Abstract
We present a new viable modified theory of gravity in which the matter sector is characterized by a logarithmic Lagrangian density. The modified Einstein’s field equations are derived, and they are characterized by the emergence of an effective gravitational coupling constant and an effective negative cosmological constant both coupled to the Lagrangian of matter. Applied to the Friedmann-Robertson-Walker cosmological framework, it leads to motivating phenomenology. In particular, the universe is free from the initial singularity, and a unified description of the early inflationary phase, the succeeding non-accelerating, matter-dominated expansion, and then the transition to a late-time accelerating phase is obtained as well. Moreover, the effective dark energy sector can be quintessence, yet the universe starts contracting if the phantom divide-line is crossed. The model is confronted with observations that agree with recent astronomical data. Moreover, the model gives rise to Einstein’s field equations which resemble the equations obtained in unimodular gravity.
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E. Komatsu et al., Five-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation. Astrophys. J. Suppl. 180, 330 (2009)
U.Y. Divya Prasanthi, A. Aditya, Anisotropic Renyi holographic dark energy models in general relativity. Res. Phys. 17, 103010 (2020)
B. Pourhassan, E.Q. Kahya, Extended Chaplygin gas model. Res. Phys. 4, 101–102 (2014)
V. Vinutha, K. Sri Kavya, Dynamics of Bianchi cosmological model in Rn gravity. Res. Phys. 23, 103863 (2021)
T.P. Sotiriou, V. Faraoni, f(R) theories of gravity. Rev. Mod. Phys. 82, 451–497 (2010)
M. Sharif, M. Zubair, Thermodynamics in f(R, T) theory of gravity. J. Cosm. Astropart. Phys. 1203, 028 (2012)
L.K. Sharma, A.K. Yadav, P.K. Sahoo, B.K. Singh, Non-minimal matter-geometry coupling in Bianchi I space-time. Res. Phys. 10, 738–742 (2018)
M.R. Setare, E.N. Saridakis, Non-minimally coupled canonical, phantom and quintom models of holographic dark energy. Phys. Lett. B 671, 331–338 (2009)
R.A. El-Nabulsi, Scalar tensor cosmology with kinetic, Gauss-Bonnet and nonminimal derivative couplings and supersymmetric loop corrected potential. Comm. Theor. Phys. 71, 831–832 (2019)
V. Binbay, F.F. Binbay, Would an alternative gravity theory developed from an improved gravitational action approach includes negative kinetic energy dynamic degrees of freedom? Res. Phys. 10, 145–149 (2018)
Z.E. Musielak, Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients. J. Phys. A Math. Theor. 41, 055205 (2008)
Z.E. Musielak, General conditions for the existence of non-standard Lagrangians for dissipative dynamical systems. Chaos Solitons Fractals 42, 2645–2652 (2009)
Z.E. Musielak, N. Davachi, M. Rosario-Franco, Lagrangians, gauge transformations and Lie groups for semigroup of second-order differential equations. J. Appl. Math. (2020). https://doi.org/10.1155/2020/3170130
R.A. El-Nabulsi, Nonlinear dynamics with nonstandard Lagrangians. Qual. Theor. Dyn. Syst. 12, 273–329 (2012)
R.A. El-Nabulsi, T.A. Soulati, H. Rezazadeh, Non-standard complex Lagrangian dynamics. J. Adv. Res. Dyn. Cont. Syst. 5, 50–62 (2013)
R.A. El-Nabulsi, Non-standard fractional Lagrangians. Nonlinear Dyn. 74, 381–394 (2013)
R.A. El-Nabulsi, Nonstandard Lagrangian cosmology. J. Theor. Appl. Phys. 7, 58 (2013)
Y. Zhang, X.S. Zhou, Noether theorem and its inverse for nonlinear dynamical systems with nonstandard Lagrangians. Nonlinear Dyn. 84, 1867–1876 (2016)
J. Jiang, Y. Feng, S. Xu, Noether’s symmetries and its inverse for fractional Logarithmic Lagrangian systems. J. Syst. Sci. Inform. 7, 90–98 (2019)
A. Saha, B. Talukdar, Inverse variational problem for non-standard Lagrangians. Rep. Math. Phys. 73, 299–309 (2014)
J. Song, Y. Zhang, Noether’s theorems for dynamical systems of two kinds of non-standard Hamiltonians. Acta Mech. 229, 285–297 (2018)
X.S. Zhou, Y. Zhang, Routh method of reduction for dynamical systems with non-standard Lagrangians. Chin. Quart. Mech. 37, 15–21 (2016)
Y. Zhang, X.-P. Wang, Mei symmetry and invariants of quasi-fractional dynamical systems with non-standard Lagrangians. Symmetry 11, 1061 (2019)
R.A. El-Nabulsi, Gravitational field as a pressure force from logarithmic Lagrangians and non-standard Hamiltonians: the case of stellar halo of Milky Way. Comm. Theor. Phys. 69, 233 (2018)
V.V. Kiselev, Vector field as a quintessence partner. Class. Quantum Gravit. 21, 3323 (2003)
G. Ellis, R. Maartens, M. MacCallum, Causality and the speed of sound. Gen. Relativ. Gravit. 39, 1651–1660 (2007)
L. Visinelli, S. Vagnozzi, U. Danielsson, Revisiting a negative cosmological constant from low-redshift data. Symmetry 11, 1035 (2019)
K. Maeda, N. Ohta, Cosmic acceleration with a negative cosmological constant in higher dimensions. J. High Energy Phys. 2014, 95 (2014)
J. B. Hartle, S. W. Hawking, T. Hertog, Accelerated expansion with negative , arXiv: 1205.3807
R.A. El-Nabulsi, Phase transitions in the early universe with negatively induced supergravity cosmological constant. Chin. Phys. Lett. 23, 1124 (2006)
R.A. El-Nabulsi, Effective cosmological constant from supergravity arguments and non-minimal coupling. Phys. Lett. B 619, 26–29 (2005)
R.A. El-Nabulsi, Spontaneous symmetry breaking in the early universe with a negative temperature and a broken Lorentz symmetry. Proc. Natl Acad. Sci. India Sect. A Phys. Sci. 85, 395–399 (2015)
R. Calderon, R. Gannouji, B. L’Huillier, D. Polarski, Negative cosmological constant in the dark sector? Phys. Rev. D 103, 023506 (2021)
S. Kumar, Observational constraints on Hubble constant and deceleration parameter in power-law cosmology. Mon. Not. R. Astron. Soc. 422, 2532–2538 (2012)
A.A. Mamon, Constraints on a generalized deceleration parameter from cosmic chronometers. Mod. Phys. Lett. A 33, 1850056 (2018)
S. Khakshournia, A note on the generalized Friedmann equations for a thick brane. Gen. Relativ. Gravit. 40, 1791–1796 (2008)
W. Buchmuller, N. Dragon, Einstein gravity from restricted coordinate invariance. Phys. Lett. B 207, 292–294 (1998)
G.F. Ellis, H. van Elst, J. Murugan, J.-P. Uzan, On the trace-free Einstein equations as a viable alternative to general relativity. Class. Quant. Gravit. 28, 225007 (2011)
G.F.R. Ellis, The trace-Free Einstein equations and inflation. Gen. Relativ. Gravit. 46, 1619 (2014)
M. Shaposhnikov, D. Zenhausern, Scale invariance, unimodular gravity and dark energy. Phys. Lett. B 671, 187–192 (2009)
A.O. Barvinsky, A.Y. Kamenshchik, Darkness without dark matter and dark energy-generalized unimodular gravity. Phys. Lett. B 774, 59–63 (2017)
S.-W. Kim, Creation and annihilation of a wormhole in a matter-dark universe. J. Korean Phys. Soc. (2021). https://doi.org/10.1007/s40042-021-00087-1
J.-W. Lee, Zero cosmological constant and nonzero dark energy from the holographic principle. J. Korean Phys. Soc. 63, 1088–1093 (2013)
S. Kouwn, P. Oh, Dark energy with logarithmic cosmological fluid. J. Korean Phys. Soc. 65, 814–820 (2014)
H.-C. Kim, A new variable in scalar cosmology with an exponential potential. J. Korean Phys. Soc. 63, 1675–1680 (2013)
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El-Nabulsi, R.A. Logarithmic Lagrangian matter density, unimodular gravity-like and accelerated expansion with a negative cosmological constant. J. Korean Phys. Soc. 79, 345–349 (2021). https://doi.org/10.1007/s40042-021-00233-9
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DOI: https://doi.org/10.1007/s40042-021-00233-9