BEHAVIOR OF q-DEFORMED QUANTUM PARTICLE STATISTICS ON THE HOLOGRAPHIC SCREEN

Year 2023, Volume: 9 Issue: 1, 87 - 91, 30.06.2023

Mustafa Şenay

https://doi.org/10.22531/muglajsci.1295528

Abstract

In this study, we propose an approach to investigate the relationship between MOND theory and the holographic principle by incorporating q-deformed theory. We first present a brief overview of Verlinde's entropic gravity assumption, which suggests that gravity can be interpreted as an entropic force arising from the statistical mechanics of quantum fields. Some thermo-statistical properties of q-deformed fermion gas model in two spatial dimensions are introduced. At the low-temperature limit, we derive the q-deformed thermal energy and analyze the impacts of fermionic q-deformation on MOND theory. Specifically, we consider the q-deformed Fermi-Dirac statistics of the bits on the holographic screen and examine MOND theory depending on q-deformed acceleration scale. Deformed Friedmann equation is studied by taking into account Friedmann–Robertson–Walker (FRW) universe. This equation shows a modified identification of the evolution of the universe that is compatible with both MOND theory and the holographic principle

Keywords

Entropic Gravity, MOND Theory, q-Deformed Fermion

References

• Blumenthal, G.R., Faber, S.M., Primack, J.R. and Rees, M.J., "Formation of Galaxies and Large-scale Structure with Cold Dark Matter", Nature, 311, 517-525, 1984.
• Ellis, R.E., "Gravitational Lensing a Unique Probe of Dark Matter and Dark Energy", Philosophical Transaction of the Royal Society A, 368, 967-987, 2010.
• Trimble, V.,"Existence and Nature of Dark Matter in The Universe", Annual Review of Astronomy and Astrophysics, 25, 425-472, 1987.
• Li, X., Tang, L., Lin, H. N., "Comparing Dark Matter Models, Modified Newtonian Dynamics and Modified Gravity in Accounting for Galaxy Rotation Curves", Chinese. Physics C, 41, 055101, 2017.
• Nojiri, S. and Odintsov, S.S.,"Introduction to Modified Gravity and Gravitational Alternative for Dark Energy", International Journal of Geometric Methods in Modern Physics, 04, 115-145, 2007.
• Carroll, S.M. Duvvuri, V., Trodden, M. and Turner, M.S., "Is Cosmic Speed-up Due to New Gravitational Physics?", Physical Review D, 70, 043528, 2004.
• Maartens, R., "Brane-World Gravity", Living reviews in Relativity, Article Number 7, 2004.
• Milgrom, M., "A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis", Astrophysical Journal, 270, 365-370, 1983.
• Milgrom, M., "A Modification of the Newtonian Dynamics Implications for Galaxies", Astrophysical Journal, 270, 371-383, 1983.
• Milgrom, M., "Solutions for the Modified Newtonian Dynamics Field Equations", Astrophysical Journal, 302, 617, 1986.
• Verlinde, E., "On the Origin of Gravity and Laws of Newton", Journal of High Energy Physics, 2011, Article Number 29, 2011.
• Moradpour, H., Sheykhi, A., Corda, C. and Salako, I.G., "Implications of the Generalized Entropy Formalisms on the Newtonian Gravity and Dynamics", Physics Letters B, 783, 82-85, 2018.
• Wang, S., Wang, Y. and Li, M., "Barrow Holographic Dark Energy", Physical Review D, 696, 1-57, 2017.
• Saridakis, E.N., "Barrow Holographic Dark Energy", Physics Reports, 102, 123525, 2020.
• Zhang, Y. Gong, Y. and Zhu, Z.H., "Modified Gravity Emerging from Thermodynamics and Holographic Principle", International Journal of Modern Physics D, 20, 1505-1519, 2011.
• Senay, M. and Kibaroğlu S., "q-Deformed Einstein Equations from Entropic Force", International Journal of Modern Physics A, 33, 1850218, 2018.
• Dil, E., "Can Quantum Black Holes be (q,p)-fermions?", International Journal of Modern Physics A, 32, 1750080, 2017.
• Liu, B., Dai, Y.C., Hu, X.R. and Deng, J.B "The Friedmann Equations in Modified Entropy-Area Relation From Entropy Force ", Modern Physics Letters A, 26, 489-500, 2011.
• Kibaroğlu, S., and Senay, M. "Friedmann Equations for Deformed Entropic Gravity", International Journal of Modern Physics D, 29, 2050042, 2020.
• Unruh, W.G., "Notes on Black-hole Evaporation", Physical Review D, 14, 870, 1976.
• Parthasarathy, R., and Viswanathan, K.S., "A q-Analogue of the Supersymmetric Oscillator and Its q-Superalgebra ", Journal of Physics A:Mathematical and General, 24, 613, 1991.
• Viswanathan, K.S., Parthasarathy, R., and Jagannathan R., "Generalized q-Fermion Oscillators and q-Coherent States", Journal of Physics A:Mathematical and General, 25, L335, 1992.
• Chaichian, M., Felipe, R.G. and Montonen, C., "Statistics of q-Oscillators, Quons and Relations to fractional statistics", Journal of Physics A:Mathematical and General, 26, 4017, 1993.
• Algin, A. and Senay, M., "High-temperature Behavior of a Deformed Fermi Gas Obeying Interpolating Statistics", Physical Review E, 85, 041123, 2012.
• Algin, A. and Senay, M., "General Thermostatistical Properties of a q-Deformed Fermion Gas in Two Dimensions", Journal of Physics: Conference Series, 766, 012008, 2016.
• Khare, A., Fractional Statistics and Quantum Theory, World Scientific, Singapore, 2005.
• Pathria, R.K. and Beale, P.D., Statistical Mechanics, Butterworth-Heinemann, New York, 2011.
• Pazy, E. and Argaman, N., "Quantum Particle Statistics on the Holographic Screen Leads to Modified Newtonian Dynamics", Physical Review D, 85, 104021, 2012.
• Sanders, R.H., "Cosmology with Modified Newtonian Dynamics (MOND)", Monthly Notices of the Royal Astronomical Society, 296, 1009-1018, 1998.
• Neto, J.A., "Nonhomogeneous Cooling Entropic Gravity and MOND Theory", International Journal of Theoretical Physics, 50, 3552-3559, 2011.