# Cosmological Model Tests with JWST

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## Abstract

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## 1. Introduction

- There is an excessively large number of galaxies at very high redshifts, which is not foreseen by the Standard Cosmological Model;
- Galaxies at these redshifts have disks and bulges, which indicates that they have passed through a long period of evolution;
- Spectroscopically, these galaxies resemble their counterparts in the local Universe;
- Smaller galaxies are more massive than larger ones, which is quite the opposite of the common view.

## 2. Materials and Methods

#### 2.1. Observational Data for the Early-Universe Objects

#### 2.2. Cosmographic Tests

- Expanding universes based on the Friedmann–Lemaitre–Robertson–Walker (FLRW) metric with a time-dependent scale factor;

#### 2.2.1. Angular Diameter—Redshift Relationship in the ΛCDM Model

- the comoving distance

- and the luminosity distance

- the latter being defined as the relationship between the bolometric flux F and the bolometric luminosity L:

#### 2.2.2. Static-Universe Models

- Compton scattering on free electrons;
- Gravitational redshift due to gravitational potential wells of galaxies or galaxy clusters along the photon’s path;
- General-relativistic transfer of photon energy/mass to the masses distributed along the photon’s path.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CMB | Cosmic Microwave Background (radiation) |

FLRW | Friedmann–Lemaitre–Robertson–Walker (metric) |

JWST | James Webb Space Telescope |

HST | Hubble Space Telescope |

$\mathsf{\Lambda}$CDM | Lambda Cold-Dark Matter (cosmological model) |

TL | Tired-light (photon-energy loss) |

## Notes

1 | The same work also provides a detailed overview of theoretical constrains on structure formation time due to BAO within the $\mathsf{\Lambda}$CDM framework. |

2 | https://archive.stsci.edu, accessed on 1 October 2022. |

3 | https://astroquery.readthedocs.io/en/latest/mast/mast.html, accessed on 1 October 2022. |

4 | nevertheless, we shall see that it fails to fit the recent JWST observations. |

5 | although abandoned by him in favour of his other expanding-Universe model [48]. |

6 | https://www.jwst.nasa.gov/content/about/faqs/faq.html#sharp, accessed on 1 October 2022. |

7 | Pluralitas non est ponenda sine necessitate (William of Occam). |

8 | actually, it is not completely ignored by astrophysicists, and the majority of them are thinking about (contriving of) new possibilities in order to theoretically accelerate the process of galaxy formation immediately after the Big Bang, by introducing, for example, non-trivial non-Gaussianities into the initial conditions of the cosmological perturbations [110], contrary to Occam’s principle. While some others embrace the idea that the Universe might be much older than what follows from the $\mathsf{\Lambda}$CDM theory and publish their arguments [111] or report this idea to the general public via documentaries produced by influential media like the BBC https://www.youtube.com/watch?v=vAxgaTvYA7Y (accessed on 1 October 2022). |

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**Figure 1.**Angular-diameter distance ${D}_{A}$ (purple curve) as calculated within the $\mathsf{\Lambda}$CDM model for ${H}_{0}=70$ km s${}^{-1}$ Mpc${}^{-1}$. The luminosity distance ${D}_{L}$ (dashed line) and comoving distance ${D}_{C}$ (dotted curve) are also shown for comparison.

**Figure 2.**Angular diameter of a 10 kpc-size object (

**left**) and the linear diameter $\delta $ of a one-arcsec-size object (

**right**) as functions of redshift z, corresponding to various models within the expanding-universe framework (FLRW). The purple curves show the $\theta \left(z\right)$ relation for the standard $\mathsf{\Lambda}$CDM model with ${\mathsf{\Omega}}_{\mathrm{M}}=0.3$ and ${H}_{0}=70.0$ km s${}^{-1}$ Mpc${}^{-1}$. The green curves correspond to the Einstein-de Sitter Universe (${\mathsf{\Omega}}_{\mathrm{M}},{\mathsf{\Omega}}_{\mathsf{\Lambda}})=(1,0)$. The blue and yellow curves show $\theta \left(z\right)$ for two values of ${\mathsf{\Omega}}_{\mathrm{M}}$ for FLRW models without dark energy.

**Figure 3.**Angular size of a 10 kpc-size object as a function of redshift z within the framework of the static-Universe model (the red curve) as compared to the same relationship within the framework of the $\mathsf{\Lambda}$CDM model (purple curve) for ${H}_{0}=70$ km s${}^{-1}$ Mpc${}^{-1}$.

**Figure 4.**JWST galaxy physical sizes (effective radii ${r}_{e}$, in kpc) as estimated within the framework of the standard $\mathsf{\Lambda}$CDM cosmological model [5,28,29,81,82,83,84,85,86,87] (purple points) and sizes of the same galaxies as they would appear in a static Universe (green points), for which we have used the formalism of Zwicky’s dissipative (tired-light) model.

**Figure 5.**Angular diameters of a 10-kpc-size object as expected to be seen at different redshifts within the frameworks of $\mathsf{\Lambda}$CDM (dashed curve) and of the non-expanding Universe model, TL (dotted curve). These expectations are compared with the actual angular sizes found in the recent JWST observations (red points) and some pre-JWST observations (black points). The solid curve indicates the simplest linear function for angular diameters based on the Hubble constant ${H}_{0}$.

**Figure 6.**

**Left**: Masses of high-redshift galaxies as determined within the framework of $\mathsf{\Lambda}$CDM using the recent JWST observations (red points) and some pre-JWST observations (black points); the dashed curve indicates the factor ${(1+z)}^{-2}$ of the distance-luminosity relationship in the standard cosmology;

**Right**: the same masses corrected for the factor ${(1+z)}^{-2}$ in order to transform them to the static-Universe framework.

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Lovyagin, N.; Raikov, A.; Yershov, V.; Lovyagin, Y. Cosmological Model Tests with JWST. *Galaxies* **2022**, *10*, 108.
https://doi.org/10.3390/galaxies10060108

**AMA Style**

Lovyagin N, Raikov A, Yershov V, Lovyagin Y. Cosmological Model Tests with JWST. *Galaxies*. 2022; 10(6):108.
https://doi.org/10.3390/galaxies10060108

**Chicago/Turabian Style**

Lovyagin, Nikita, Alexander Raikov, Vladimir Yershov, and Yuri Lovyagin. 2022. "Cosmological Model Tests with JWST" *Galaxies* 10, no. 6: 108.
https://doi.org/10.3390/galaxies10060108