Cosmology in modified f(R,T)f(R,T)-gravity

In present paper we propose further modification of $f(R,T)$-gravity (where $T$ is trace of energy-momentum tensor) by introducing higher derivatives matter fields. We discuss stability conditions in proposed theory and find restrictions for parameters to prevent appearance of main type of instabilities, such as ghost-like and tachyon-like instabilities. We derive cosmological equations for a few representations of theory and discuss main differences with convenient $f(R,T)$-gravity without higher derivatives. It is demonstrated that in presented theory inflationary scenarios appears quite naturally even in the dust-filled Universe without any additional matter sources. Finally we construct inflationary model in one of the simplest representation of the theory, calculate main inflationary parameters and find that it may be in quite agreement with observations

Stability in higher-derivative matter fields theories

We discuss possible instabilities in higher-derivative matter fields theories. These theories has two free parameters $\beta_1$ and $\beta_4$. By using dynamical system approach we explicitly demonstrate that for stability of Minkowski space in expanding Universe it is need condition $\beta_4<0$. By using quantum field theory approach we also find additional restriction for parameters $\beta_1>-\frac{1}{3}\beta_4$ which is need to avoid tachyon-like instability

From inflation to dark energy in the non-minimal modified gravity

We consider the modified gravity non-minimally coupled with matter Lagrangian for the description of early-time and late-time universe. Such $F(R)$ ($F(G)$) gravity in the absence of non-minimal coupling is viable theory which passes the local tests and reproduces the $\Lambda$CDM era. For qualitatively similar choice of non-minimal gravitational coupling function it is shown that the unified description of early-time inflation and late-time cosmic acceleration is possible. It is interesting that matter (scalar) which supports the inflationary era is gravitationally screened at late times. Hence, it may be effectively invisible at current universe.Comment: LaTeX file, 10 pages, based on the talk given by S.D. Odintsov at ICGA8 conference, Nara, Japa

Reconstruction and deceleration-acceleration transitions in modified gravity

We discuss the cosmological reconstruction in modified Gauss-Bonnet and F(R) gravities. Two alternative representations of the action (with and without auxiliary scalar) are considered. The approximate description of deceleration-acceleration transition cosmologies is reconstructed. It is shown that cosmological solution containing Big Bang and Big Rip singularities may be reconstructed only using the representation with the auxiliary field. The analytical description of the deceleration-acceleration transition cosmology in modified Gauss-Bonnet gravity is demonstrated to be impossible at sufficiently general conditions.Comment: LaTeX 8 pages, published version

Quantum effects, soft singularities and the fate of the universe in a braneworld cosmology

We examine a class of braneworld models in which the expanding universe encounters a "quiescent" future singularity. At a quiescent singularity, the energy density and pressure of the cosmic fluid as well as the Hubble parameter remain finite while all derivatives of the Hubble parameter diverge (i.e., ${\dot H}$, ${\ddot H}$, etc. $\to \infty$). Since the Kretschmann invariant diverges ($R_{iklm}R^{iklm} \to \infty$) at the singularity, one expects quantum effects to play an important role as the quiescent singularity is approached. We explore the effects of vacuum polarization due to massless conformally coupled fields near the singularity and show that these can either cause the universe to recollapse or, else, lead to a softer singularity at which $H$, ${\dot H}$, and ${\ddot H}$ remain finite while {\dddot H} and higher derivatives of the Hubble parameter diverge. An important aspect of the quiescent singularity is that it is encountered in regions of low density, which has obvious implications for a universe consisting of a cosmic web of high and low density regions -- superclusters and voids. In addition to vacuum polarization, the effects of quantum particle production of non-conformal fields are also likely to be important. A preliminary examination shows that intense particle production can lead to an accelerating universe whose Hubble parameter shows oscillations about a constant value.Comment: 19 pages, 3 figures, text slightly improved and references added. Accepted for publication in Classical and Quantum Gravit