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The story of the universe seems pretty settled; it started with a "Big Bang" followed by rapid expansion and cooling as fundamental particles, then protons and neutrons and then hydrogen condensed out along with photons that become the Cosmic Microwave Background (CMB). Gravity assembled the gas into stars and then galaxies and finally collections of galaxies. 

The current (2022) mathematical model linking the CMB data set  to todays galaxies dataset  relies  on 3 assumptions; that the universe is flat, and the dark matter and dark energy exist. Dark matter and dark energy have not been independently detected or have theoretical explanation. 

NEWS 2/19/23

The idea is that as the universe expands, so do black holes creating vacuum energy. Dark energy and mass are both hidden in black holes. The team calculated that these black holes that formed billions of years ago are anywhere from seven to 20 times more massive than similar, recently formed black holes.

Lifecycle  of the Universe 

The universe starts with a Big Bang.  The "inflation era" covers the time from initiation, to the flash of light from the bang.  The inflation model suggests that at the beginning of the big bang a patch matter (smaller than the size of a proton) underwent a phase transition bringing about a huge gravitational repulsion. This is the driving force behind the space-explosion that was the big bang.  

The phenomenon of particle creation in an expanding universe  is associated with the appearance and disappearance of particle–antiparticle pairs in the vacuum. Such energy non-conserving processes are permitted as long as they take place on a sufficiently short timescale  However, when the space is rapidly expanding, that is, the expansion rate was larger than the annihilation rate, real particles were created. This hot, dense, uniform collection of particles is  the postulated initial state of the standard big bang model.  The epoch when charged nuclear ions and electrons were transformed into neutral atoms is called the photon-decoupling time. This took place when  the thermal energy of photons just dropped below the threshold required to ionize the newly formed atoms. The redshifted light from the big bang, is seen in the Cosmic Microwave Background. Because of gravitational instability, this nonuniform distribution of matter in the CMB eventually evolved into the stars and galaxies  we see today.

We now have a qualitative picture of the evolution of the Universe.  It started with the big bang 13.5 Byrs ago, and we can see the residual light emission from the Bang  in the Cosmic Microwave Background (CMB). Non uniformities in the matter shown in CMB  emissions evolve into the first stars, that then assemble into galaxies after around 1M years. Universe doubling every 20B years.

Stars go through a life cycle of generating enough dense mass to ignite fission, followed by collapse when their fuel runs out  or  with an explosion that creates fuel for new stars. The bigger the star, the brighter and shorter their life.  First stars appeared 13.3 Byrs ago, we are 4.5 Byrs into the lifetime of our sun that is around 12 Byrs.  As the star matter gets recycled, presumably the thermodynamics means that some of the matter gets converted to heat, so over time the total mass of the universe must decline. 


Galaxies also have  cycles of star birth, merge  and death. Some of the stars in the Milky Way were formed in the earliest universe. The Milky way will merge with Andromeda Galaxy in 4.5B yrs.

When we look out at the universe, the finite speed of light means that we also look back in time as illustrated by the light triangle in the sketch. 

Quantitative cosmology  

3 critical pieces of hard data;​

  • Receding Galaxies - confirms Big Bang

  • Rotation of Galaxies 

  • Cosmic Microwave Background - confirms Big Bang 

Receding galaxies

The observable universe is limited to stars that are close enough that photons travelling at the speed of light can get here, illustrated by the light triangle in the sketch. Hubble telescope enabled the observation of much dimmer objects, James Webb telescope sees even dimmer and colder objects in the IR. The Plank telescope sees the CMB in the deep IR at a wavelength of 10,000 um. These telescopes have transformed our understanding of the Universe, with images of orders of magnitude more galaxies and the CMB. 

Universe is doubling in size every 20B years.

The first quantitative insight into the evolution of the universe came from Hubble in the 1920's when he showed that mores distant galaxies were moving away quicker. This proved that the universe is expanding and must have started in a Big Bang.

 H0 = (72 ± 7 km/s)Mpc−1 , (7.7) where the subscript 0 stands for the present epoch H0 ≡ H(t0). An inspection of the Hubble’s law (7.6) shows that H0 has the dimension of inverse time, and the measured value in (7.7) can be translated into Hubble time tH ≡ H −1 0 ≃ 13.6 Gyr and Hubble length lH = ctH ≃ 4,200 Mpc

The classic display of raw galaxy data is Luminosity of 1a supernova as a proxy for Distance vs. Redshift as a proxy for velocity. The accelerating universe is indicated by distant (old) galaxies that have less red shift than linear extrapolation. The review by Riess in 2000 showed the original Reiss and Permutter publications. There is enough noise in the raw data to question any non linear hypothesis. The authors used correlations to parametrized Cosmological Constant to extract the signal from the noise, and claim an ACCELERATING  expanding universe and support for dark energy.

Relativity, Gravitation, and Cosmology A basic introduction TA-PEI CHENG














Rotation of galaxies

Spiral galaxies are rotating at at roughly  uniform angular rate, just like a frisbee, consistent with a  long term stable structure. 


The latest images from  the Webb Telescope show increased IR luminosity out at the edge of the galaxies.  Other data includes; the angle of the spirals is related to the size of the black hole at the center of galaxies (Seigar). 

The simplest possible model based on Newtonian gravity where the gravitational effect of a distributed sphere can be approximated by a point source at the center. It predicts that the rotation speed should drop as the square of the 1/ radius and that the galaxy will fall apart in a few rotations. 

          GMm/r^2=mV^2/r   so V=(GM/r)^0.5

Thus the tangential velocity inside a galaxy is expected to rise linearly with the distance from the center v ∼ r if the mass density is approximately constant. For a light source located outside the galactic mass distribution the velocity is expected to decrease as v ∼ 1/ √ r. If gravity is linear with radius, then V would be constant.

Comprehensive studies of the rotation of galaxies includes data from CO emissions, optical spectroscopy and microwave studies of H1 emissions. The visible edge of galaxies is typically around radius of  10-20 kparsecs, and direct rotation measurements have been made out to 30 kparsecs.  Andromeda M31 has been studies using interactions with other galaxies in the Local Group, velocity curves out to 200 kparsecs = 600 kLyrs. 


Sofue has used the velocity curves to calculate what the mass distribution must look like. The results for multiple galaxies show a simple exponentially declining mass out to 300-500 kparsecs. There is no sign of a new structure. 

They also decomposed the mass distribution into gaussian components. In their decomposition, the dark matter halo is roughly 10-20x the mass of the luminous matter because even though it is very dilute, it is spread over a large area.  


Matter made up of protons and neutrons is generally referred to as “baryonic matter.” As it turns out, we have methods that can distinguish between baryonic and exotic dark matter because of their different interactions. The light nuclear elements (helium, deuterium, etc.) were produced predominantly in the early universe at the cosmic time O(102 s), cf. Section 8.4. Their abundance (in particular deuterium) is sensitive to the baryonic abundance. From such considerations we have the result (Burles et al., 2001) .

        Baryonic Dark  Matter Fraction = 4%,

        Luminous Matter Fraction = 0.5%

A plot of Mass/Luminosity against radius, suggests that the outer galaxy contains progressively more dark matter.  It seems likely that the dark halo is in fact "Baryonic dark matter" such as gas and star remnants. This is consistent with other estimates of Baryonic Dark Matter as discussed below.

Cosmic Microwave Background CMB

The discovery of the CMB was the second key evidence that the universe started with a big bang. A series of satellites have made detailed measurements. After removing the shadows caste by the Milky Way, the CMB looks uniform across the sky with local non-uniformities. 

A 2D Fourier Transform gives the power spectrum of the non - uniformities or "anisotropy" of the CMB. The multiple frequencies in the power spectrum has been taken as evidence supporting the "Inflation" model of the pre CMB universe.  The inflation model also proposes a flat universe,

The CMB power spectrum monopole frequency. In a flat universe we expect the frequency of the monopole to be 200. The angular non-uniformity  in temperature fluctuations reflect the sound wave spectrum of the photon–baryon fluid at photon decoupling time.  However, the fits to the power spectrum do not allow unique values for flatness and mass known as "degeneracy"

Lamda CDM model

The  Hubble plot and CMB power spectrum form 2 independent data sets of different metrics for 2 different era's and are  the  perfect basis for a complete model of the universe. 


Todays  "standard model" of the universe is "Lambda CDM". The model is based on the "Friedman Equations" derived from General Relativity. The mass -  energy balance and the shape of the universe are critical.


The inflation model suggests that the universe is flat. IF this is correct, the Hubble Constant gives a value for all the mass in the universe - "critical mass". We can total all the mass that we know about, luminous mass and baryonic dark matter and we get roughly 4% of the critical mass. The difference between known mass and critical mass must be undiscovered "dark" and can be energy or mass.  

The independent fits to Hubble and CMB data cannot discriminate  dark  energy and  matter. The best simultaneous fit relies on 2 adjustable parameters "dark matter" at 27% of the total mass, and "dark energy" at 68% of the total energy of the universe. The presence of dark energy would imply that the expansion of the universe is accelerating, and requires the Cosmological Constant 'Lambda" in General Relativity. The "Cold Dark Matter" (CDM),  explains the expansion of the early universe. 


To date there is no quantitative theoretical rationale or direct experimental observation of either dark matter or dark energy. Futhermore, as quality of observations has improved the estimate of Hubble constant from applying Lamda CDM model to CMB is now statistically significantly different from the measured Hubble constant from galaxy motion - even after invoking dark matter and dark energy.

IF the universe follows General Relativity without the Cosmological Constant, then the universe is open (never closes) and negatively curved.

There is no need for dark energy or dark matter, BUT there is no model parameters that fit Hubble and CMB simultaneously. 

Further evidence that challenges dark energy "Professor Subir Sarkar from the Rudolf Peierls Centre for Theoretical Physics, Oxford along with collaborators at the Institut d'Astrophysique, Paris and the Niels Bohr Institute, Copenhagen have used observations of 740 Type Ia supernovae to show that this acceleration is a relatively local effect—it is directed along the direction we seem to be moving with respect to the cosmic microwave background (which exhibits a similar dipole anisotropy). While the physical reason for this acceleration is unknown, it cannot be ascribed to dark energy which would have caused equal acceleration in all directions."

"Thus the cosmic acceleration deduced from supernovae may be an artefact of our being non-Copernican observers, rather than evidence for a dominant component of “dark energy” in the Universe." In summary, the model-independent evidence for acceleration of the Hubble expansion rate from the largest public catalogue of SNe Ia is only 1.4σ. This is in contrast to the claim (Scolnic et al. 2018) that acceleration is established by SNe Ia at >6σ in the framework of the ΛCDM model.

Jacques Colin et al. Evidence for anisotropy of cosmic acceleration, Astronomy & Astrophysics (2019). DOI: 10.1051/0004-6361/201936373

Still many unsolved problems Although we have a self-consistent cosmological description, many mysteries remain. We do not really know what makes up the bulk of the dark matter, even though there are plausible candidates as predicted by some yet-to-be-proven particle physics theories. The most important energy component is the mysterious “dark energy,” although a natural candidate is the quantum vacuum-energy. Such an identification leads to an estimate of its size that is completely off the mark (cf. Section A.4). If one can show that the quantum vacuum-energy must somehow vanish due to some yet-to-be-found symmetry principle, a particular pressing problem is to find out whether this dark energy is time-independent, as is the case of the cosmological constant, or is it more like an effective Lambda coming from some quintessence scalar field like the case of inflation.


Despite our lack of understanding of this dark energy, the recent discoveries constitute a remarkable affirmation of the inflationary theory of the big bang. Still, even here the question remains as to the true identity of the inflation/Higgs field. We need to find ways to test the existence of such a field in some noncosmological settings. Besides the basic mystery of dark energy (“the cosmological constant problem”) there are other associated puzzles, one of them being the “cosmic coincidence problem”: we have the observational result that in the present epoch the dark energy density is comparable to the matter density, X ⋍ M. Since they scale so differently (M ∼ a −3 vs. X ∼ a 0 ) we have M ≃ 1 in the cosmic past, and ≃ 1 in the future. Thus, the present epoch is very special— the only period when they are comparable. Then the question is why? How do we understand this requirement of fine tuning the initial values in order to have M ⋍ X now? 

Spirals in galaxies

Together with irregular galaxies, spiral galaxies make up approximately 60% of galaxies in today's universe.[6] They are mostly found in low-density regions and are rare in the centers of galaxy clusters.[7]

Spiral galaxies may consist of several distinct components:

The black hole in the center of the galaxy NGC 1362 is spinning at 84% of the speed of light. Black holes wobble. 

Since the 1970s, there have been two leading hypotheses or models for the spiral structures of galaxies:

  • star formation caused by density waves in the galactic disk of the galaxy.

  • the stochastic self-propagating star formation model (SSPSF model) – star formation caused by shock waves in the interstellar medium. The shock waves are caused by the stellar winds and supernovae from recent previous star formation, leading to self-propagating and self-sustaining star formation. Spiral structure then arises from differential rotation of the galaxy's disk.


These different hypotheses are not mutually exclusive, as they may explain different types of spiral arms.

Density waves  theory or the Lin–Shu density wave theory is a theory proposed by C.C. Lin and Frank Shu in the mid-1960s to explain the spiral arm structure of spiral galaxies.[1][2]  The spiral pattern rotates in a particular angular frequency (pattern speed), whereas the stars in the galactic disk are orbiting at a different speed depending on their distance to the galaxy center.

"Spiral arms are shown to be stable configurations of stellar orbits,. Pitch angle is directly related to the distribution of orbital eccentricities in a given spiral galaxy.  We conclude that spiral galaxies evolve toward grand design two-armed spirals. We infer from the velocity distributions that the Milky Way evolved into this form about 9 Gyrs ago"


There is  a significant correlation between the rotation velocity of a galaxy and the pitch angle of its spiral arms.

This  is  suggestive of star orbits dragged along the background geometry. We confirmed that geometry is a manifestation of gravity according to the Einstein theory, in particular the weak gravitational effect, due to the off-diagonal term of the metric could account for a ”Dark Matter-like” effect in the observed flatness of the MW rotation curve.

A spinning disk will not radiate gravitational waves. This can be regarded as a consequence of the principle of conservation of angular momentum. However, it will show gravitomagnetic effects.  Too small to affect orbits.

Gravitoelectromagnetism and stellar orbits in galaxies Viktor T. Toth‡

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Radial velocity.jpg
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Extended rotation curve for M31


Figure 23. (a) Direct SMD in spiral galaxies with end radii of RC greater than 15 kpc (from Sofue 2016) calculated under flat disk assumption, and the same in logarithmic radius (Sofue 2016). Red dashed lines indicates the Milky Way. 


Figure 22. Directly calculated SMD of the Milky Way by spherical (black thick line) and flat-disk assumptions by log-log plot, compared with the result by deconvolution method (dashed lines). The straight line represents the black hole with mass 3.6 × 106 M⊙.

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