Evolution of Size, Mass, and Density of Galaxies Since Cosmic Dawn

Technical Summary: Evolution of Size, Mass, and Density of Galaxies Since Cosmic Dawn

Problem Statement
Recent observations from the James Webb Space Telescope (JWST) and the Atacama Large Millimeter/submillimeter Array (ALMA) have revealed massive, bright, and highly evolved galaxies in the early universe (cosmic dawn, $z > 10$). These observations present significant tensions with the standard $\Lambda$CDM cosmological model. Specifically, the $\Lambda$CDM framework struggles to explain:

1. Angular Diameters: Early galaxies appear larger than predicted by $\Lambda$CDM angular diameter distance relations.
2. Excess Density: The number density of luminous and quiescent galaxies at high redshifts ($z > 7$) exceeds theoretical predictions by orders of magnitude.
3. Formation Timescales: The existence of massive black holes (e.g., $10^{10} M_\odot$) and evolved spiral galaxies within the first few hundred million years of the universe's age ($\sim 400$ Myr) implies formation rates that are physically unrealistic under standard accretion and merger models.
4. Compactness and Density: "Little Red Dots" (LRDs) and other early galaxies exhibit extremely high stellar surface densities and small effective radii ($r_e \sim 100\text{--}300$ pc), challenging standard formation scenarios.

Methodology
The paper proposes an alternative cosmological framework, the CCC+TL (Covarying Coupling Constants + Tired Light) model, to resolve these tensions without invoking exotic physics like primordial massive black hole seeds or super-Eddington accretion. The methodology involves:

1. Theoretical Framework (CCC): The model assumes that dimensionful physical constants (speed of light $c$, gravitational constant $G$, Planck constant $\hbar$, Boltzmann constant $k_B$) evolve over time according to a common dimensionless function $f(t) = \exp[\alpha(t - t_0)]$. This leads to modified Friedmann equations and a modified FLRW metric where the scale factor and physical distances depend on this evolution.
2. Redshift Mechanism (TL): The model incorporates the "tired light" (TL) hypothesis, where photons lose energy over cosmic distances, coexisting with metric expansion. The observed redshift $z$ is the product of expansion redshift $z_x$ and tired light redshift $z_t$: $(1+z) = (1+z_x)(1+z_t)$.
3. Comparative Analysis: The author derives the physical properties of galaxies (size, mass, density, luminosity) in the CTL model and compares them directly to values derived under the standard $\Lambda$CDM model. Key calculations include:
   • Angular Diameter Distance ($d_A$): Recalculated using the modified metric and the relationship between $d_A$ and the proper distance $d_p$ in the CTL framework.
   • Luminosity and Flux: Adjusted for the absence of time dilation in the tired light component, altering the flux-luminosity relation.
   • Mass Scaling: Stellar mass ($M_*$) is assumed proportional to luminosity ($L$), while dynamical mass ($M_{dyn}$) is derived from velocity dispersion ($\sigma$) and effective radius ($r_d$) using $M \propto \sigma^2 r_d / G$. The evolution of $G$, $\sigma$, and $r_d$ under CCC is accounted for.

Key Contributions and Results
The paper demonstrates that the CCC+TL model fundamentally alters the interpretation of high-redshift observations, effectively resolving the "impossible early galaxy" problem through three primary mechanisms:

1. Size Evolution ($r_e$):

   • In $\Lambda$CDM, galaxy effective radii are observed to decrease with redshift as $r_e \propto (1+z)^s$ with $s \approx -1.0$.
   • In the CTL model, the physical size of an object with a fixed angular size is significantly larger due to the modified angular diameter distance. The paper derives a size scaling factor of $r_e \propto (1+z)^{0.93}$ relative to the $\Lambda$CDM model.
   • Result: The combined evolution in CTL is $r_e \propto (1+z)^{s+0.93}$. For example, a galaxy at $z=14$ with an observed UV radius of 260 pc in $\Lambda$CDM becomes $\sim 3172$ pc in CTL. This eliminates the "compactness" problem, as early galaxies are physically much larger.

2. Mass and Density Evolution:

   • Stellar Mass ($M_*$): Increases modestly in CTL (factor of $\sim 1.7$ at $z=14$) because it scales with luminosity, which sees a relatively small correction.
   • Dynamical Mass ($M_{dyn}$): Increases dramatically (factor of $\sim 12.2$ at $z=14$) because it scales with the effective radius.
   • Density: Since volume scales with the cube of the size increase, the number density and surface density of galaxies decrease significantly in CTL.
   • Result: The "excess" number density of quiescent galaxies at $z \sim 7$ (reported as $>100\times$ predictions in $\Lambda$CDM) is reduced by a factor of $\sim 385$ in CTL, bringing observations into alignment with theoretical expectations. Similarly, the extreme stellar surface densities of LRDs are reduced by factors of $\sim 30\text{--}40$, making them consistent with local galaxy densities.

3. Cosmic Age and Formation Timescales:

   • The CTL model predicts a significantly older universe at high redshifts. For instance, at $z=15$, the universe age is $\sim 280$ Myr in $\Lambda$CDM but $\sim 4.35$ Gyr in CTL.
   • Result: This "stretched" timeline provides ample time for stars, black holes, and galaxies to evolve to their observed states without requiring unrealistic formation rates. The existence of a quiescent galaxy at $z=7.3$ (age $\sim 700$ Myr in $\Lambda$CDM) becomes plausible when the universe age is $\sim 7$ Gyr in CTL.

Significance and Claims
The paper claims that the CCC+TL cosmology eliminates or significantly moderates the tensions between JWST observations and standard cosmology. By attributing the discrepancies to the evolution of fundamental constants and the tired light effect, the model suggests that:

• Early galaxies are not "impossible" but are simply larger, older, and less dense than currently interpreted under $\Lambda$CDM.
• The "Little Red Dots" are not necessarily over-massive black holes or ultra-dense stellar clusters but are standard galaxies with parameters that align with local universe analogs when corrected for the CTL framework.
• The model is consistent with a wide range of independent datasets, including Pantheon+ supernovae, Baryon Acoustic Oscillations (BAO), CMB sound horizon, galaxy rotation curves, and time dilation observations, without invoking the coincidence problem associated with dark energy.

The author concludes that applying the CTL framework prudently can resolve most surprises regarding the early universe, suggesting that the current "crisis" in cosmology may stem from the limitations of the $\Lambda$CDM model's assumptions regarding constant physical laws and the sole origin of redshift.