# Does Flat Universe mean even distribution?

I've read through all the other related answers to "flatness" questions but I need a bit more clarification.

I understand that a triangle in a 2D universe would not equal 180 degrees in both a closed and open universe. If I am correct, not being flat during the initial conditions would mean exponential expansion or collapse as time went by.

Given the above, could we explain flatness as uniform density of the universe, meaning all of the universe is the same approximate "consistency" on a large scale (homogeneity).

No, being flat and being homogeneous is not equivalent$^dagger!!!$.

Flatness refers to the geometry, which depends on the total energy density $ho$; if it is above or below a certain critical threshold $ho_mathrm{cr}$, we call the Universe "closed" or "open", respectively, while if $ho$ is exactly equal to $ho_mathrm{cr}$, we call it "flat".

Homogeneity refers, as you say, to matter being evenly distributed (on large scales). If the Universe is not only homogeneous, but also isotropic (i.e. looks the same in all directions), then there are three different possible geometries, namely flat, open, or closed. But a homogeneous universe doesn't have to be isotropic, and both open and closed universes can have evenly distributed matter.

Thus, $$mathrm{homogeneity} Rightarrow mathrm{flatness}$$

Whereas the local geometry depends on the local density$^ddagger$, the global geometry does not depend on how the matter is distributed. For instance, you could in principle have a universe with no upper limit of structure size. In our Universe, we find observationally that the largest structures have sizes of roughly half a gigalightyear. Above this scale, it is homogeneous (although it could be inhomogeneous on scales larger than the particle horizon). But another universe might have structure on all scales and thus not be homogeneous, but still meet the criterion $ho = ho_mathrm{cr}$ and thus be flat. You could also, as discussed in this answer about homogeneity and isotropy, imagine a universe originating at a central point away from which the density always decreases (i.e. is isotropic around this point), but which still has $ho = ho_mathrm{cr}$.

Thus, $$mathrm{flatness} Rightarrow mathrm{homogeneity}$$

Note that while your statement about the geometry determining the fate of the Universe would be correct if it contained only matter and radiation, it seems that $sim70$% of the density making it flat has the annoying propety of accelerating the expansion of the Universe. Thus, whereas a flat, matter-dominated universe would expand asymptotically toward a finite size, our Universe is dominated, it seems, by something dubbed dark energy making it expand exponentially despite being flat.

$^dagger$For a universe, at least. For a roadkill, it might be equivalent.

$^ddagger$For instance, space "bends" enough around a massive cluster of galaxies to make gravitational lenses.

Does a flat universe mean even distribution?

Strictly speaking no. But there's no actual evidence for any kind of "higher dimensional curvature". See https://arxiv.org/abs/1303.5086 where the Planck mission reported on the Background geometry and topology of the Universe. They found no evidence for any kind of "asteroids" toroidal universe.

I understand that a triangle in a 2D universe would not equal 180 degrees in both a closed and open universe. If I am correct, not being flat during the initial conditions would mean exponential expansion or collapse as time went by.

That's what people tend to say, but IMHO you shouldn't treat it as settled science. See "The Waters I am Entering No One yet Has Crossed": Alexander Friedman and the Origins of Modern Cosmology. It's by Ari Belenkiy, who credits Friedmann with the expanding universe. He also refers to Friedmann's m-for-monotonic M1 universe which expands from a singularity and has an inflexion point, his M2 universe which expands from a non-zero radius, and his p-for-periodic P universe which expands and contracts. The thing is, that we don't actually know for sure that any of these options properly describe the universe. Particularly since we have good evidence that the universe was once very dense, but nevertheless expanded.

Given the above, could we explain flatness as uniform density of the universe, meaning all of the universe is the same approximate "consistency" on a large scale (homogeneity).

I would say this: given that we don't know that Friedmann cosmology is correct, we might explain flatness as uniform density of the universe.

## Does the Universe have a center of gravity?

Space is flat and simply connected. This implies that it is in fact Euclidean space, and is infinite. Then you cannot average the position of masses in the Universe because the sum diverges. The mass distribution is uniform on very large scales, and this goes on forever.

Space is curved and/or not simply connected. This means that positions cannot be thought of as vectors and they cannot be summed, therefore they cannot be averaged.

I read something about 'The Great Attractor'. Isn't that also a thing in terms of a "gravitational" center

Isnt there curved space in General Relativity? Isn't there a definable centre of gravity in GR? Can't we do that for the universe?

Can you explain what simply connected means?

What about the centre of gravity of the observable universe?

Why does being flat and simply connected imply that it's infinite?

Also, even if it is infinite, why would that mean the mass distribution is uniform?

Really top notch question. I feel like this answer has got a lot to go with the Homogeneity principle. Einstein did propose that at large scales space is homogeneous, meaning if you go at really large distances (Mpcs or parsecs) space on the left will look no different from the space on your right. Imagine looking at a web that has no center, web made of galaxies in this case.

Today this principle is being challenged as we notice at large distances the stuff in the local universe has structure. Sloan great wall, the 24 quasar collection - a study done by ESA that basically mapped out different quasars in 3D and postulates a structure of some sort implying each of these quasars are gravitationally linked. That breaks the Homoginiety and a structure that large shouldn't exist. Large scale structure

That's once side of the story the other being the shape of the universe itself. As far as what know there are theories, mind you Theories claim that space is mostly flat and other theories postulate a donut/saddle/spherical shape. So the best of my knowledge there isn't any experimental way the shape of the universe can be found.

Sadly there really isn't a way to answer that question and probably wont be answered for a longtime.

## Contents

While some people think the universe was created over a six-day span around 6,000 to 10,000 years ago, the facts as measured show them to be painfully wrong, unless you subscribe to Last Thursdayism or a similar idea, but that is irrelevant conjecture here.

The universe seems to have formed approximately 13.8 billion years ago in a rapid and massive expansion of space-time called the Big Bang. After the initial inflation, the energetic particles cooled, and nuclear reactions created what was to become matter, which eventually clumped together to form galaxies and stars. Over the course of stellar evolution heavier elements were produced, leading to later generation stellar systems having planets sometimes largely made of those heavy elements - rocky planets.

Our solar system is roughly 4.5 billion years old, and features a handful of such rocky planets and smaller debris, along with four gas giants, which are largely composed of lighter elements and compounds. After a long period of cooling, our planet became hospitable to the evolution of the very complex organic compounds which are now known to be abundant in the universe. Α] One collection of said compounds typed this not long ago, while another collection is now reading it.

## What's the matter with the Universe? About 31%.

If you want to understand the Universe — and we do — you have to understand what's in it. I don't mean stars and planets and black holes and such. We need to be even broader.

How much energy is there in the Universe? How much matter? And to be a little more specific, what kinds of energy and matter?

We call this the mass/energy budget of the Universe. Like a household budget, it (hopefully) accounts for everything in it, divided by type. In the case of the Universe, we know it's made up of — in decreasing order — dark energy, dark matter, and normal matter. But how much of each?

A new study looked at just matter, and came up with a fairly narrow number: 31.5 ±1.3% of the Universe is made of matter (which, in turn, implies 68.5% is dark energy).

These numbers are pretty important. If the Universe had less matter, it would expand more rapidly — in a sense, the gravity of that matter slows the expansion.

The mass/energy budget of the Universe shows us that most of the stuff in the cosmos is dark energy, then next is dark matter, then finally the normal matter that makes up gas, dust, and stars. Credit: UCR/Mohamed Abdullah

This also has implications for stuff in the Universe, and not just the Universe itself. For example, in the early Universe gravity helped clump up matter, since it was attracted to itself. It condensed out of the hot soup of stuff, forming galaxies and clusters of galaxies. Had the matter budget been different, galaxies and clusters would look different, or may not have formed at all.

We owe our existence to these numbers.

In fact, it was galaxy clusters that the new work focused on. These are immense collections of entire galaxies, hundreds or thousands of them, all held together by their mutual gravity. Their structure depends on the density of matter in the Universe, so by examining them the scientists could figure out that density.

The number of clusters in a given volume of the Universe depends on the mass density (denoted by Ωm), so measuring the masses of clusters tells you the mass density of the Universe. Credit: UCR/Mohamed Abdullah

They developed a method to find clusters in as unbiased a way as possible. They looked at a staggering 700,000 galaxies, then examined their locations and motions in space to see if they belonged to clusters. From this sample they selected 756 nearby galaxy clusters (up to about 1.6 billion light years away, so "nearby" is relative) to use in their analysis.

Then they found what's called the cluster mass function, which is the number of clusters out there in the Universe in a given volume of space for a given mass of the cluster. So in some part of the Universe you might see lots of low-mass clusters, fewer middleweight ones, and a smaller number of truly ginormous ones, for example. This distribution is sensitive to the density of matter in the Universe, and is complicated by things like the fact that the density changes over time as the Universe expands, as well as the difficulty in determining the mass of the cluster.

That last bit is a toughie. There are a lot of ways to estimate the mass of a cluster, many of which are statistical in nature (looking at lots of clusters to average out noisy statistics). These introduce other issues, though, making this difficult. In this case, the scientists opted to use what's called the virial method to get the mass — as galaxies move around in a cluster, they interact and exchange energy (faster ones pull on slower ones, for example, speeding them up). This depends on the total mass of the cluster, and provides a pretty good way to get that number.

They then ran the numbers to see what cosmic mass density they needed to explain the mass distribution of clusters, and got 31.5% (using just their data they got 31% with an uncertainty of about 2.3%, but combining their results with other studies got the slightly more accurate figure).

In general, this number is a little bit higher than most other methods (it ranges from 25–35% depending on how you measure it), but not alarmingly so. They claims theirs is the most accurate measurement of this number ever made, but I'll let other experts hash that claim out.

It also allows you to calculate the average density of matter in the Universe, and it's about 10 -23 grams per cubic meter. That's teeny. It's the equivalent of about 6 hydrogen atoms per cubic meter. For comparison, at sea level air has about 1,200 grams per cubic meter, or roughly 10 25 atoms per cubic meter — a factor of about a septillion (or a million million million million) more. Space is really empty.

I'll note too this is total matter, including dark and "normal" matter. The budget of matter itself in the Universe is about 5-to-1 dark to normal matter, so roughly an 84/16 split. That ratio isn't hugely well known though. One idea, incidentally, is that dark matter is made of axions, which are a theoretical particle with very low mass. If that's the case, then that cubic meter of space would have more like 1 hydrogen atom in it and many many billions of axions.

So there you go. This new study, should it pan out, is another step to getting all this straightened out. Every day we get a little bit closer to figuring out, well, the Universe, and why we're here at all. It may seem a little esoteric, but look around you. All that stuff you see exists, and it does so because of how the Universe works. Looking under its hood is one of the coolest things humans do.

## Higgs Boson Seems To Prove That The Universe Doesn't Exist

None of us should be here. In fact, the whole world, the stars and the galaxies shouldn’t be here either. According to a new cosmological study, our whole Universe should have blinked out of existence an instant after it was first created.

Research from British cosmologists at King’s College London (KCL) suggests that the Universe shouldn’t have lasted for more than a second after the Big Bang, according to the Standard Model that’s suggested by the Higgs boson seen in 2012 along with recent astronomical observations.

After the Universe began in the Big Bang, it is theorised that it went through a short period of rapid expansion known as cosmic inflation. The Universe is still expanding today, but at a rather sedate pace astronomically-speaking. In the inflationary period, matter was flung outward at an exponential rate in all directions, rippling space-time into waves of gravitational energy as it went.

The BICEP2 telescope in Antarctica, seen at twilight. (Credit: Steffen Richter, Harvard University)

This theory explains a number of features of the Universe, including the fact that it seems to be the same in all directions, is flat and has evenly distributed cosmic microwave background radiation. Although scientists don’t fully understand the whole process of inflation, they’re still able to make predictions about how it should make the Universe today look.

Presenting to the Royal Astronomical Society’s National Astronomy Meeting, KCL’s Robert Hogan outlined the research, which combines the latest observations of the sky with the properties of the particle seen by the CMS and ATLAS experiments at the Large Hadron Collider to come up with the slightly discomfiting conclusion that we shouldn’t exist.

In March this year, scientists using one of the Background Imaging of Cosmic Extragalactic Polarisation (BICEP2) telescopes claimed to have detected one of the predicted effects of cosmic inflation on the Universe today. They believe they have picked up on the very faint signal that the gravitational energy waves left on the cosmic microwave background, known as B-mode polarisation.

The results have proved controversial and have yet to be accepted by cosmologists, but if proven right, they would confirm the inflation theory and hugely advance science’s understanding of the Universe.

Looking into the results, the KCL team analysed what BICEP2’s observations would mean for the stability of the Universe by combining the data with information gleaned by particle physics from the Higgs boson.

Measuring that particle has allowed physicists to show that our Universe is sitting in a valley of the “Higgs field”, which is part of the mechanism that gives mass to particles. However, there is another theoretical valley in the field that is much deeper, but our Universe is saved from tipping into it by a large energy barrier.

The problem with BICEP2’s results is that they predict that the Universe would have received large jolts during the cosmic inflation phase, which would have pushed it into the other valley of the Higgs field within a fraction of a second. And that would have collapsed the entire nascent Universe in a Big Crunch.

It’s possible that BICEP2’s findings were actually caused by similar polarisation effects that can be generated by nearby dust in our own galaxy, a point that the researchers conceded was possible in their study.

Aside from an error like this in the BICEP2 results, the only option to explain why we’re still around to wonder about the origins of the Universe is if there is some other process going on that scientists have yet to discover.

"If BICEP2 is shown to be correct, it tells us that there has to be interesting new particle physics beyond the Standard Model,” Hogan explained.

For more on the annihilation of the Universe and other science and tech news, follow me on Twitter and Google +.

## Study finds that patterns formed by spiral galaxies show that the universe may have a defined structure

An all-sky mollweide map of the quadrupole in the distribution of galaxy spin directions. In this image, the different colors mean different statistical strength of having a cosmological quadrupole at different points in the sky. Credit: Kansas State University

An analysis of more than 200,000 spiral galaxies has revealed unexpected links between spin directions of galaxies, and the structure formed by these links might suggest that the early universe could have been spinning, according to a Kansas State University study.

Lior Shamir, a K-State computational astronomer and computer scientist, presented the findings at the 236th American Astronomical Society meeting in June 2020. The findings are significant because the observations conflict with some previous assumptions about the large-scale structure of the universe.

Since the time of Edwin Hubble, astronomers have believed that the universe is inflating with no particular direction and that the galaxies in it are distributed with no particular cosmological structure. But Shamir's recent observations of geometrical patterns of more than 200,000 spiral galaxies suggest that the universe could have a defined structure and that the early universe could have been spinning. Patterns in the distribution of these galaxies suggest that spiral galaxies in different parts of the universe, separated by both space and time, are related through the directions toward which they spin, according to the study.

"Data science in astronomy has not just made astronomy research more cost-effective, but it also allows us to observe the universe in a completely different way," said Shamir, also a K-State associate professor of computer science. "The geometrical pattern exhibited by the distribution of the spiral galaxies is clear, but can only be observed when analyzing a very large number of astronomical objects."

A spiral galaxy is a unique astronomical object because its visual appearance depends on the observer's perspective. For instance, a spiral galaxy that spins clockwise when observed from Earth, would seem to spin counterclockwise when the observer is located in the opposite side of that galaxy. If the universe is isotropic and has no particular structure—as previous astronomers have predicted—the number of galaxies that spin clockwise would be roughly equal to the number of galaxies that spin counterclockwise. Shamir used data from modern telescopes to show that this is not the case.

With traditional telescopes, counting galaxies in the universe is a daunting task. But modern robotic telescopes such as the Sloan Digital Sky Survey, or SDSS, and the Panoramic Survey Telescope and Rapid Response System, or Pan-STARRS, are able to image many millions of galaxies automatically as they survey the sky. Machine vision can then sort millions of galaxies by their spin direction far faster than any person or group of people.

When comparing the number of galaxies with different spin directions, the number of galaxies that spin clockwise is not equal to the number of galaxies that spin counterclockwise. The difference is small, just over 2%, but with the high number of galaxies, there is a probability of less than 1 to 4 billion to have such asymmetry by chance, according to Shamir's research.

The patterns span over more than 4 billion light-years, but the asymmetry in that range is not uniform. The study found that the asymmetry gets higher when the galaxies are more distant from Earth, which shows that the early universe was more consistent and less chaotic than the current universe.

But the patterns do not just show that the universe is not symmetric, but also that the asymmetry changes in different parts of the universe, and the differences exhibit a unique pattern of multipoles.

"If the universe has an axis, it is not a simple single axis like a merry-go-round," Shamir said. "It is a complex alignment of multiple axes that also have a certain drift."

The concept of cosmological multipoles is not new. Previous space-based observatories—such as the Cosmic Background Explorer, or COBE, satellite the Wilkinson Microwave Anisotropy Probe, or WMAP mission and the Planck observatory—showed that the cosmic microwave background, which is electromagnetic radiation from the very early universe, also exhibits multiple poles. But the measurement of the cosmic microwave background is sensitive to foreground contamination—such as the obstruction of the Milky Way—and cannot show how these poles changed over time. The asymmetry between spin directions of spiral galaxies is a measurement that is not sensitive to obstruction. What can obstruct galaxies spinning in one direction in a certain field will necessarily also obstruct galaxies spinning in the opposite way.

"There is no error or contamination that could exhibit itself through such unique, complex and consistent patterns," Shamir said. "We have two different sky surveys showing the exact same patterns, even when the galaxies are completely different. There is no error that can lead to that. This is the universe that we live in. This is our home."

## What Do You Mean, the Universe Is Flat? Part II: In Which We Actually Answer the Question

Now the next time you walk 10 feet ahead, you’ll trace the fourth and last side of a square, and you’ll end up where you started. If you turn by 90 degrees for a fourth time, you’ll face in the original direction, too.

This seems intuitively obvious, even tautological—if you trace a square on the ground, well, you trace a square on the ground—but it is actually an empirical fact. And it's important, so I’m gonna say it out loud:

There is no a priori reason why walking four equal sides and turning four right angles should take you exactly back to the same place. It is purely an empirical thing of our everyday experience.

As a matter of fact, it is not exactly true empirically, either. The failure to come back to the exact same spot—to precisely close a square—is not just true it is one of the most important phenomena ever observed in the history of science. It is at the heart of everything. It is the way that gravity works the way that Einstein understood it. It tells us how black holes form and why they trap light. And it tells us if and how the universe should expand.

Our intuition tells us that every square should close. The world is far stranger than our intuition would have us believe.

In the previous part of this series, Part I, I promised that Part II would explain what it means for the universe to be flat. In this second part, I will talk about the concept—no, the phenomenon—of curved space, which is essentially when square paths fail to close, and about why flat space is where all square paths do close up.

Euclid Tried

So far I have intentionally emphasized the physical nature of this phenomenon called curvature of space. Most authors when they write about it follow a very different approach: they start with history.

You see, mathematicians came up with the idea of curvature—as a logically consistent but abstract concept—long time before anyone proved that it was relevant to reality. And measuring the curvature of space is actually very hard to do in practice, so it’s possible that no one would have tried if mathematicians had not told them that it was at least a possibility worth considering.

The mathematics required to fully make sense of curvature was invented in the mid-1800s by Georg Bernhard Riemann, and it is rather intricate. But curved space is a fact of life. In principle, you could discover it by walking around your room, without the need for mathematicians or physicists or philosophers to come up with abstract concepts first.

Euclid, the great geometer of Hellenistic Alexandria, was well aware of the fact that the closing of square paths is not a priori true. Euclid might have said it this way: the inner angles of a square (or of a rectangle or, for that matter, of a parallelogram) add up to 360 degrees. Going around a square means making four 90-degree turns.

Another way that Euclid might have put it is by stating a related fact: that the inner angles of a triangle always add up to 180 degrees. Cut any rectangle into two triangles along its diagonal, and you’ll see why: your four right angles get divided into 6 angles, but the sum is still the same.

But geometry does not have to work that way. When it does, it is called Euclidean. But in the vast majority of cases when it does not, it is called non-Euclidean geometry.

Oftentimes, the way that authors introduce the idea of non-Euclidean geometry is by giving examples of what happens when instead of tracing triangles on a plane you trace them on a curved surface—say, on the surface of the Earth.

So start at any point on the equator and head for the North Pole. Once you get there, you’ve covered one-fourth of the circumference of the globe, or about 10,000 kilometers. Now turn left by 90 degrees and start walking south. After 10,000 kilometers, you’ll reach the equator again. But you won’t be at the place where you started. Instead, you’ll be at a place 10,000 kilometers to the west of the starting point. Now turn left by 90 degrees so that you’re facing East, and walk another 10,000 kilometers: you’ll be back where you started.

You have traced a triangle on the surface of the Earth—and the inner angles are all right angles, so they add up to 270 degrees, not 180.

Notice that you have only done three legs of your trip. If you were to follow the instructions at the beginning of this post, you would still have another 90-degree turn and another full side to walk. In this case, the failure to close the square would be rather spectacular: instead of coming back to the original point on the equator, you would have ended up at the North Pole.

Tracing squares with sides that are 10,000 kilometers long is kind of extreme, of course. If you were to try a similar experiment with sides of, say, 1,000 kilometers instead, the error would be a lot smaller, but still conspicuous. And if you tried moving in 10-foot legs, you would notice nothing amiss: the world would look perfectly Euclidean to you. You could be forgiven for thinking that the Earth is flat.

In any event, the sphere a totally legit example of a non-Euclidean geometry, but can also be confusing. “Ok, the Earth is curved,” you say, “but what does that tell me about the curvature of space?”

“What if I had dug tunnels straight across the Earth, joining the two points on the equator and those two points with the North Pole? Together, the three tunnels would form an equilateral triangle. I could then imagine pointing lasers down the tunnels to join the three points with one another into a triangle of laser light. That triangle would surely have angles that add up to 180 degrees.”

Space in Outer Space

So here we come to the basic fact of life that I was referring to at the beginning of this post. The curvature of space itself.

To avoid any confusion caused by the Earth, take a trip to outer space. You could think of a spacecraft tracing a triangle or a square by traveling in space. That would not be ideal, though, because it raises all sort of thorny issues about what exactly it means for a spacecraft to fly straight ahead or to turn by 90 degrees to the left.

Instead, you and two buddies each have a spaceship, and each of the three travels to some place in the near universe. Once you’re there, you point lasers at one another and form a triangle of beams.

Now each of you can measure the angle between the two beams that go in or out of the respective spaceship.

Fact: Those three angles won’t always add up to 180 degrees.

You could do the appropriate calculations and realize that this fact is a consequence of Einstein’s general theory of relativity. Or you could distrust math and physics and just go out to space to see for yourself.

Regardless, this is what it means for space to be curved. Whenever you can find three points in space, and join them with laser beams, and find that the triangle doesn’t have the expected 180 degrees, that means that space is curved.

And when no matter where the spacecraft are the angles add up to 180 degrees--that is what it means for space to be flat.

The mathematical machinery of Riemannian geometry goes much further and actually gives you a way to define and calculate numerical measures of curvature—not to just say if there is some or none.

There are two important special types of curved space. If in a certain region of space, no matter where you place your three spaceships the three angles they form always add up to more than 180 degrees, then the curvature is positive throughout the region. When they always add up to less than 180 degrees, that means the region has negative curvature. In the flat case, it’s precisely zero.

This post is part of a series on cosmology. Here are the previous posts:

What Do You Mean, The Universe Is Flat? Part I

(On what I mean by "the universe")

Being Mister Fantastic

(On visualizing a finite speed of light)

Under a Blood Red Sky

(On the afterglow of the big bang, and why the sky used to glow red)

Still to come: how do we know that the curvature of space is a fact of life what would the world look like if space were very curved what is the curvature (and the size) of the observable universe and what the heck does the observable universe have to do with Dante.

Footprint icon courtesy of palomaironique/Open Clip Art Library.

Spacecraft image courtesy of NASA. The artist's impression represents the planned Laser Interferometry Space Antenna, or LISA, international space mission, which would in fact be unmanned. Also, LISA is not designed to measure the angles of the triangle but temporary changes in the distances of the space probes from one another due to the passage of gravitational waves--which are themselves perturbations in the curvature of space.

The views expressed are those of the author(s) and are not necessarily those of Scientific American.

Davide Castelvecchi is a senior reporter at Nature in London covering physics, astronomy, mathematics and computer science.

## Our e-dimensional universe

Here’s the layman’s explanation of my theory that physical space is e-dimensional (e = 2.71828…) (for links to the papers, see [1][2]).

It is easy to see that it is a surprising new idea that could lead to new physics, but how can physical dimensions be anything but 3? And the most troubling thing is that it is not even a rational number!

The answer is that three-dimensional v iew of physical space is merely a convention that we have gotten used to. We use this convention to mark points on Earth, but we can’t really check this easily at either the local or the cosmological levels.

In the big bang model, the universe expanded from a singularity (initial state of extremely high density and high temperature) which explains the cosmic microwave background (CMB) radiation, and together with gravity (whose origin is unknown but which is seen to work through either Newton’s or Einstein’s theory) it is consistent with the large-scale structure of the universe with its patterns of galaxies and matter on scales much larger than individual galaxies or groupings of galaxies.

There is divergence between the expansion rates obtained from early universe (captured by CMB data) and the late universe (considering the receding of stars and galaxies) aspects of the universe.

The divergence can be explained away of we accept that space is not quite three-dimensional, but rather e-dimensional

Why hasn’t it been thought of before?

The three-dimensional nature of space is an implicit assumption in Western physical thought and so it has not been questioned. When the idea of information is probed deeply we realize that mathematics compels us to abandon the assumption of a three-dimensional space (References[3][4][5]).

The beginnings of the universe and the nature of space are connected to many deep questions concerning not only physics but also philosophy. These include:

What is the origin of space?

What are the ultimate components of the universe?

What is the relationship between physics and consciousness?

What is space?

The formal use of three-dimensional space is part of modern physics. We can also speak biological space within which biological structure evolve.

Newton took space to be absolute and to be three-dimensional. This was extension of the Aristotelian view of the universe as a container in which the sun, the moon, planets and stars are embedded in perfectly concentric crystal spheres that rotate at fixed rates. In the observer-centric Indian physics that goes back to Kaṇāda, physical laws must be based only on substances, their properties, and their motion, but the experience of time and space is a consequence of the relation between the observer and the world being observed.

There is striking similarity between physical and biological structures. This must be the result of the commonality in the nature of physical and biological spaces, or perhaps the two are identical. Patterns in brain structure and the filament structure and distribution of matter in cosmology are quite similar.

But how morphogenesis may be related to biological space is not known. Indeed this could very well become an exciting new field of research connecting physics and biology.

A new theory of gravity

The new papers provide an explanation for gravity that has been missing in physics, for Newton’s law was based on experiment. The new theory doesn’t change the inverse square law of gravitation but explains why it has this form and suggests that gravity has weakened by about 20% in the last 4 billion years (Reference [6]).

According to current theory, about 96% of the universe is dark matter and dark energy (of which there is no direct evidence) and what is observable is only 0.5% (because another 4.5 % is interstellar gas). Although some scientists are confident that dark matter and dark energy will be eventually discovered, there is no observational evidence in support of it. My theory shows there is no need to speak of dark matter and dark energy.

It shows that the currently accelerating expansion of the universe will eventually slow down and finally reverse. This ties up many loose ends in current physics.

Meaning of e-dimensionality

What is the meaning of an e-dimensional universe? To answer this, we must ask what we mean by the word “dimension” (see References [2]–[7]).

Dimension 0 is a point, dimension 1 is a line, dimension 2 is a plane, and dimension 3 is a solid. An object with dimension between 2 and 3, or e-dimensions, is like sponge or cheese. Another way of seeing it as an object whose density in the limit is less than that of a three-dimensional object.

Fractals have dimensionality that is often noninteger. Two examples of fractals are the Whirlpool Galaxy and the Nautilus shell shown below.

But how can space be like a sponge, with holes? The answer to this is that the sponge-view is one way of looking at space another is that dynamics itself is an expression of this sponge-like nature. Such disparate views can be harmonized by the principle of complementarity, which is one of the deepest philosophical ideas in science (see [8] and references therein).

The most astonishing thing about noninteger dimensionality is that it can be shown to be the origin of gravity. If gravity is a property of space, it solves a puzzle for which science has had no answer until now.

This research also explains the counterintuitive idea of asymptotic freedom [2].

It can have uses for the military, for space travel, and for the understanding of turbulence that Feynman called “the most important unsolved problem of classical physics.” It can also lead to insights that help in the design of novel metamaterials.

## Does Flat Universe mean even distribution? - Astronomy

The curvature of the universe is determined by the density of the universe. You can do a cosmic inventory of all of the mass from ordinary matter in a representative region of the universe to see if the region's density is above the critical density. Such an inventory gives 10 to 20 times too little mass to close the universe. The primordial deuterium abundance provides a sensitive test of the density of ordinary matter in the early universe. Again, you get 15 to 20 times too little mass to close the universe. However, these measurements do not take into account all of the dark matter known to exist. Dark matter is all of the extra material that does not produce any light, but whose presence is detected by its significant gravitational effects.

### Dark Matter

#### Orbital speeds of stars in galaxies

1. Flat rotation curves of spirals even though the amount of the light-producing matter falls off as the distance from the galaxy center increases. Remember the enclosed mass = (orbital speed) 2 × (orbit size)/G. Below is the rotation curve for our Milky Way Galaxy (a typical spiral galaxy).

Also, the orbital speeds of stars in elliptical galaxies are too high to be explained by the gravitational force of just the luminous matter in the galaxies. The extra gravitational force is supplied by the dark matter in the ellipticals.

#### Dark Matter separation from ordinary matter

Current tallies of the total mass of the universe (visible and dark matter) indicate that there is only 32% of the matter needed to halt the expansion---we live in an open universe. Ordinary matter amounts to almost 5% and dark matter makes up the other 27%. One possible dark matter candidate was the neutrino. There are a lot of them, they have neutral charge and photons do not bump into them. Unfortunately, their mass is too small and they move much too fast to create the clumpy structure we see of the dark matter and ordinary matter. The universe would not have been able to make the galaxies and galaxy clusters if the dark matter was neutrinos. To create the lumpy universe, astronomers are looking at possible massive neutral particles that move relatively slowly. Various candidates fall under the heading of "WIMPs"&mdashweakly interacting massive particles (sometimes, astronomers & physicists can be clever in their names). Another possible dark matter candidate was simply ordinary matter locked up in dim things like white dwarfs, brown dwarfs, neutron stars, or black holes in the halos of the galaxies. These massive compact halo objects ("MACHOs") can be detected via microlensing like that used to detect exoplanets. Some MACHOs have been found but the number (and resulting total mass) of them appears to be much too small to account for the dark matter. Big Bang nucleosynthesis and the microwave background radiation (as described below) also provide a strict upper limit on the amount of ordinary matter that could produce the MACHOs in any case. As if the dark matter mystery were not enough, astronomers and physicists have now found that there is an additional form of energy not associated with ordinary or dark matter, called "dark energy", that has an even greater effect on the fate of the universe. This is discussed in the last section of this chapter.

### Deriving the Geometry of the Universe from the Background Radiation

An independent way to measure the overall geometry of the universe is to look at the fluctuations in the cosmic microwave background radiation. If the universe is open (saddle-shaped), then lines starting out parallel will diverge (bend) away from each other. This will make distant objects look smaller than they would otherwise, so the ripples in the microwave background will appear largest on the half-degree scale. If the universe is flat, then lines starting out parallel will remain parallel. The ripples in the microwave background will appear largest on the 1-degree scale. If the universe is closed, the lines starting out parallel will eventually converge toward each other and meet. This focusing effect will make distant objects look larger than they would otherwise, so the ripples in the microwave background will appear largest on scales larger than 1-degree. Select the image below to go to the WMAP webpage from which the image came.

The resolution of the COBE satellite was about 7 degrees---not good enough to definitively measure the angular sizes of the fluctuations. After COBE, higher-resolution instruments were put up in high-altitude balloons and high mountains to observe the ripples in small patches of the sky. Those experiments indicated a flat geometry for the universe (to within 0.4% uncertainty). Cosmologists using the high resolution of the WMAP satellite to look at the distribution of sizes of the ripples confirmed that conclusion using its all-sky map of the microwave background at a resolution over 30 times better than COBE. WMAP also gave a much improved measurement of the ripples. The distribution of the ripples peaks at the one-degree scale---the universe is flat, a result confirmed by the even higher precision Planck satellite with over 2.5 times higher resolution than WMAP.

This result from the WMAP and Planck satellites and the too meager amount of matter in the universe to make the universe geometry flat along with the observed acceleration of the universe's expansion rate (discussed in the last section of this chapter) are forcing astronomers to conclude that there is another form of energy that makes up 68.5% of the universe (called "dark energy" for lack of anything better). The "dark energy" is probably the "cosmological constant" discussed in the last section of this chapter. Furthermore, the distribution of the sizes of the ripples shows that some sizes are preferred and other sizes are damped out as would be the case if the dark matter was different from ordinary matter. The size distribution (the spectrum of sizes) gives the ratio of dark matter to ordinary matter. Dark matter not made of atoms or other particles in the Standard Model makes up 26.5% of the critical density, leaving just 5.0% of the universe with what the rest of the previous chapters of this website have been about (ordinary matter). That ratio matches up very nicely with the ratios found using the other independent methods of Big Bang nucleosynthesis and the motions of galaxies.

In addition to the dark energy, dark matter, and ordinary matter terms, the model used to fit the observed spectrum of the sizes of the ripples and the polarization spectrum also includes terms for how far sound waves traveled when the microwave background photons were released, the scattering of the microwave background photons by high energy electrons in galaxy clusters, and a couple of terms for the density fluctuations at the end of the "inflation period" described in the last section of this chapter. The closest or best fit of the model to the ripple size and polarization spectra can be used to derive what the Hubble Constant should be for today. The result is 67.4 km/sec/Mpc with an uncertainty of just 0.5 km/sec/Mpc.

## Inflation station

Of course, inflation is a hypothetical solution to a hypothetical problem. Perhaps we're wrong about GUT physics and monopole production is a nonstarter. And we don't exactly understand the mechanisms of inflation, either. But that model has become a fixture of modern-day cosmology because, GUT monopoles or not, inflation is a handy device for explaining so many other features of the universe.

Why is the universe so flat? Because inflation made it so big that it can't help but be flat, like a tiny ant measuring the local curvature of an overinflated balloon. [The Universe Is Flat — Now What?]

Why do large patches of the cosmic microwave background have roughly the same temperature, despite being so far apart that there wasn't enough time in the early universe to even them out? Because they were connected before inflation ripped them apart.

Inflation theory goes one step further: It makes firm predictions about how matter ought to be clumped together on large scales — predictions that agree with later observations.

So what started as an out-there solution to an out-there problem turned into a cornerstone of modern cosmology.

Maybe someday we'll actually fully understand how inflation works. And maybe we'll find a monopole, too.