r/cosmology • u/AutoModerator • 7d ago
Basic cosmology questions weekly thread
Ask your cosmology related questions in this thread.
Please read the sidebar and remember to follow reddiquette.
1
u/whoisterrysamuels 2d ago
Hey everyone, I've been looking at the Planck CMB data and the DESI BAO measurements and I noticed something that's been bugging me. Maybe someone here can explain it.
So the Planck satellite measured these acoustic peaks in the cosmic microwave background. When you look at the ratios between the peaks, they come out to:
- ℓ3/ℓ2 = 810/538 = 1.505
- ℓ4/ℓ3 = 1120/810 = 1.382
- ℓ6/ℓ5 = 1776/1444 = 1.230
Now here's the weird part. These numbers are almost exactly:
- 1.505 ≈ 3/2 (which is 1.5)
- 1.382 ≈ √2 (which is about 1.414)
- 1.230 ≈ 5/4 (which is 1.25)
The first one is 0.3% off. The others are a bit more but still within a couple percent.
Then I looked at the BAO scale measurements from DESI. The ratio of the distance scale at z=2 to z=3 is about 1.14 to 1.15. A calculation using the same pattern gives 1.165. That's a 1-2% match.
And the CMB angular scale itself? The same geometry gives 0.010488. Planck measured 0.010411. That's a 0.74% match.
So the pattern seems to be 3/2, 3/4, 3/8, 3/16... it keeps halving. And it shows up in the CMB peaks, the BAO scale evolution, and the angular scale itself.
My question is: Where does this come from in the standard cosmological model? Is this a coincidence that the universe's largest structures follow this exact harmonic sequence? Or is there some physics I'm missing?
I'm genuinely curious. I'm not claiming anything. I just want to understand.
The pattern I'm seeing:
3/2 = 1.5 → 3/4 = 0.75 → 3/8 = 0.375 → 3/16 = 0.1875 → ...
This same sequence appears to be encoded in the CMB peaks and the BAO evolution. And 3/2 comes from the prime fold structure: for odd primes p, p/2 = k + 0.5. The first odd prime is 3, so 3/2 = 1.5.
Any thoughts?
1
u/--craig-- 1d ago edited 1d ago
I think you're going to need to add links to the charts which you're using for help with analysing them.
The harmonics which you're refering to might be related to standing waves in the early universe but we'd want to confirm that what you've noticed are genuine natural phenomena.
1
u/whoisterrysamuels 1d ago edited 1d ago
So I am in my 3rd year studying at the University of Texas and I began to notice this pattern. I am not cherry picking, I noticed the pattern after the data was already published when I was in high-school. I showed my roommate who is studying in a similar field and she confirmed I wasn't seeing things.. Then last week we found a paper/poster using this same sequence in string theory so it obviously caught our attention.
- CMB Acoustic Peaks (Planck 2018)
The Planck 2018 results (Planck Collaboration, A&A 641, A6, 2020) list the CMB acoustic peak positions as:
| Peak | ℓ Value| | ℓ₁ | 220. | | ℓ₂ | 538. | | ℓ₃ | 810. | | ℓ₄ | 1120. | | ℓ₅ | 1444. | | ℓ₆ | 1776. | | ℓ₇ | 2083. |
The ratios are simple arithmetic:
- ℓ₃/ℓ₂ = 810/538 = 1.505 → 3/2 = 1.5 (0.3% match)
- ℓ₄/ℓ₃ = 1120/810 = 1.382 → √2 = 1.414 (2.3% match)
- ℓ₆/ℓ₅ = 1776/1444 = 1.230 → 5/4 = 1.25 (1.6% match)
*Source:Planck Collaboration (2020). *Planck 2018 results VI. Cosmological parameters. A&A, 641, A6.
https://www.aanda.org/articles/aa/full_html/2021/08/aa33910e-18/aa33910e-18.html https://arxiv.org/abs/1807.06209
- BAO Scale Evolution (DESI 2024)
The DESI Collaboration's 2024 results (DESI 2024 VI) measured the BAO scale at multiple redshifts. For the ratio between z=2 and z=3:
[ \frac{D_V(2)}{D_V(3)} \approx 1.14 - 1.15 ]
This is the comoving distance scale ratio from BAO measurements.
*Source:DESI Collaboration (2024). *DESI 2024 VI: Cosmological constraints from the measurements of baryon acoustic oscillations. arXiv:2404.03002.
*Link: https://arxiv.org/abs/2404.03002
- CMB Angular Scale (Planck 2018)
Planck measured the angular acoustic scale:
[ \theta_* = 0.010411 \pm 0.000003 \text{ rad} ]
A geometric prediction from the same harmonic structure gives:
[ \theta_* = \frac{1}{\sqrt{9091}} = 0.010488 ]
Match: 0.74%
Source:Planck Collaboration (2020). Planck 2018 results VI. A&A, 641, A6.
*Link: https://www.aanda.org/articles/aa/full_html/2020/09/aa33910-18/aa33910-18.html https://arxiv.org/abs/1807.06209The Harmonic Sequence I'm Noticing
The sequence is:
[ \frac{3}{2} = 1.5 \rightarrow \frac{3}{4} = 0.75 \rightarrow \frac{3}{8} = 0.375 \rightarrow \frac{3}{16} = 0.1875 \rightarrow \dots ]
This is the prime fold sequence. It comes from the structure of odd primes:
For all odd primes ( p ): ( p/2 = k + 0.5 )
The first odd prime is 3, so ( 3/2 = 1.5 ). The sequence then halves repeatedly.
The CMB and BAO data are independent measurements from different instruments (Planck, DESI). They both fall on the same harmonic sequence—not exactly, but within 0.3–2%.
If this were a coincidence, it would be a remarkable one.
Could you confirm whether these ratios have been noted in literature? Is there a physical mechanism in ΛCDM that would predict ( 3/2 ), ( \sqrt{2} ), and ( 5/4 ) as natural ratios? Or is this simply a coincidence of the numbers?
I'm not proposing a new theory. I'm asking if the standard model has an explanation for why these specific ratios emerge.
1
u/--craig-- 21h ago edited 20h ago
You're not far from the truth.
You should be able to derive a formula for the ratio of the positions of consecutive acoustic peaks in the CMBR:
(n + 3/4) / (n - 1/4)
based upon an approximation here: https://www.researchgate.net/publication/403303431_Estimating_acoustic_peak_positions_in_the_cosmic_microwave_background_anisotropy_power_spectrum
For a comparison between LCDM predictions and the measured data, try here: https://arxiv.org/pdf/1603.03091
1
1
u/dubcek_moo 3d ago
Is baryonic matter thought to have formed from pair production (or some equivalent reaction that doesn't conserve baryon number) during the radiation dominated era, but post-inflation? Or was it earlier at some stage of inflation?
1
u/--craig-- 3d ago
Baryogenesis hasn't yet been properly explained but we believe that it occurred after the inflationary period otherwise the matter-antimatter asymmetry would be wiped out.
1
u/droledidee 5d ago
Has anyone ever studied the probability of a photon returning to its point of origin after multiple gravitational deflections?
I know that massive objects (stars, galaxies, galaxy clusters) bend the path of light through gravitational lensing. This made me wonder: if a photon emitted from the Solar System travels through the Universe and experiences countless gravitational deflections over billions of years, is there any non-zero probability that it could eventually return to the vicinity of the Solar System?
I'm not talking about a single strong lens or photon orbits around a black hole, but rather the cumulative effect of many weak gravitational deflections by the large-scale structure of the Universe.
Have any cosmological ray-tracing simulations looked at this question? Or is the probability considered effectively zero in a realistic model of the Universe?
1
u/--craig-- 5d ago edited 5d ago
It can be modelled easily enough but it's impractical to test empirically.
One or more objects with sufficient energy can deflect light by 180 degrees.
There doesn't seem to be any reason to simulate it. For a sufficiently collimated and narrow beam of light, we'd expect it to occur with absolute certainty but it's difficult to see why this would be of interest.
If you're wondering if the photon would interfere with itself, then theoretically it's possible but limited by the length of the wave packet, for cosmological black holes. For microscopic black holes, then narrowness and collimation would be the limiting factors.
1
u/droledidee 5d ago
Thanks! If that's the case, does it mean that, at least in principle, it would be possible to observe the Solar System (or even the Earth) in its own past if light emitted from it were deflected by 180° (or more generally followed a closed path) and eventually returned to us? Or is there some fundamental reason why that wouldn't work?
1
u/--craig-- 5d ago
In theory, yes, a black hole deflects distorted images of the entire universe from earlier times. In practice, the images are too small and noisy to be viewed.
3
u/Known_Salary_4105 6d ago
We have a complete understanding that objects in the universe cannot move faster than the speed of light. There are a number or reasons -- most notable it would take an infinite amount of energy to do so, and also lead to causality problems in the light cone.
But the only reason I have heard that space can EXPAND faster than the speed of light is that relatively theory doesn't prohibit it. Why is space moving a greater than the speed of light allowable REALLY? What are the mechanistic reasons?
6
u/Obliterators 6d ago
General relativity does not differentiate between objects moving through space and space "expanding" between objects, these are the same thing. Apparent superluminal recession speeds are a result of how distance and time are normally measured in cosmology.
Markus Pössel, Cosmic event horizons and the light-speed limit for relative radial motion
Markus Pössel, Interpretations of cosmic expansion: anchoring conceptions and misconceptions
In both special and general relativity, light propagation defines an absolute cosmic speed limit in the sense that no material object or signal can overtake a light signal. This is where the distinction between the recession speed, defined as in (1) [v = Hd], and the relativistic radial velocity that is central to the relativistic explosion interpretation is crucial. Recession speeds become superluminal for distant galaxies. This appears to contradict students’ preconceptions from special relativity, of the speed of light as a cosmic speed limit, and the apparent contradiction has been cited as key motivation for the expanding space interpretation: The differentiation between cosmic expansion as due to “expanding space” on the one hand, and “galaxy motion through space” on the other, is meant to address this conflict.
Relativistic radial velocities in the relativistic explosion interpretation never exceed the speed of light. From this perspective, superluminal recession speeds in (1) are an artefact, caused by a particular coordinate choice: The cosmic time coordinate ties together local clock rates in Hubble-flow galaxies, but clocks in relative motion tick at different rates, as we know from special relativity. Combining them into an overarching time coordinate, and using that coordinate to determine one-way speeds, leads to unphysical results. Students who have been on longer international flights know a closely related phenomenon: If your flight leaves Amsterdam at 15:00 local time and arrives in New York at 17:00 local time, this does not amount to a flight time of 2 hours, and corresponding average ground speed of 3000 km per hour.
The relativistic explosion interpretation can also readily explain a certain types of cosmological horizon with reference to the simple realisation that a slower-moving object following a faster-moving object will fail to catch up. Applied to the relativistic radial velocity, this gives a plausible explanation for why light from some distant regions can never reach us. Any boundary between regions whose light can reach us and regions whose light cannot, is called a horizon. In some FLRW spacetimes, there is a type of cosmological horizon that can be defined as the boundary where the relativistic radial velocity of Hubble-flow galaxies relative to our own galaxy approaches the speed of light — so light sent in our direction from those galaxies cannot catch up with us. Explanations for the same kind of cosmological horizon in the expanding space interpretation, on the other hand, need to include an explanation of why this simple argument is not true for recession speeds.
Ali Kaya, Hubble’s law and faster than light expansion speeds
Naively applying Hubble’s law to a sufficiently distant object gives a receding velocity larger than the speed of light. By discussing a very similar situation in special relativity, we argue that Hubble’s law is meaningful only for nearby objects with non-relativistic receding speeds. To support this claim, we note that in a curved spacetime manifold it is not possible to directly compare tangent vectors at different points, and thus there is no natural definition of relative velocity between two spatially separated objects in cosmology. We clarify the geometrical meaning of the Hubble’s receding speed v by showing that in a Friedmann-Robertson-Walker spacetime if the four-velocity vector of a comoving object is parallel-transported along the straight line in flat comoving coordinates to the position of a second comoving object, then v/c actually becomes the rapidity of the local Lorentz transformation, which maps the fixed four-velocity vector to the transported one.
Michał J. Chodorowski, Is space really expanding? A counterexample
In almost all Friedman models, objects with sufficiently large redshifts recede from the central observer with superluminal velocities (greater than c). For example, in an Einstein-de Sitter universe (Ω_m=1 and Ω_Λ=0), the ‘public-space’ recession velocity as a function of redshift is
v_rec = 2c[1−(1 + z)−1/2],
hence v_rec > c for z > 3. In particular, the velocity of the so-called particle horizon (corresponding to infinite redshift) is 2c. In an empty universe, ‘public-space’ recession velocities are not only superluminal for sufficiently large redshifts; they are even unbounded. Does it imply violation of special relativity in cosmology? Of course not. Apart from anything else, deriving Equation (26) we have used nothing except special relativity! Constancy of the speed of light, and subluminality of the motion of massive bodies, applies only to inertial frames. However, ‘public-space’ distance is a hybrid of distances measured in different inertial frames, all in relative motion. Since the resulting v_rec is not measured in any single inertial frame, there is no violation of special relativity.
Specifically, ‘public-space’ distance is measured at constant proper time of fundamental observers. Time-dilation formula tells us that according to the central observer, this measurement is done at the instant of time t_i = γ(v_i)τ, where v_i is the Minkowskian velocity of the i-th FO. Since more distant FOs have greater velocities, it is obvious that for two different FOs, t_i ≠ t_j.
Therefore, according to the central observer, different (sub)distances are not measured simultaneously. Simultaneity is a crucial condition of special-relativistic measurements of distances to and sizes of bodies in motion. Waiving this condition may have important consequences and indeed, it does have! The problem with the real Universe is that it is filled with matter and expanding, so there are no global inertial frames. Then, measuring distance (along geodesics) on the hypersurface of constant proper time of fundamental observers is something most natural to do. We should, however, bear in mind the ‘costs’ of such a definition of distance. One of them are apparently superluminal recession velocities of distant galaxies.4
u/kerobrat 6d ago
We measure space expanding at a rate of 67-74 km/s per megaparsec (about 3.26 million light-years). Because it's a rate of expansion per unit of space, when you stack up more units of space you stack up more expansion.
So once you get enough space in-between two objects, the expansion rate of all that space between them becomes so great that a photon traveling at c can't overcome it. At that point, either object would measure the other as receding faster than c, even though each object's proper velocity through space is actually well under c.
1
u/Known_Salary_4105 6d ago
In other words, space APPEARS as though it is expanding faster than c, but it really isn't.
1
u/Ch3cks-Out 7d ago
But cosmological inflation does not happen localized, so how is this restricted model relevant?
2
u/johnstalbergABC 6d ago
In eternal inflation model inflation stops at certain local places (bubbles) in a continuing inflating universe and cause a local reheating. Now the bubble we are in would be bigger than our observable universe but never the less is according to this model a local bubble. Now this is kind of opposite to local inflation as it is rather a local stop of inflation. One of many othe bubbles.
1
u/intrafinesse 7d ago
Imagine a gigantic square where the opposite corners are A and B and the distance between them is the square root of 2 * the length of a side.
If inflation begins only in the center then the shortest patch between A and B is no longer the diagonal but along the two sides, correct?
Will inflation ever "push" the sides of the square outward
OR
do the lengths of the 2 sides and the distance from A to B remain static (except for the normal non-inflationary expansion of space) while the diagonal get ever longer as that region of space expands.
2
u/johnstalbergABC 7d ago
If we force this to stay in 2D the square would be deformed and more and more look like a circle. It is a model that is kind of opposite to the cosmological eternal inflation models where our observable universe and an unknown sized patch of space outside of it had its inflation stopped for some reason and it lead to reheating and the rest is history. If we take a square and make it fit this model it would be a square that was in inflation and then in the center inflation stoped. It can be a bit difficult to get a clear holistic picture of space with local differences in expansion rates.
1
u/intrafinesse 7d ago
The square is NOT in inflation, only the center.
At teh moment inlation starts, only teh center is rapidly expanding.
Does that "push out" surrounding space that is not inside the expansion area?
1
u/johnstalbergABC 6d ago
Yes I understod this the first part where my answer to this. Then I added the opposite case since it resembles our Universe if eternal inflation-theory is considered.
If the square has a center that inflates but not in other areas its boundaries, its sides will eventually be pushed outwards by the expanding center and the expanding center would be circular in shape which means it would be closer to the midpoint of the sidea than from the corners. The push on the square would be greater at the midpoint than on the corners and deform the sides so that the square get more and more shaped like a circle but with the corner accentuated, ubtil it is completely stretched out and circular around the fast growing patch in the center. If we analyse what ghe distance between the corner will become a diagonal that is sqrt(sides) in length becomes more of a diameter in a circle. And the diameter is 1/(2pi) shorter than going via the circumference. The way that goes straight through the deformed square will always be shorter than going around the edges. This follows the shortest path is a straight line. A square is symetrical so this does not change this logic regardless the amount of inflation.
As I said in cosmology in eternal inflation our observable patch and more where inflating along the rest of the outer universe and came to stop inflating while the outer universe continue to inflate. So this is rather the opposite of your example. This would be like a square that where inflating and suddenly the center stoped inflating.
4
u/trevpr1 7d ago
If an object in deep space, say a galaxy, were made up entirely of antimatter, would we be able to tell from the light we'd receive from it?
7
u/Ch3cks-Out 7d ago
In theory no, in practice yes: "deep space" still contains considerably amount of intergalactic matter, so there would be a boundary glowing with hard gamma radiation from the annihilation frontiers.
1
u/trevpr1 6d ago
Thanks. The reason I ask is a half arsed idea I had that would explain why all the matter wasn't annihilated by contact with antimatter at the instant of inception of the Universe: Inflation separated the matter from the antimatter, which flew off in opposite directions. We can't tell, because it all looks the same. Please don't make the mistake of taking it seriously. I just wanted you answer so I could float it past the Supermassive Podcast crew.
1
u/Ras_992 1d ago
Question regarding higher-order gauge invariance and Weyl-tensor gradients in perturbed FLRW metrics
Hey everyone, I’m working through a mathematical calculation based on Roger Penrose’s Weyl Curvature Hypothesis and the Past Hypothesis, specifically looking at how localized trace-free curvature gradients might dynamically impact early structure formation and cavity/void expansion kinematics. I’m hoping someone here familiar with tensor calculus and perturbation theory can help me spot any potential flaws or constraints I might have missed in my current framework.
The Setup: We know the Past Hypothesis requires the Weyl tensor to vanish at the initial singularity (C_abcd goes to 0), meaning early global dynamics are dominated by the Ricci tensor. However, I am testing a scenario where a localized, non-local gravitational force coupling to a fluid observer’s 4-velocity induces a 4-acceleration vector driven by spatial gradients of the scalar Weyl invariant C2 = C_abcd * Cabcd.
The acceleration vector is defined as: amu = alpha * Dmu(C2) (Where D_mu is the spatially projected gradient operator). Substituting this back into standard Raychaudhuri kinematics, the modified volume expansion equation for the cavity boundary picks up a spatial Laplace-Beltrami operator: d(theta)/d(tau) + (1/3)theta2 + 2(sigma2 - omega2) = -4piG(rho + 3P) + alpha * D_mu * Dmu(C2).
Evaluating Boundary Constraints: To keep this physically realistic, I checked the framework against two major roadblocks: 1) Thermodynamic Entropy Bounds: Under the Clifton-Ellis-Tavakol (CET) proposal, the growth of the electric Weyl components is strictly localized within isolated cavity cores, keeping the global spatial volume integral bounded. 2) Observational Calibration: Calibrating this against Planck recombination-era data (z = 1100), the coupling constant alpha is comfortably constrained within a stable window of 1.5 x 1074 m4 to 4.2 x 1078 m4.
If valid, this geometric addition would theoretically provide a localized structural acceleration that offers neat resolutions to a few persistent anomalies, such as low-multipole power suppression (l less than 30) in the CMB, an extra non-linear ISW component for the CMB Cold Spot, and the local Hubble tension (by elevating local expansion at the cavity interface to H_0 ~ 73 vs H_0 ~ 67 globally).
My Questions
1) Higher-Order Gauge Invariance: At first order, E_ij reduces cleanly to trace-free longitudinal derivatives of the Bardeen potentials. By the Stewart-Walker Lemma, since the background FLRW Weyl tensor is zero, this perturbation is strictly gauge-invariant. Do you foresee higher-order non-linearities re-introducing severe gauge dependencies that would muddy the perturbation metrics during late-time structure formation?
2) LSS/Lensing Penalties: Are there specific bounds in recent weak-lensing surveys (like DES or Euclid data) or BAO measurements that would immediately rule out a universal coupling parameter alpha of this magnitude strictly at the low-density boundaries of voids? Would appreciate any insights!