Anisotropic solution in phantom cosmology via Noether symmetry approach

The late time crossover from a power-law to an exponential expansion of the Universe evolution is the major problem in today’s physical cosmology. Unless this critical transition problem is solved, it is not possible to reach a holistic theory of cosmology. In this study, we propose a simple model in the FLRW framework, where dark matter and dark energy interact through a potential. We analytically solve this model and obtain scale factor a(t) from the presented model. Mainly, employing numerical solutions we show that the scale parameter has a hybrid form which includes power and exponential terms. The numerical results clearly show that there is a time crossover tc in the scale factor a(t) curve, which indicates the transition from the power-law to the exponential expansion of the Universe. We ﬁt these unscaled curves and obtain that scale factor behaves as a(t) ∝ t2/3 below t ≤ tc, and as a(t) ∝ exp(H0t) with H0 = 0.4 and H0 = 0.3 for the relatively weak and strong interactions above t > tc, respectively. It is the ﬁrst time that we explicitly obtain a hybrid scale factor incorporating the power and exponential terms as a(t) ∝ t2/3eH0t . We conclude that the presented model can solve the late time transition problem of the Universe based on dark matter and dark energy interaction. Additionally, we numerically obtain other kinematic parameters depending upon the scale factor. We discuss the limit behaviors of all relevant cosmological parameters. Our results are completely in good agreement with observational data. Finally, we state that this work makes essential steps towards solving a critical outstanding problem of the cosmology, and has a potential to creates a paradigm for future studies in this ﬁeld.

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“…( 14) and analytically obtain the scale factor a(t) in Eq. (20). Now, we give the numerical result of the scale factor in Fig.…”

Section: Numerical Resultsmentioning

confidence: 99%

Late time transition in the evolution of the Universe

Aydıner

Öz

Dereli

et al. 2021

Preprint

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“…Furthermore, to the best of our knowledge, so far, a model that represents the matter-dominant period and the dark-energy-dominant period together with a single or hybrid scale factor has not yet been obtained, although numerous models have been proposed to explain this phenomenon, for instance, in Refs. [12][13][14][15][16][17][18][19][20][21][22]. Therefore, this theoretical problem deserves attention.…”

Section: Late Time Transitionmentioning

confidence: 99%

Late time transition of Universe and the hybrid scale factor

et al. 2022

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In this study, we propose an interacting model to explain the physical mechanism of the late time transition from matter-dominated era to the dark energy-dominated era of the Universe evolution and to obtain a scale factor a(t) representing two eras together. In the present model, we consider a minimal coupling of two scalar fields which correspond to the dark matter and dark energy interacting through a potential based on the FLRW framework. Analytical solution of this model leads to a new scale factor a(t) in the hybrid form $$a(t)=a_{0} (t/t_{0})^{\alpha } e^{ht/t_{0}}$$ a ( t ) = a 0 ( t / t 0 ) α e h t / t 0 . This peculiar result reveals that the scale factor behaving as $$a (t) \propto (t/t_{0})^{\alpha }$$ a ( t ) ∝ ( t / t 0 ) α in the range $$t/t_{0}\le t_{c}$$ t / t 0 ≤ t c corresponds to the matter-dominated era while $$a(t) \propto \exp (ht/t_{0})$$ a ( t ) ∝ exp ( h t / t 0 ) in the range $$t/t_{0}>t_{c}$$ t / t 0 > t c accounts for the dark energy-dominated era, respectively. Surprisingly, we explore that the transition from the power-law to the exponential expansion appears at the crossover time $$t_{0} \approx 9.8$$ t 0 ≈ 9.8 Gyear. We attain that the presented model leads to precisely correct results so that the crossover time $$t_{0}$$ t 0 and $$\alpha $$ α are completely consistent with the exact solution of the FLRW and re-scaled Hubble parameter $$H_{0}$$ H 0 lies within the observed limits given by Planck, CMB and SNIa data (or other combinations), which lead to consistent cosmological quantities such as the dimensionless Hubble parameter h, deceleration parameter q, jerk parameter j and EoS parameter w. We also discuss time dependent behavior of the dark energy and dark matter to show their roles on the time evolution of the universe. Additionally, we observe that all main results completely depend on the structure of the interaction potential when the parameter values are tuned to satisfy the zero energy condition. Finally, we conclude that interactions in the dark sector may play an important role on the time evolution and provides a mechanism to explain the late time transition of the Universe.

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“…Noether symmetry approach has been widely used in the literature to find exact solutions, particularly of modified gravity theories [33,43,44,45,46,47,48,49,50] . It opens the way of the solution by decreasing the degrees of freedom of the dynamic system and/or determining the unknown functions of the system.…”

Section: Noether Gauge Symmetrymentioning

confidence: 99%

New static cylindrical symmetric solutions in GR for unfamiliar EoS parameter values via Noether symmetry

Öz¹,

Bamba²

2021

Preprint

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The solutions for the field equations of f (R) gravity are investigated in static cylindrically symmetric space-time. Conserved quantities of the system, as well as unknown functions, can be determined with the help of the Noether symmetry method. In this article, some unknown values of the equations of state parameter (EoS) have emerged as a result of the constraints obtained by analyzing the Noether symmetry equations for the f (R) = f0R case. Consequently, several new exact solutions have been found for cases of General Relativity in static cylindrically symmetrical space-time for the non-dust matter.

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Anisotropic solution in phantom cosmology via Noether symmetry approach

Cited by 14 publications

References 37 publications

Late time transition in the evolution of the Universe

Late time transition in the evolution of the Universe

Late time transition of Universe and the hybrid scale factor

New static cylindrical symmetric solutions in GR for unfamiliar EoS parameter values via Noether symmetry

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