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Register a new user$f(R,{T_{mu u} T^{mu u}})$ gravity and Cardassian-like expansion as one of its consequences
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We propose a new model of gravity where the Ricci scalar (R) in Einstein-Hilbert action is replaced by an arbitrary function of R and of the norm of energy-momentum tensor i.e., $f(R,T_{mu u}T^{mu u})$. Field equations are derived in the metric formalism. We find that the equation of motion of massive test particles is non-geodesic and these test particles are acted upon by a force which is orthogonal to the four-velocity of the particles. We also find the Newtonian limit of the model to calculate the extra acceleration which can affect the perihelion of Mercury. There is a deviation from the general relativistic(GR) result unless the energy density of fluid is constant. Arranging $alpha$ parameter gives an opportunity to cure the inconsistency between the observational values for the abundance of light elements and the standard Big Bang Nucleosynthesis results. Even the dust dominated universe undergoes an accelerated expansion without using a cosmological constant in Model II. With this specific choice of $f(R,T_{mu u}T^{mu u})$, we get the a Cardassian-like expansion.
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Dynamical behavior and future singularities of $f(R, T,R_{mu u}T^{mu u})$ gravitational theory are investigated. This gravitational model is a more complete form of the $f(R,T)$ gravity which can offer new dynamics for the universe. We investigate this gravitational theory for the case $f = R + alpha R_{mu u}T^{mu u}$ using the method of autonomous dynamical systems and by assuming an interaction between matter and dark energy. The fixed points are identified and the results are consistent with standard cosmology and show that for small $alpha$, the radiation dominated era is an unstable fixed point of the theory and the universe will continue its procedure toward matter era which is a saddle point of the theory and allows the evolution to dark energy dominated universe. Finally the dark energy dominated epoch is a stable fixed point and will be the late time attractor for the universe. We also consider future singularities for the two $f = R + alpha R_{mu u}T^{mu u}$ and $f = R +alpha RR_{mu u}T^{mu u}$ cases and for $w = 0,dfrac{1}{3},1$ and $-1$. Our results show that for the case of $f = R + alpha R_{mu u}T^{mu u}$, the future singularities of the universe will happen in the same condition as do for the Einstein-Hilbert FRW universe. However, a new type of singularity is obtained for $f = R +alpha RR_{mu u}T^{mu u}$ that is captured by $trightarrow t_s; a rightarrow a_s; rhorightarrow infty;$ and $ |p| rightarrow 0$.
We investigate whether the new horizon first law still holds in $f(R,R^{mu u}R_{mu u})$ theory. For this complicated theory, we first determine the entropy of black hole via Wald method, then we derive the energy by using the new horizon first law, the degenerate Legendre transformation, and the gravitational field equations. For application, we consider the quadratic-curvature gravity and firstly calculate the entropy and the energy for a static spherically symmetric black hole, which reduces to the results obtained in literatures for a Schwarzschild-(A)dS black hole.
In this paper, we investigate irregularities in a cylindrical self-gravitating system which contains the properties of an imperfect matter and electromagnetic field. For $f(R,T,Q)$ theory, in which $R$ represents the Ricci scalar and $T$ shows the trace of matter stress-energy tensor while $Qequiv R_{gammadelta}T^{gammadelta}$, the field equations containing electric charge, mass functions and Darmois junction conditions at the hypersurface are examined. We have adopted new definition of complexity introduced by Herrera cite{herrera2018new}, generalized it for the static charged cylindrically symmetric case in $f(R,T,Q)$ theory by performing a detailed analysis on the orthogonal splitting of the Riemann curvature tensor. One of the effective scalars, $Y_{TF}$, has been recognized as a complexity factor. This factor is comprised of certain physical components of the fluid such as irregularity in energy density, locally pressure anisotropy and electric charge (arranged in a specific way). In addition, the effects of extra curvature terms of modified gravity are examined by making the relations among the complexity factor, Weyl scalar and Tolman mass.
We compute the one-loop divergences in a theory of gravity with Lagrangian of the general form $f(R,R_{mu u}R^{mu u})$, on an Einstein background. We also establish that the one-loop effective action is invariant under a duality that consists of changing certain parameters in the relation between the metric and the quantum fluctuation field. Finally, we discuss the unimodular version of such a theory and establish its equivalence at one-loop order with the general case.
In all $n(ge 3)$-dimensional gravitation theories whose Lagrangians are functions of the Riemann tensor and metric, we prove that static solutions are absent unless the total energy-momentum tensor for matter fields is of type I in the Hawking-Ellis classification. In other words, there is no hypersurface-orthogonal timelike Killing vector in a spacetime region with an energy-momentum tensor of type II, III, or IV. This asserts that ultra-dense regions with a semiclassical type-IV matter field cannot be static even with higher-curvature correction terms.
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