# Fitting Type Ia Supernova Data to a Cosmological Model Based on Einstein–Newcomb–De Sitter Space

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Physical Interpretation of Identified Antipodal Points

#### 2.2. Red Shift–Distance Relationship

#### 2.3. Comparison with Observations

## 3. Results

## 4. Discussion

#### 4.1. Validation Using a Gamma-Ray Burst Sample

#### 4.2. Experimental Challenges of Static and Dynamic Cosmological Models

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CMB | Cosmic microwave background (radiation) |

ENdS | Enstein–Newcomb–de Sitter (space) |

EPR | Einstein–Podolsky–Rosen (paradox) |

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

GRB | Gamma-ray burst |

JWST | James Webb Space Telescope |

$\mathrm{\Lambda}$CDM | Lambda cold–dark matter (cosmological model) |

SN | supernova. |

## Notes

1 | In fact, this is the only viable way of understanding what matter is and what particles of matter are made of: “there is nothing in the world except empty curved space” [31]. It is also a way of answering the question as to the origin of particle species and the pattern of three generations of fundamental fermions. These are incorporated into the Standard Model of particle physics as something given to us by nature, setting aside the question, “why do we have this particular set of fundamental particles and not something else?”. This is a related but different question, discussed by the author elsewhere. |

2 | There might be small differences in algorithms and software used by different research groups, so our results might also be slightly different from other previously published results. We conduct our calculations here using the R package cosmoFns [35] and the formulae presented above. |

## References

- Einstein, A. Kosmologische betrachtungen zur allgemeinen Relativitätstheorie. Sitz. Preuss. Akad. Wiss Phys.
**1917**, VL, 142–152. [Google Scholar] - de Sitter, W. On Einstein’s theory of gravitation, and its astronomical consequences. Third paper. Mon. Not. R. Astron. Soc.
**1917**, 78, 3–28. [Google Scholar] [CrossRef] [Green Version] - Newcomb, S. Elementary theorems relating to the geometry of a space of three dimensions and of uniform positive curvature in the fourth dimension. J. Für Die Reine Und Angew. Math.
**1877**, LXXXIII, 293–299. [Google Scholar] - Hubble, E. A relation between distance and radial velocity among extragalactic nebulae. Proc. Natl. Acad. Sci. USA
**1929**, 15, 168–173. [Google Scholar] [CrossRef] [Green Version] - Friedmann, A. Über die Krümmung des Raumes. Z. Phys. A
**1922**, 10, 377–386. [Google Scholar] [CrossRef] - Lemaître, G. Un univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques. Ann. Soc. Sci. Brux. A
**1927**, 47, 49–59. [Google Scholar] - Robertson, H.P. Kinematics and world structure. Astrophys. J.
**1935**, 82, 284–301. [Google Scholar] [CrossRef] - Walker, A.G. On Milne’s theory of world-structure. Proc. Lond. Math. Soc. Ser. 2
**1937**, 42, 90–127. [Google Scholar] [CrossRef] - Riess, A.G.; Filippenko, A.V.; Challis, P.; Clocchiatti, A.; Diercks, A.; Garnavich, P.M.; Gillil, R.L.; Hogan, C.J.; Jha, S.; Kirshner, R.P.; et al. Observational evidence from supernovae for an accelerating Universe and cosmological constant. Astron. J.
**1998**, 116, 1009–1038. [Google Scholar] [CrossRef] [Green Version] - Schmidt, B.P.; Suntzeff, N.B.; Phillips, M.M.; Schommer, R.A.; Clocchiatti, A.; Kirshner, R.P.; Garnavich, P.; Challis, P.; Leibundgut, B.R.; Spyromilio, J.; et al. The high-z supernovae search: Measuring cosmic deceleration and global. Astrophys. J.
**1998**, 507, 46–63. [Google Scholar] [CrossRef] - Perlmutter, S.; Aldering, G.; Goldhaber, G.; Knop, R.A.; Nugent, P.; Castro, P.G.; Deustua, S.; Fabbro, S.; Goobar, A.; Groom, D.E.; et al. Measurement of Ω and Λ from 42 high-redshift supernovae. Astrophys. J.
**1999**, 517, 565–586. [Google Scholar] [CrossRef] - Dolgov, A.D. Massive and supermassive black holes in the contemporary and early Universe and problems in cosmology and astrophysics. Phys. Uspekhi
**2018**, 61, 115–132. [Google Scholar] [CrossRef] [Green Version] - Lerner, E.J. Observations contradict galaxy size and surface brightness predictions that are based on the expanding universe hypothesis. Mon. Not. R. Astron. Soc.
**2018**, 477, 3185–3196. [Google Scholar] [CrossRef] [Green Version] - Lovyagin, N.; Raikov, A.; Yershov, V.; Lovyagin, Y. Cosmological model tests with JWST. Galaxies
**2022**, 10, 108. [Google Scholar] [CrossRef] - Zwicky, F. On the redshifts of spectral lines through interstellar space. Proc. Natl. Acad. Sci. USA
**1929**, 15, 773–779. [Google Scholar] [CrossRef] [Green Version] - Tolman, R.C. On the estimation of distances in a curved universe with a non-static line element. Proc. Nat. Acad. Sci. USA
**1930**, 16, 511–520. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hubble, E.; Tolman, R.C. Two methods of investigating the nature of the nebular redshift. Astrophys. J.
**1935**, 82, 302–337. [Google Scholar] [CrossRef] - Burbidge, G.R. Was there really a Big Bang? Nature
**1971**, 233, 36–40. [Google Scholar] [CrossRef] [PubMed] - Burbidge, G.R.; Hoyle, F. The origin of helium and the other light elements. Astrophys. J.
**1998**, 509, L1–L3. [Google Scholar] [CrossRef] - Baryshev, Y. The hierarchical structure of metagalaxy a review of problems. Rep. Space Astrophys. Obs. Russ. Acad. Sci.
**1981**, 14, 24–43. [Google Scholar] - Troitskij, V.S. A static model of the universe. Astrophys. Space Sci.
**1995**, 229, 89–104. [Google Scholar] [CrossRef] - Baryshev, Y.; Teerikorpi, P. Fundamental Questions of Practical Cosmology; Springer: Dordrecht, The Netherlands, 2012; p. 332. [Google Scholar]
- Cirkovic, M.M.; Perovic, S. Alternative explanations of the Cosmic Microwave Background: A historical and an epistemological perspective. Stud. Hist. Philos. Mod. Phys.
**2018**, 62, 1–18. [Google Scholar] [CrossRef] [Green Version] - Amati, L.; D’Agostino, R.; Luongo, O.; Muccino, M.; Tantalo, M. Addressing the circularity problem in the E
_{p}-E_{ISO}correlation of gamma-ray bursts. Mon. Not. R. Astron. Soc. Lett.**2019**, 486, L46–L51. [Google Scholar] [CrossRef] [Green Version] - Einstein, A.; Rosen, N. The Particle Problem in the General Theory of Relativity. Phys. Rev.
**1935**, 48, 73–77. [Google Scholar] [CrossRef] - Morris, M.S.; Thorne, K.S. Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity. Am. J. Phys.
**1988**, 56, 395–412. [Google Scholar] [CrossRef] [Green Version] - Morris, M.S.; Thorne, K.S.; Yurtsever, U. Wormholes, time machines, and the weak energy condition. Phys. Rev. Lett.
**1988**, 61, 1446–1449. [Google Scholar] [CrossRef] [Green Version] - Einstein, A.; Podolsky, B.; Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev.
**1935**, 47, 777–780. [Google Scholar] [CrossRef] [Green Version] - Tamburini, F.; Licata, I. General relativistic wormhole connections from Planck-scales and the ER = EPR conjecture. Entropy
**2020**, 22, 3. [Google Scholar] [CrossRef] [Green Version] - Einstein, A. The Born-Einstein Letters: Correspondence between Albert Einstein and Max and Hedwig Born from 1916–1955, with Commentaries by Max Born; Walker & Company Publ.: New York, NY, USA, 1971; p. 158. [Google Scholar]
- Misner, C.; Wheeler, J.A. Classical physics as geometry. Ann. Phys.
**1957**, 2, 525–603. [Google Scholar] [CrossRef] - Scolnic, D.; Brout, D.; Carr, A.; Riess, A.G.; Davis, T.M.; Dwomoh, A.; Jones, D.O.; Ali, N.; Charvu, P.; Chen, R.; et al. The Pantheon+ Analysis: The Full Dataset and Light-Curve Release. Astrophys. J.
**2022**, 938, 113. [Google Scholar] [CrossRef] - Brout, D.; Scolnic, D.; Popovic, B.; Riess, A.G.; Carr, A.; Zuntz, J.; Kessler, R.; Davis, T.M.; Hinton, S.; Jones, D.; et al. The Pantheon+ Analysis: Cosmological Constraints. Astrophys. J.
**2022**, 938, 110. [Google Scholar] [CrossRef] - Riess, A.G.; Yuan, W.; Macri, L.M.; Scolnic, D.; Brout, D.; Casertano, S.; Jones, D.O.; Murakami, Y.; An, G.S.; Breuval, L.; et al. A comprehensive measurement of the local value of the Hubble constant with 1 km/s/Mpc uncertainty from the Hubble Space Telescope and the SH0ES team. Astrophys. J.
**2022**, 934, L7. [Google Scholar] [CrossRef] - Harris, A. cosmoFns Functions for cosmological distances, times, luminosities, etc. R J.
**2012**, 4, 90. [Google Scholar] - Cash, W. Parameter estimation in astronomy through application of likelihood ratio. Astrophys. J.
**1979**, 228, 939–947. [Google Scholar] [CrossRef] - López-Corredoira, M.; Calvo-Torel, J.L. Fitting of supernovae without dark energy. Int. J. Mod. Phys. D
**2022**, 31, 2250104. [Google Scholar] [CrossRef] - Scolnic, D.M.; Jones, D.O.; Rest, A.; Pan, Y.C.; Chornock, R.; Foley, R.J.; Huber, M.E.; Kessler, R.; Narayan, G.; Riess, A.G.; et al. The complete light-curve sample of spectroscopically confirmed SNe Ia from Pan-STARRS1 and cosmological constraints from the combined Pantheon sample. Astrophys. J.
**2018**, 859, 101. [Google Scholar] [CrossRef] - Civano, F.; Eggleston, L.; Elvis, M.; Fabbiano, G.; Gilli, R.; Marconi, A.; Paolillo, M.; Piedipalumbo, E.; Salvestrini, F.; Signorini, M.; et al. Quasars as standard candles. A&A
**2020**, 642, A150. [Google Scholar] - Raikov, A.; Lovyagin, N.; Yershov, V. Superluminous quasars and mesolensing. In Aastronomy at the Epoch of Multimessenger Studies. VAK-2021 Proceedings; Cherepashchuk, A.M., Emelyanov, N.V., Fedorova, A.A., Gayazov, I.S., Ipatov, A.V., Ivanchik, A.V., Malkov, O.Y., Obridko, V.N., Rastorguev, A.S., Samus, N.N., et al., Eds.; Janus-K Publ.: Moscow, Russia, 2022; pp. 392–394. [Google Scholar]
- López-Corredoira, M. Pending Problems in QSOs. Int. J. Astron. Astropys.
**2011**, 1, 73–82. [Google Scholar] [CrossRef] [Green Version] - Khadka, N.; Ratra, B. Do quasar X-ray and UV flux measurements provide a useful test of cosmological models? Mon. Not. Roy. Astron. Soc.
**2022**, 510, 2753–2772. [Google Scholar] [CrossRef] - Eddington, A.S. Internal Constitution of the Stars; Cambridge University Press: Cambridge, UK, 1926; p. 407. [Google Scholar]
- Nernst, W. Weitere prüfung der annahme lines stationären zustandes im weltall. Z. Phys.
**1937**, 106, 633–661. [Google Scholar] [CrossRef] - Gamow, G. The expanding universe and the origin of galaxies. Kgl. Dan. Vidensk. Selsk. Mat. Fys. Medd.
**1953**, 27, 3–15. [Google Scholar] - Baryshev, Y.V.; Raikov, A.A.; Tron, A.A. Microwave background radiation and cosmological large numbers. Astron. Astroph. Trans.
**1996**, 10, 135–138. [Google Scholar] [CrossRef] - Muller, S.; Beelen, A.; Black, J.H.; Curran, S.J.; Horellou, C.; Aalto, S.; Combes, F.; Guélin, M.; Henkel, C. A precise and accurate determination of the cosmic microwave background temperature at z=0.89. Astron. Astrophys.
**2013**, 551, A109. [Google Scholar] [CrossRef] [Green Version] - Luzzi, G.; Shimon, M.; Lamagna, L.; Rephaeli, Y.; De Petris, M.; Conte, A.; De Gregori, S.; Battistelli, E.S. Redshift dependence of the cosmic microwave background temperature from Sunyaev-Zeldovich measurements. Astron. J.
**2009**, 705, 1122–1128. [Google Scholar] [CrossRef] [Green Version] - Salvaterra, R.; Ferrara, A. Is primordial
^{4}He truly from the Big Bang? Mon. Not. R. Astron. Soc.**2003**, 340, L17–L20. [Google Scholar] [CrossRef] [Green Version] - Pagel, B.E.J. Abundances of elements of cosmological interest. Philos. Trans. R. Soc. Lond. A
**1982**, 307, 19–35. [Google Scholar] - Spite, F.; Spite, M. Abundances of Lithium in unevolved halo stars and old disk stars: Interpretations and consequences. Astron. Astrophys.
**1982**, 115, 357–366. [Google Scholar] - Reeves, H.; Fpwler, W.A.; Hoyle, F. Galactic cosmic ray origin of Li, Be and B in stars. Nature
**1970**, 226, 727–729. [Google Scholar] [CrossRef] - Austin, S.M. The creation of the light elements—Cosmic rays and cosmology. Prog. Part. Nucl. Phys.
**1981**, 7, 1–46. [Google Scholar] [CrossRef] - Silverberg, R.; Tsao, C.H. Spallation processes and nuclear interaction products of cosmic rays. Phys. Rep.
**1990**, 191, 351–408. [Google Scholar] [CrossRef] - Olive, K.A.; Schramm, D.N. Astrophysical
^{7}Li as a product of Big Bang nucleosynthesis and galactic cosmic-ray spallation. Nature**1992**, 360, 439–442. [Google Scholar] [CrossRef] - Yamanaka, M.; Jittoh, T.; Kazunori Kohri, K.; Koike, M.; Sato, J.; Sugai, K.; Yazaki, K. Big-bang nucleosynthesis with a long-lived CHAMP including He4 spallation process. J. Phys. Conf. Ser.
**2014**, 485, 012020. [Google Scholar] [CrossRef] [Green Version] - Meyer, B.S.; Woosley, S.E.; Hoffman, R.D.; Mathews, G.J.; Wilson, J.R. Neutrino spallation reactions on
^{4}He and the r-process. AIP Conf. Proc.**1995**, 327, 441–445. [Google Scholar] - Oliver, B.M.; James, M.R.; Garner, F.A.; Maloy, S.A. Helium and hydrogen generation in pure metals irradiated with high-energy protons and spallation neutrons in LANSCE. J. Nucl. Mat.
**2002**, 307–311, 1471–1477. [Google Scholar] [CrossRef] - Abbott, B.P. et al. (LIGO, Virgo and other collaborations). Multi-messenger Observations of a Binary Neutron Star Merger. Astrophys. J.
**2017**, 848, L12. [Google Scholar] [CrossRef] - Gompertz, B.P.; Ravasio, M.E.; Nicholl, M.; Levan, A.J.; Metzger, B.D.; Oates, S.R.; Lamb, G.P.; Fong, W.F.; Malesani, D.B.; Rastinejad, J.C.; et al. The case for a minute-long merger-driven gamma-ray burst from fast-cooling synchrotron emission. Nat. Astron.
**2022**, 7, 67–79. [Google Scholar] [CrossRef] - Eddington, A.S. On the instability of Einstein’s spherical world. Mon. Not. R. Astron. Soc.
**1930**, 90, 668–678. [Google Scholar] [CrossRef] [Green Version] - Rosen, N. Static universe and cosmic field. Ann. Math. Pure Appl.
**1970**, 14, 305–308. [Google Scholar] [CrossRef] - Sargent, W.L.W.; Searle, L. The interpretation of the helium weakness in halo stars. Astrophys. J.
**1967**, 150, L33–L37. [Google Scholar] [CrossRef] - Terlevich, E.; Terlevich, R.; Skillman, E.; Stepanian, J.; Lipovetskii, V. The extremely low He abundance of SBS:0335-052. In Elements and the Cosmos; Edmunds, M.G., Terlevich, R., Eds.; Cambridge University Press: Cambridge, UK, 2010; pp. 21–27. [Google Scholar]
- Izotov, Y.I.; Thuan, T.X. The primordial abundance of
^{4}He: Evidence for non-standard Big Bang nucleosynthesis. Astrophys. J.**2010**, 710, L67–L71. [Google Scholar] [CrossRef] [Green Version] - Di Valentino, E.; Melchiorri, A.; Silk, J. Planck evidence for a closed Universe and a possible crisis for cosmology. Nat. Astron.
**2020**, 4, 196–203. [Google Scholar] [CrossRef] [Green Version] - Durk, J.; Clifton, T. A quasi-static approach to structure formation in black hole universes. J. Cosmol. Astropart. Phys.
**2017**, 10, 12. [Google Scholar] [CrossRef] [Green Version] - Yershov, V.N.; Orlov, V.V.; Raikov, A.A. Correlation of supernova redshifts with temperature fluctuations of the cosmic microwave background. Mon. Not. R. Astron. Soc.
**2012**, 423, 2147–2152. [Google Scholar] [CrossRef] [Green Version] - Yershov, V.N.; Orlov, V.V.; Raikov, A.A. Possible signature of distant foreground in the Planck data. Mon. Not. R. Astron. Soc.
**2014**, 445, 2440–2445. [Google Scholar] [CrossRef] [Green Version] - Yershov, V.N.; Raikov, A.A.; Lovyagin, N.Y.; Kuin, N.P.M.; Popova, E.A. Distant foreground and the Planck-derived Hubble constant. Mon. Not. R. Astron. Soc.
**2020**, 492, 5052–5056. [Google Scholar] [CrossRef] - Mylläri, A.A.; Raikov, A.A.; Orlov, V.V.; Tarakanov, P.A.; Yershov, V.N.; Yezhkov, M.Y. Fractality of isotherms of the Cosmic Microwave Background based on data from the Planck spacecraft. Astrophysics
**2016**, 59, 31–37. [Google Scholar] [CrossRef] - Coleman, P.H.; Pietronero, L. The fractal structure of the universe. Phys. Rep.
**1992**, 213, 311–389. [Google Scholar] [CrossRef] - Gaite, J. The fractal geometry of the cosmic web and its formation. Adv. Astron.
**2019**, 2019, 6587138. [Google Scholar] [CrossRef] - Teles, S.; Lopes, A.R.; Ribeiro, M.B. Galaxy distributions as fractal systems. Eur. Phys. J. C
**2021**, 82, 896. [Google Scholar] [CrossRef] - Granett, B.R.; Neyrinck, M.C.; Szapudi, I. An imprint of superstructures on the microwave background due to the integrated Sachs-Wolfe effect. Astrophys. J.
**2008**, 683, L99–L102. [Google Scholar] [CrossRef] [Green Version] - Cai, Y.-C.; Neyrinck, M.C.; Szapudi, I.; Cole, S.; Frenk, C.S. A possible cold imprint of voids on the microwave background radiation. Astrophys. J.
**2014**, 786, 110. [Google Scholar] [CrossRef] [Green Version] - Kovács, A.; García-Bellido, J. Cosmic troublemakers: The Cold Spot, the Eridanus supervoid, and the Great Walls. Mon. Not. R. Astron. Soc.
**2016**, 462, 1882–1893. [Google Scholar] [CrossRef] [Green Version] - Kovács, A.; Jeffrey, N.; Gatti, M.; Chang, C.; Whiteway, L.; Hamaus, N.; Lahav, O.; Pollina, G.; Bacon, D.; Kacprzak, T.; et al. The DES view of the Eridanus supervoid and the CMB cold spot. Mon. Not. R. Astron. Soc.
**2021**, 510, 216–229. [Google Scholar] [CrossRef] - Labbé, I.; van Dokkum, P.; Nelson, E.; Bezanson, R.; Suess, K.A.; Leja, J.; Brammer, G.; Whitaker, K.; Mathews, E.; Stefanon, M.; et al. A population of red candidate massive galaxies ∼600 Myr after the Big Bang. Nature
**2023**, 616, 266–269. [Google Scholar] [CrossRef] - Yan, H.; Ma, Z.; Ling, C.; Cheng, C.; Huang, J.-S. First batch of z≈11–20 candidate objects revealed by the James Webb Space Telescope early release observations on SMACS 0723-73. Astrophys. J. Lett.
**2023**, 942, L9. [Google Scholar] [CrossRef]

**Figure 1.**Embedding diagram of Einstein–Newcomb–de Sitter elliptical space with two antipodal points topologically identified (the dashed line). The radius of curvature (R) is neglected in this plot for simplicity. The distance between two antipodal points is measured along the spatial coordinate (thin solid and dot-dashed line) by the projective angle ($\chi $), which is equal to $\pi $ for the maximal possible separation in the elliptical space.

**Figure 2.**Embedding diagram depicting a possible physical realisation of the topological connection between two distant (antipodal) regions of space via a wormhole structure. Here, ${r}_{o}$ and ${r}_{s}$ are distances of the observer (o) and source (s) from the wormhole’s far throat, opposite to the near throat in the vicinity of the observer; and ${r}_{g}$ is the gravitational radius of the wormhole.

**Figure 3.**Distance moduli ($\mu $) from the type Ia SNe Pantheon+ sample (red points) as a function of red shift (z), with the minimal ${\chi}^{2}$-fitted theoretical curves for the flat $\mathrm{\Lambda}$CDM model (thin solid curve) and the ENdS model (dashed curve).

**Figure 4.**Distance moduli $\mu $ from the Pantheon+ type Ia SNe sample (red points), together with the distance moduli from the GRB sample (blue points) calibrated using the Amati relation. The thin, solid and thick, dashed curves indicate the minimum ${\chi}^{2}$-fitted theoretical curves for the flat $\mathrm{\Lambda}$CDM and ENdS models, respectively.

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**MDPI and ACS Style**

Yershov, V.N.
Fitting Type Ia Supernova Data to a Cosmological Model Based on Einstein–Newcomb–De Sitter Space. *Universe* **2023**, *9*, 204.
https://doi.org/10.3390/universe9050204

**AMA Style**

Yershov VN.
Fitting Type Ia Supernova Data to a Cosmological Model Based on Einstein–Newcomb–De Sitter Space. *Universe*. 2023; 9(5):204.
https://doi.org/10.3390/universe9050204

**Chicago/Turabian Style**

Yershov, Vladimir N.
2023. "Fitting Type Ia Supernova Data to a Cosmological Model Based on Einstein–Newcomb–De Sitter Space" *Universe* 9, no. 5: 204.
https://doi.org/10.3390/universe9050204