$ f(R,T_{\mu\nu}T^{\mu\nu})$ gravity and Cardassian-like expansion as one of its consequences

Katırcı, Nihan; Kavuk, Mehmet

doi:10.1140/epjp/i2014-14163-6

Cited by 156 publications

(97 citation statements)

References 85 publications

(74 reference statements)

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“…(31) or (32) for the cases f RR = 0 and f RR = 0 respectively, and also the hydrodynamics Eqs. (40) and (42). The physical quantities are considered to be as X = X 0 + X 1 , where X 1 ≪ X 0 and the "0" (1) index indicates the background (perturbed) quantities.…”

Section: Jeans Analysis In the Emsgmentioning

confidence: 99%

Jeans analysis in energy–momentum-squared gravity

et al. 2020

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In this paper, we study the Jeans analysis in the context of energy-momentum-squared gravity (EMSG). More specifically we find the new Jeans mass for non-rotating infinite mediums as the smallest mass scale for local perturbations that can be stable against its own gravity. Furthermore, for rotating mediums, specifically for rotating thin disks in the context of EMSG, we find a new Toomre-like criterion for the local gravitational stability. Finally, the results are applied to a hyper-massive neutron star, as an astrophysical system. Using a simplified toy model we have shown that, for a positive (negative) value of the EMSG parameter α, the system is stable (unstable) in a wide range of α. On the other hand, no observational evidence has been reported on the existence of local fragmentation in HMNS. Naturally, this means that EMSG with positive α is more acceptable from the physical point of view.

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Section: Jeans Analysis In the Emsgmentioning

confidence: 99%

Jeans analysis in energy–momentum-squared gravity

et al. 2020

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“…As well know, the big bang nucleosynthesis (BBN) provides very stringent constraints on the evolution of the early universe [28][29][30][31][32][33][34][35] and has been used to test cosmological models (for example, see references [36][37][38][39][40][41][42][43][44][45][46]). From equations (25) and (39) and taking 0.85 < s < 1.15 [32], we find the parameter α is constrained as −0.141 < α < 0.09 or 1.000025 < α < 1.000046.…”

Section: Cosmological Applicationsmentioning

confidence: 99%

Effects of quantum fluctuations of metric on the universe

Yang

2015

Chin. Sci. Bull.

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We consider a model of modified gravity from the nonperturbative quantization of a metric. We obtain the modified gravitational field equations and the modified conservational equations. We apply it to the FLRW spacetime and find that due to the quantum fluctuations a bounce universe can be obtained and a decelerated expansion can also possibly be obtained in a dark energy dominated epoch. We also discuss the effects of quantum fluctuations on inflation parameters (such as slowroll parameters, spectral index, and the spectrum of the primordial curvature perturbation) and find values of parameters in the comparing the predictions of inflation can also work to drive the current epoch of acceleration. We obtain the constraints on the parameter of the theory from the observation of the big bang nucleosynthesis.

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“…In 2014, Katirci and Kavuk in Ref. [38] proposed such a theory for the first time. It is actually a covariant generalization of GR which allows the existence of a term proportional to T µν T µν in the action functional.…”

Section: Introductionmentioning

confidence: 99%

“…One interesting model is the one where the Lagrangian is constructed by taking it as an arbitrary function of the curvature scalar R and of the trace of the stress-energy tensor T . Such modifications gave rise to f (R, T ) theories [37][38][39]. Here the dependence from T may be induced by exotic imperfect fluids or quantum effects (conformal anomaly).…”

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confidence: 99%

Dynamical system analysis of generalized energy-momentum-squared gravity

Bahamonde

Marciu

Rudra³

2019

Phys. Rev. D

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In this work we have investigated the dynamics of a recent modification to the general theory of relativity, the energy-momentum squared gravity model f (R, T 2 ), where R represents the scalar curvature and T 2 the square of the energy-momentum tensor. By using dynamical system analysis for various types of gravity functions f (R, T 2 ), we have studied the structure of the phase space and the physical implications of the energy-momentum squared coupling. In the first case of functional where f (R, T 2 ) = f0R n (T 2 ) m , with f0 constant, we have shown that the phase space structure has a reduced complexity, with a high sensitivity to the values of the m and n parameters. Depending on the values of the m and n parameters, the model exhibits various cosmological epochs, corresponding to matter eras, solutions associated to an accelerated expansion, or decelerated periods. The second model studied corresponds to the f (R, T 2 ) = αR n + β(T 2 ) m form with α, β constant parameters.In this case it is obtained a richer phase space structure which can recover different cosmological scenarios, associated to matter eras, de-Sitter solutions, and dark energy epochs. Hence, this model represent an interesting cosmological model which can explain the current evolution of the Universe and the emergence of the accelerated expansion as a geometrical consequence.The second approach aims at modifying the geometry of spacetime, i.e. the Einstein's gravity in the general theory of relativity (GR) at large distances, specifically beyond our Solar System to produce accelerating cosmological solutions [5][6][7]. This has given rise to the concept of "modified gravity". There are numerous such theories available in literature, such as Brans-Dicke theory [8], Einstein-Cartan theory [9], Brane gravity theory [10-13], Rosen's Bimetric theory of gravity [14][15][16], Kaluza-Klein theory [17][18][19][20][21], Hořava-Lifshitz theory [22,23], etc. Extensive reviews in modified gravity theories can be found in the Refs. [24,25]. All these have their own share of merits and de-merits. Many of the theories of modified gravity aims at modifying the linear function of scalar curvature, R responsible for the Einstein tensor in the Einstein equations of GR. So it is obvious that the alterations are brought about in such a way so as to generalize the gravitational Lagrangian which takes a special form L GR = R in case of GR. An extensively studied theory in this context is the f (R) gravity where the gravitational Lagrangian L GR = R is replaced by an analytic function of R, i.e., L f (R) = f (R). Via this generalization, we can explore the non-linear effects of the scalar curvature R in the evolution of the universe by choosing a suitable function for f (R). Extensive reviews on this theory is available in the Refs. [26,27].The cosmological viability of f (R) dark energy models have been studied in [28]. In this paper the authors ruled out the f (R) theories where a power of R is dominant at large or small R. Conditions for the cosmological via...

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$ f(R,T_{\mu\nu}T^{\mu\nu})$ gravity and Cardassian-like expansion as one of its consequences

Cited by 156 publications

References 85 publications

Jeans analysis in energy–momentum-squared gravity

Jeans analysis in energy–momentum-squared gravity

Effects of quantum fluctuations of metric on the universe

Dynamical system analysis of generalized energy-momentum-squared gravity

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