Question related to formation of galaxies

Question

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1. What is being asked?

The student is asking:

“Is there any modern scientific theory that can confirm the explanation of galaxy formation given in *Science of Time and the Theory of Everything (Bhausaheb Bhosle, based on the ancient text Surya‑Siddhanta)? If we use the information supplied in that book, can we calculate the result and compare it with observations?”*

In plain language the question is:

“Do any accepted physical theories reproduce the galaxy‑formation story described in that book, and can we work out the numbers to see whether it matches what astronomers observe?”

2. Step‑by‑step analysis

Below is a systematic way to address any claim about how galaxies form, whether it comes from a modern textbook, an ancient manuscript, or a popular‑science book.

Step 1 – Identify the explicit physical ingredients that the claim uses

Typical ingredient in a galaxy‑formation model	What the claim must specify
Initial conditions (density fluctuations, temperature, composition)	amplitude of perturbations, matter‑radiation ratio, etc.
Governing equations (gravity, hydrodynamics, radiation)	Newton/Einstein gravity, Navier–Stokes, radiative transfer
Contents of the Universe (dark matter, dark energy, baryons, neutrinos)	fractions Ω_dm, Ω_b, Ω_Λ
Timeline (age of the Universe, redshift of key events)	numerical values for when “first galaxies” appear
Physical processes (cooling, star formation, feedback, mergers)	cooling functions, star‑formation efficiency, supernova/AGN feedback

Action: Write down every number, equation, or qualitative rule that the book supplies. If the book does not give any of the above, the claim cannot be turned into a calculable model.

Step 2 – Translate those ingredients into the standard cosmological framework

The current, widely‑tested framework is the ΛCDM (Lambda‑Cold‑Dark‑Matter) model. Its core equations are:

Friedmann equation (expansion of the Universe)

[ H^{2}(z)=H_{0}^{2}\big[\,\Omega_{\rm m}(1+z)^{3} +\Omega_{\rm r}(1+z)^{4} +\Omega_{\Lambda}\big], ]

where (H(z)) is the Hubble parameter at redshift (z).
Linear growth of density perturbations

[ \ddot\delta +2H\dot\delta -4\pi G\bar\rho_{\rm m}\,\delta =0, ]

whose solution gives the growth factor (D(z)).
Press–Schechter (or modern Sheth–Tormen) halo mass function – predicts the number density of dark‑matter haloes of mass (M) at a given redshift:

[ \frac{{\rm d}n}{{\rm d}M}(M,z)=\sqrt{\frac{2}{\pi}}\, \frac{\bar\rho_{\rm m}}{M}\, \frac{\delta_{\rm c}}{\sigma(M,z)}\, \left|\frac{{\rm d}\ln\sigma}{{\rm d}\ln M}\right| \exp!\Big[-\frac{\delta_{\rm c}^{2}}{2\sigma^{2}(M,z)}\Big]. ]

Here (\sigma(M,z)) is the rms fluctuation of the density field filtered on scale (M); (\delta_{\rm c}\simeq1.686).
Baryonic physics (cooling, star formation, feedback) are added through semi‑analytic recipes or full hydrodynamic simulations (e.g., Illustris, EAGLE, TNG).

Action: Map the book’s numbers onto these equations. For example, if the book says “the Universe began with a uniform sphere of radius (R_0) and density (\rho_0)”, compute (\Omega_{\rm m}) and the corresponding (H_0) using the Friedmann equation. If it gives a “critical mass for a galaxy” of (10^{11}M_\odot), see whether that mass appears with the right abundance in the Press–Schechter formula at the stated epoch.

Step 3 – Perform a concrete calculation

Below is a template calculation that can be filled in with any numerical values the book supplies.

Quantity	Formula (ΛCDM)	What you need from the book	Example (using Planck 2018 values)
Age of Universe today, (t_0)	(\displaystyle t_0 = \int_{0}^{\infty}\frac{dz}{(1+z)H(z)})	(H_0) and (\Omega)s	(t_0\approx13.8) Gyr
Redshift of first galaxy formation, (z_{\rm f})	–	Stated redshift or time	If (z_{\rm f}=10), (t(z_{\rm f})\approx0.5) Gyr
Typical halo mass at (z_{\rm f})	Use Press–Schechter to get (M_{\star}(z_{\rm f})) where (\sigma(M_{\star})=\delta_c/D(z_{\rm f}))	Desired mass (e.g., (10^{11}M_\odot))	At (z=10), (M_{\star}\sim10^{9}M_\odot) (much smaller)
Stellar mass‑to‑halo‑mass ratio	Empirical relation (M_\star/M_{\rm halo}\approx0.01) for (M_{\rm halo}\sim10^{11}M_\odot)	Any claimed ratio	Gives (M_\star\approx10^{9}M_\odot)

Procedure

Insert the book’s numbers into the left‑hand column.
Compute the right‑hand side using a calculator or a simple script.
Compare the result with the observational benchmarks (e.g., galaxy stellar mass functions at the quoted redshift, Hubble‑deep‑field counts).

If the book does not provide the necessary numerical inputs, the calculation cannot be completed; the claim remains qualitative.

Step 4 – Compare with observations

Key observational tests for any galaxy‑formation scenario are:

Observation	What it measures	Typical ΛCDM prediction
Galaxy luminosity/stellar‑mass function (z≈0–10)	Number density vs. mass	Matches Schechter function with faint‑end slope ≈‑1.4
Cosmic microwave background (CMB) anisotropies	Initial density perturbation spectrum (P(k))	Nearly scale‑invariant (n≈0.965)
Large‑scale structure (BAO, clustering)	Spatial distribution of galaxies	Correlation function with BAO peak at ~150 Mpc
Rotation curves of spiral galaxies	Dark‑matter halo profiles	Flat curves ⇒ Navarro‑Frenk‑White (NFW) profile

Action: After performing the calculation, ask: Does the predicted number of galaxies of mass (M) at redshift (z) agree with the observed mass function? If the answer is “no”, the theory is not supported by data.

Step 5 – Decide whether the claim is confirmed

If the book’s quantitative predictions exactly reproduce the ΛCDM results and those results match observations → the claim is consistent (though it would be a coincidence that an ancient text anticipated modern cosmology).
If the predictions differ (e.g., galaxy formation at age < 10 Myr, or without dark matter) → the claim is not supported by current evidence.

3. Final answer

There is currently no accepted scientific theory that confirms the galaxy‑formation description given in Science of Time and the Theory of Everything based on Surya‑Siddhanta.

The standard, observationally verified framework is the ΛCDM cosmology combined with hierarchical structure formation. Using the ΛCDM equations (Friedmann expansion, linear growth, Press–Schechter halo mass function, and baryonic cooling/feedback recipes) one can compute the expected timing, masses, and abundances of galaxies. All of these predictions have been extensively tested against observations (CMB, deep‑field galaxy surveys, large‑scale structure) and are in agreement to within a few percent.

Unless the book provides explicit, numerically testable statements that can be mapped onto the ΛCDM equations and shown to reproduce the observed galaxy population, its explanation remains unverified by modern physics. In practice, the information supplied in the cited work is qualitative and does not contain the necessary parameters (e.g., density fluctuation spectrum, matter/energy fractions, cooling rates) to perform a rigorous calculation. Consequently, no contemporary astrophysical theory confirms the book’s narrative.

4. Common mistakes when evaluating unconventional galaxy‑formation claims

Mistake	Why it’s wrong	How to avoid it
Assuming “qualitative similarity” means “quantitative confirmation.”	A story that sounds like “matter clumps together” does not give the precise numbers (mass function, redshift distribution) that observations demand.	Always demand explicit equations and numbers; then test them.
Ignoring the role of dark matter.	Modern observations (rotation curves, CMB, lensing) require a non‑baryonic matter component; any model that omits it cannot match data.	Check whether the claim includes a dark‑matter analogue; if not, it cannot reproduce the measured dynamics.
Treating the age of the Universe as a free parameter.	The age is tightly constrained by the CMB (≈13.8 Gyr). Claims of a much younger or older Universe clash with many independent measurements.	Compare the claimed age with the Friedmann integral using the supplied (H_0) and (\Omega) values.
Using “order‑of‑magnitude” arguments without error analysis.	Galaxy formation spans many orders of magnitude; a rough estimate can be off by factors of 10⁴–10⁶, which is fatal when comparing to observed number densities.	Propagate uncertainties and see whether the result lies within the observational error bars.
Equating “scriptural description” with a scientific model.	Religious or mythological language is not constrained by empirical testing and often lacks falsifiable predictions.	Translate any scriptural statement into testable physics; if it cannot be done, it remains outside the scientific domain.

By following the systematic steps above and avoiding these pitfalls, one can objectively decide whether any proposed galaxy‑formation scenario—whether from a modern textbook or an ancient manuscript—holds up to the rigorous standards of contemporary astrophysics.

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