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Register a new userCosmology of $f(R, Box R)$ gravity
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Using dynamical system analysis, we explore the cosmology of theories of order up to eight order of the form $f(R, Box R)$. The phase space of these cosmology reveals that higher-order terms can have a dramatic influence on the evolution of the cosmology, avoiding the onset of finite time singularities. We also confirm and extend some of results which were obtained in the past for this class of theories.
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In literature there is a model of modified gravity in which the matter Lagrangian is coupled to the geometry via trace of the stress-energy momentum tensor $T=T_{mu}^{mu}$. This type of modified gravity is called as $f(R,T)$ in which $R$ is Ricci scalar $R=R_{mu}^{mu}$. We extend manifestly this model to include the higher derivative term $Box R$. We derived equation of motion (EOM) for the model by starting from the basic variational principle. Later we investigate FLRW cosmology for our model. We show that de Sitter solution is unstable for a generic type of $f(R,Box R, T)$ model. Furthermore we investigate an inflationary scenario based on this model. A graceful exit from inflation is guaranteed in this type of modified gravity.
Braneworld scenarios consider our observable universe as a brane embedded in a 5D space, named bulk. In this work, I derive the field equations of a braneworld model in a generalized theory of gravitation, namely $f(R,T)$ gravity, with $R$ and $T$, representing the Ricci scalar and the trace of the energy-momentum tensor, respectively. The cosmological parameters obtained from this approach are in agreement with recent constraints from Supernovae Ia data combined with baryon acoustic oscillations and cosmic microwave background observations, favouring such an alternative description of the universe dynamics.
The article communicates an alternative route to suffice the late-time acceleration considering a bulk viscous fluid with viscosity coefficient $zeta =zeta _{0}+ zeta _{1} H + zeta _{2} H^{2}$, where $zeta _{0}, zeta _{1}, zeta _{2}$ are constants in the framework of $f(R,T)$ modified gravity. We presume the $f(R,T)$ functional form to be $f=R+2alpha T$ where $alpha$ is a constant. We then solve the field equations for the Hubble Parameter and study the cosmological dynamics of kinematic variables such as deceleration, jerk, snap and lerk parameters as a function of cosmic time. We observe the deceleration parameter to be highly sensitive to $alpha$ and undergoes a signature flipping at around $tsim 10$ Gyrs for $alpha=-0.179$ which is favored by observations. The EoS parameter for our model assumes values close to $-1$ at $t_{0}=13.7$Gyrs which is in remarkable agreement with the latest Planck measurements. Next, we study the evolution of energy conditions and find that our model violate the Strong Energy Condition in order to explain the late-time cosmic acceleration. To understand the nature of dark energy mimicked by the bulk viscous baryonic fluid, we perform some geometrical diagnostics like the ${r,s}$ and ${r,q}$ plane. We found the model to mimic the nature of a Chaplygin gas type dark energy model at early times while a Quintessence type in distant future. Finally, we study the violation of continuity equation for our model and show that in order to explain the cosmic acceleration at the present epoch, energy-momentum must violate.
A review of the new of the problem of dark energy using modified gravity approach is considered. An explanation of the difficulties facing modern cosmology is given and different approaches are presented. We show why some models of gravity may suffer of instabilities and how some are inconsistent with observations.
We consider f(R) modified gravity theories in the metric variation formalism and attempt to reconstruct the function f(R) by demanding a background LCDM cosmology. In particular we impose the following requirements: a. A background cosmic history H(z) provided by the usual flat LCDM parametrization though the radiation (w_eff=1/3), matter (w_eff=0) and deSitter (w_eff=-1) eras. b. Matter and radiation dominate during the `matter and `radiation eras respectively i.e. Omega_m =1 when w_eff=0 and Omega_r=1 when w_eff=1/3. We have found that the cosmological dynamical system constrained to obey the LCDM cosmic history has four critical points in each era which correspondingly lead to four forms of f(R). One of them is the usual general relativistic form f(R)=R-2Lambda. The other three forms in each era, reproduce the LCDM cosmic history but they do not satisfy requirement b. stated above. Only one of these forms (different from general relativity) is found to be an attractor of the dynamical cosmological evolution. It has (Omega_DE=1, Omega_r=0, Omega_m=0) throughout the evolution. Its phase space trajectory is numerically obtained.
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