An accelerating flat universe with an inverse square variation of the equation of state parameter with scale factor.
Published 2025-09-29
Keywords
- Accelarating expansion,
- Hubble parameter,
- Pressure parameter,
- Dark energy
Copyright (c) 2025

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Abstract
The pressure parameter in the equation of state (EoS) of the cosmic fluid that varies inversely as the square of the scale factor is a possibility to explain the evolution of our flat universe, presently expanding with an increasing acceleration under the negative pressure of a dynamic dark energy. The proposed model demonstrates the switch over from a state of decelerating expansion to a state of accelerating expansion of the universe using a simple equation of state consistent with the cosmological observations by introducing an effective pressure parameter in the equation of state for the cosmic fluid which comprises of radiation, matter and dark energy.
References
- . P. J. E. Peebles: Principles of Physical Cosmology, Princeton University Press, Princeton, 1993.
- . J. V. Narlikar: Introduction to cosmology, Cambridge university press, Cambridge, 1993.
- . A. G. Riess et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astronomical Journal 116: 1009-1038, 1998.
- . S. Perlmutter et al. Ap. J. 517: 565-586, 1999.
- . N. Aghanim et al. Planck 2018 results: Cosmological parameters, Astron. Astrophys. 641: A6, 2020.
- . S. Alam et al. Phys. Rev. D 103: 083533, 2021.
- . E. Tomasetti et al. Constraints on dynamical dark energy models using the latest data, Astron. Astrophys. 679: A96, 2023.
- . R. Jimenez et al. Updated observational constraints on H(z) measurements and the Hubble tension, JCAP 11: 047, 2023.
- . M. Li et al. Dark energy, Commun. Theor. Phys. 56: 525-604, 2011.
- . G. Gu et al. Observational signatures of dynamical DE models, RAA 24: 065001, 2024.
- . T. Padmanabhan: Cosmological constant, Phys. Rep. 380: 235-320, 2003.
- . W. Giare et al. A cosmological analysis of dark energy evolution, JCAP 10: 035, 2024.
- . S. Weinberg: The cosmological constant problem, Rev. Mod. Phys. 61: 1-23, 1989.
- . J. Martin: Everything you always wanted to know about the cosmological constant problem, Comp. Ren. Phys. 13: 566-665, 2012.
- . I. Zlatev, L. Wang and P. J. Steinhardt: Quintessence, cosmic coincidence and the cosmological constant, Phys. Rev. Lett. 82: 896-899, 1999.
- . E. J. Copeland, M. Sami and S. Tsujikawa: Dynamics of dark energy, Int. J. Mod. Phys. D 15: 1753-1936, 2006.
- . L. K. Duchaniya et al. Generalized holographic Ricci dark energy models, Phys. Dark Univ. 44: 101461, 2024.
- . S. Nojiri and S. D. Odintsov: Phys. Rep. 505: 59-144, 2011.
- . E. D. Valentino et al. Class. Quant. Grav. 38: 153001, 2021.
- . A. G. Riess et al. A comprehensive measurement of the local value of the Hubble constant. ApJ. Lett. 934: L7, 2022.
- . L. R. Colaco et al. A joint analysis of strong lensing and type Ia supernovae to determine Hubble constant, Eur. Phys. J. C 85: 577 (2025).
- . L. Verde, T. Treu and A. G. Riess: Nat. Astron. 3: 891-895, 2019.
- . S. Pan and S. Chakraborty: A cosmographic analysis of various parametrizations of dark energy, Int. J. Mod. Phys. D 28: 1950151, 2019.
- . W. Wang et al. Interacting dark energy models after Planck 2018, JCAP 01: 047, 2024.
- . B. J. Barros et al. Observational constraints on interacting models, Eur. Phys. J. C 84: 276, 2024.
- . S. Capozziello et al. Modified gravity approaches and cosmological observations, Symmetry 15: 65, 2023.
- . S. Weinberg: Gravitation and Cosmology: Principles and applications of GTR, Wiley, New York, 1972.
- . V. Mukhanov: Physical foundations of cosmology, Cambridge university press, Cambridge, 2005.
- . B. Wang et al. Reconstructing quintessence and tachyon potentials from recent data, Phys. Rev. D 108: 043523, 2023.
- . S. D. Odintsov and V. K. Oikonomou: Singular cosmology from generalized entropy formalism, Phys. Rev. D 107: 083519, 2023.
- . O. Akarsu et al. Probing dynamical DE with cosmographic methods, Phys. Rev. D 107: 123503, 2023.
- . Y. Tada and T. Terada: Primordial black holes from the inflating curvaton, Phys. Rev. D 109: L121305, 2024.
- . M. Cortes and L. R. Liddle: Bayesian model comparison of cosmologies with dynamical DE, JCAP 12: 007, 2024.
- . L. A. Escamilla et al. Holographic dark energy in f (R, T) gravity, JCAP 2024: 091, 2024.
- . A. C. Alfano et al. Late time cosmological dynamics of generalized holographic models, Phys. Dark Univ. 42: 101298, 2023.
- . H. Wang and Y. S. Piao: Cosmological constant problem in inflationary models, Phys. Rev. D 105: 083504, 2022.
- . F. B. M. dos Santos: Observational constraints on interacting quintessence models, JCAP 07: 064, 2023.
- . K. Bamba et al. Dark energy cosmology, Ap. Space Sci. 342: 155-228, 2012.
- . J. Niu et al. Cosmic growth index in modified gravity, ApJ. 972: 14, 2024.
- . K. V. Berghaus et al. Planck constraints on extra relativistic species and DE models, Phys. Rev. D 110: 103524, 2024.
- . M. Lucca et al. Dark sector interactions and dark energy, Phys. Rev. D 108: 063501, 2023.
- . T. Clifton et al. Modified gravity and cosmology, Phys. Rep. 513: 1-189, 2012.
- . Y. F. Cai et al. f (T) teleparallel gravity and cosmology, Rep. Prog. Phys. 79: 106901, 2016.
- . M. Krssak et al. Teleparallel theories of gravity, Class. Quant Grav. 36: 183001, 2019.
- . S. Bahamonde et al. Teleparallel gravity: From theory to cosmology, Phys. Rep. 775: 1-122, 2018.
- . S. D. Odintsov et al. A novel exponential f ( R) gravity model for dark energy, Eur. Phys. J. C 85: 298, 2025.
- . M. C. B. Abdalla et al., Dark energy and dark matter interactions: theoretical models and observational constraints, Phys. Dark Univ. 38: 101256, 2022.
- . M. Tristram et al. Cosmological parameters derived from final Planck data release, A&A, 682: A37, 2024.
- . P. M. Garnavich et al. Supernova limits on the cosmic equation of state, ApJ. 509: 74-79, 1998.
- . C. Sivakumar, M. V. John and K. Babu Joseph: Stochastic evolution of cosmological parameters in the early universe, Pramana 56: 466-477, 2001.