Curves of Records in Thermal Fluctuation Analysis of the CMB and Anisotropy in Comparison with Gravitational Areas Associated with the Current Expansion Rate of the Universe - Implications for the ΛCDM Model
Creators: name: Aliaga Machado, Maicon Santiago
Publisher: name: Zenodo
Year: 2024
Subjects: CMB
Thermal fluctuations
Cosmic expansion
ΛCDM model
Gravitational lensing
Anisotropy
Hubble parameter
Dark energy
Gravitational perturbations
Einstein-Boltzmann equations
Scalar spectral index

description: The investigation of thermal fluctuations and anisotropies in the Cosmic Microwave Background (CMB) provides critical data on the early universe, with implications for the modern understanding of cosmic structure and expansion. This study analyzes the curves of records of CMB temperature and polarization anisotropies, focusing on the discrepancies arising from gravitational wells and their relationship with the rate of expansion of the current universe. The analysis integrates general relativity (GR), cosmological perturbation theory, and recent observational data from the Planck satellite to assess the impact of gravitational anomalies on the ΛCDM model.

Building on the theoretical framework of Peebles (1980) and Weinberg (2008), the study examines the scalar perturbations in the Einstein-Boltzmann equations (ä(𝑡) = − 4𝜋𝐺3(𝜌 +3𝑝)𝑎(𝑡)) and their role in modulating temperature fluctuations and anisotropic distribution. The Sachs-Wolfe effect (1967) is utilized to interpret how gravitational potentials influence the CMB at large scales, linking fluctuations in matter density to anisotropies in the radiation field.

A modified version of the ΛCDM model is employed, incorporating corrections to the Hubble parameter (𝐻0) and cosmological constant (Λ) arising from gravitational perturbations. The theoretical predictions are compared to observational data from the Planck Collaboration (2020) and Riess et al. (2019), which highlight the growing tension in the measurement of 𝐻0. The results indicate that gravitational lensing and dark energy fluctuations contribute significantly to the uncertainty in the current cosmological expansion rate, offering an explanation for the discrepancy between early-universe and local measurements of 𝐻0. Additionally, the analysis incorporates the matter-radiation transition and deceleration-acceleration phase as defined by Friedmann (1922) and Lemaître (1931), providing a nuanced interpretation of how gravitational potential fluctuations impact the scalar spectral index (𝑛𝑠) and CMB anisotropies. The study builds upon the fluid mechanics of cosmic evolution outlined by Bardeen et al. (1983), integrating these perturbative models with recent observations by Kessler et al. (2020) and MacCulloch (2017).

This work contributes to the refinement of the ΛCDM model, specifically addressing discrepancies observed in gravitationally bound systems and providing an advanced understanding of how thermal fluctuations and anisotropic patterns influence the precision of cosmological parameters. Future investigations are proposed to incorporate quantum corrections and higher-order terms in the perturbative equations, extending the contributions of Hawking (1971) and Guth (1981).

Keywords: CMB; Thermal fluctuations; Cosmic expansion; ΛCDM model; Gravitational lensing; Anisotropy; Hubble parameter; Dark energy; Gravitational perturbations; Einstein-Boltzmann equations; Scalar spectral index._____________________________

References

Peebles, P. J. E. (1980). The Large-Scale Structure of the Universe. Princeton University Press.

Weinberg, S. (2008). Cosmology. Oxford University Press.

Sachs, R. K., & Wolfe, A. M. (1967). Perturbations of the Microwave Background Radiation. The Astrophysical Journal, 147, 73–90.

Planck Collaboration (2020). Planck 2018 results. X. Constraints on inflation. Astronomy & Astrophysics, 641, A10.

Riess, A. G., et al. (2019). New Measurements of the Hubble Constant from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal, 876(1), 85.

Friedmann, A. (1922). Über die Krümmung des Raumes. Zeitschrift für Physik, 10(1), 377–386.

Lemaître, G. (1931). The Beginning of the World from the Point of View of Quantum Theory. Nature, 127, 706–707.

Bardeen, J. M., Bond, J. R., & Kaiser, N. (1983). The Statistics of Peaks of Gaussian Random Fields. The Astrophysical Journal, 264, 34–48.

Kessler, R. et al. (2020). Measurement of the Hubble constant from the angular diameter distance to the gravitational lens B1608+656. Nature Astronomy, 4(6), 659–664.

MacCulloch, D. (2017). Gravitational Lensing and the Expansion of the Universe. Monthly Notices of the Royal Astronomical Society, 465(1), 542–551.

Hawking, S. W. (1971). Gravitational radiation in an expanding universe. Physical Review Letters, 26(7), 437–439.

Guth, A. H. (1981). The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems. Physical Review D, 23(2), 347–356.