselves therefore are its only safe depositories. AND TO RENDER THEM SAFE, THEIR MINDS MUST BE IMPROVED"

Jefferson knew, as any intelligent American would, that being a "safe depository" of democracy in one's nation meant being attentive to its politics, history and political dynamics. That includes having a command of its basic principles, the Constitution - and especially what is and isn't allowed. Also a recognition of the most important, critical issues at a given time, the most rational choices in each case, and an ability to recognize a qualified candidate and distinguishing that person from an incompetent buffoon and demagogue.

Alas, the 2024 election shows too many Americans have lost that capacity for critical perception. Maybe the residue of the pandemic ate out the rest of their microglial (brain) cells or they just lost their bearings with drugs and alcohol. Or plain laziness, who knows? But their  callous  lack responsibility as voters - not to mention warped  citizenship - basically  handed the highest office in the land to an incompetent asshole as well as 34- times convicted felon.  This explains French's next observation:

"MAGA Republicans see Trump as a singular figure, but an immense number of voters thought the talk about Trump was overheated in both directions. If you’re like most Americans and don’t follow the news closely, it’s easy to see why you would see Trump in more conventional terms."

The bollocks regarding talk about Trump being "overheated" in particular showed vast number of Americans are brain-benumbed or mentally dysfunctional. I mean the man's whole being and rhetoric fairly screams abnormality and criminal, from bragging about grabbing pussies, to threatening to shoot generals, to calling soldiers who lost their lives in wars "losers".  Oh, and gushing about his 'love letters' from the bloodthirsty North Korean dictator Kim Jong -Un.

NO normal candidate does those things, says those things, and broadcasts them over his social media platform hundreds of times a day. But some form of mental numbness or derangement appears to have blunted Americans' sense of outrage as well as perceptions. I suspect it is part being pulled into the FOX orbit, part being the aftermath of the pandemic and economic dislocation and part simply not following the deep politics closely enough.

French again:

" A Politico analysis of the Trump campaign’s ads showed that “the single most-aired ad from his campaign since the start of October is all about inflation, Medicare and Social Security — arguing that” Kamala Harris “will make seniors already struggling with high prices ‘pay more Social Security taxes,’ while ‘unauthorize’ immigrants receive benefits."

French also noted the targeting of swing state votes using ads (mostly paid for by Musk) warning of Kamala 'plans' to offer more trans surgeries, as well as giving carte blanche to migrants via "open borders". We actually have received similar mailers to that effect and I have invariably ripped them up and tossed them because I know - from my political knowledge- they are a pile of horse shit. But it seems too many Americans sucked up this crap hook, line and sinker. The end result, coupled with the Gaza and Ukraine tumult, translated into either voting for a 34 count felon and traitor, or not voting at all. In any case handing the election to an unqualified ratfucker.

As one recent letter writer to the Denver Post put it:

"Most disconcerting to me as I read through Open Forum responses is the level of disconnection from the factual evidence. Trump's own actions and words have repeatedly demonstrated his attacks on democracy, bigotry and misogyny.  The evidence is  overwhelming and is not the product of 'liberal media'."

 But this political miasma is the result when people's minds are removed from the core of issues and then are no longer "safe depositories" in preserving our Republic.  As Benjamin Frankin warned, when asked what form of government we have: "A Republic, if you can keep it."

It seems too many of our fellows aren't interested in keeping it. As they behold what unfolds after this misfit takes office in January they may come to regret the decision not to keep him out of the WH again this time.; Which would have meant doing for the nation what the Supreme Court refused to do.

See Also:

2024 Elections | Democrats

There Was No Mandate for Trump. There Was No Red Shift. There Was Only a Blue Abandonment.

by Robert Reich | November 15, 2024 - 6:48am | permalink

— from Robert Reich's Substack

Friends,

Trump is saying the election gave him a “very big mandate.”

Rubbish. It wasn’t a mandate at all. It wasn’t even a “red shift” to Trump and the Republicans.

It was a blue abandonment.

We now know that nine million fewer votes were cast nationwide in 2024 than in 2020.

And:

Trump allies, Republicans eye changes to federal safety net programs - The Washington Post

Excerpt:

Among the options under discussion by GOP lawmakers and aides are new work requirements and spending caps for the programs.

However, concern is high among some Republicans about the political downsides of such cuts, which would affect programs that provide support for at least 70 million low-income Americans.

Limiting what food items SNAP (food stamp) recipients can purchase with benefits would also reduce costs.

Donald Trump

Trump Triumphs, MAGA Victorious, Putin Pleased, Cat Ladies Silenced. Are We Happy Now?

by Jaime O’Neill | November 17, 2024 - 6:37am | permalink

Yes, indeedy, fellow Americans, happy days are here again. The bells are ringing, thanksgiving is in the hearts of all Americans from the homeless to the head of Home Depot. Wall Street is euphoric. Tax reductions for the plutocrats are locked in, and more are coming for the richest Americans. Those most-deserving folk are doing their happiest happy dance. Oil company execs are ecstatic. Netanyahu is now free to be his worst self without worry about even the most feckless and limp-dicked restraint. The majority who wanted to own the liberals got their fondest wish. It’s morning once again in America, God’s in His Heaven, and all is right in the best of all possible worlds.

There is so much happiness to be found as we see the media coverage of Democrats and other lefties rummaging around for ways to blame their party for losing again. It had nothing whatsoever to do with the nihilists who voted as so many "patriots" and "Christians" did. It was all Kamala’s fault, and all because she couldn’t find the time to sit down to shoot the shit with Joe Rogan, though she did enter the lion’s den to go head-to-head with Brett Baier, that ever-so-objective journalist on Fox who pounced on every opportunity to interrupt and contradict her, no matter what. Never had any Murdoch employee questioned much of anything Trump ever said.

» article continues...

And;

Donald Trump | Economic Policy

‘Straightforward Principles of Economics’: Experts Warn ‘Food Will Get More Expensive’ Under Trump

by Elizabeth Preza | November 17, 2024 - 6:47am | permalink

— from Alternet

Donald Trump’s stated economic policies have economists “extremely confident that food will get more expensive,” Brown University professor Rachel Friedberg warns.

According to a Saturday report in the Atlantic, while Americans are “very concerned” about the price of groceries, two major Trump campaign “promises — mass deportations of undocumented immigrants and more restrictive trade regulations —would almost certainly raise food prices” as a domestic labor shortage and increased import taxes tack costs onto Americans’ grocery bills.

“It’s just very straightforward principles of economics,” Friedberg said, telling the Atlantic the “cause-and-effect dynamic ‘could be my final exam.’”

As the Atlantic reports, “the farm industry is already in a prolonged labor crisis."

» article continues...

Revisiting the Landau contour in the Plasma Physics Context

 

Landau contour when   w _i =  0.  The straight line portions of the contour are exactly on the real (Re) axis.

The Landau contour represents a special case used in plasma physics.  This is illustrated in the sketch above, where the pole can be anywhere in the upper right quadrant.

This is for the complex variable, v. What Lev Landau did was to extend his di-electric function, ε  to the entire   w- plane. In the graphic the contour follows the bold line along the Re(v_x) abscissa and then goes round the residue at x.  One must ensure the path of integration does not meet a pole, so must go around it, i.e  based on a deformed contour.  

 Hence, to make ε  an entire function one needs to follow an analytic continuation process  from the upper half plane to the lower half plane.  One must then ensure the path of integration does not meet the pole but goes around it by way of a deformed contour.  Then if u = w/ k  we will have (for  w _i  > 0):

I =  ò ^¥_-¥   du  du f _o / (u - w/ k)           (w _i  > 0)

And thence: 

I =   ò ^¥_-¥   du  du f _o / (u - w/ k)  +  2 πi (Residues)

When the pole is on the Re-axis:

I =  P  ò ^¥_-¥   du  du f _o / (u - w/ k)  +  πi (Residues)

How do we know this analytic continuation is correct?

We can take the integral I⁺  (i.e. from just above the pole):

 I⁺   =   ò ^¥_-¥  du  du f _o / (u - w/ k -   i/ d)

Also:   I^-   =   ò ^¥_-¥  du  du f _o / (u - w/ k +  i/ d) + 2πi (Res)

Taking the average of the integrations:

I*  =  ½ [I⁺  + I^-  ]  

I*  =     lim _d ® 0    [I⁺  + I ^-  ]   =

 lim _d ® 0 ½ [  ò ^¥_-¥   du  du f _o / (u - w/ k -   i d)

+   ò   du  du f _o / (u - w/ k -   id)] + πi(Res)]

Where the bracketed quantity is the Cauchy Principal Value.

See, e.g. 

• Complex Analysis – continued: The Principal Value

For advanced plasma physics, say applied to solar phenomena (e.g. corona, auroral substorms) , with normal mode (steady state) behavior assumed so we only need Landau's basic prescription.   There is no need to introduce or go back to the Laplace transform to apply it- since that contains more information than we actually need.   

What we can do for insurance is to look at the di-electric function to see if any damping is associated with the normal mode (as has been done in various numerical models of  auroral substorms, as developed at the Geophysical Institute in Fairbanks, AK). Thus we look at:

 ε   =  1 -   w _pe ²  /k ²  [ò  du  {du f _o  d(u) /  (u - w/ k )]

Suggested Problem:

For  a particular numerical model a space physicist wants to show the di-electric function can be expressed in real and imaginary parts such that: ε  _r    +  i ε _i  = 0  

Show this using integration by parts of the equation for ε   and then do a Taylor expansion.