Abstract
In the present paper we propose a further modification of f(R, T)-gravity (where T is trace of the energy-momentum tensor) by introducing higher derivatives matter fields. We discuss stability conditions in the proposed theory and find restrictions for the 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 the theory and discuss main differences with conventional f(R, T)-gravity without higher derivatives. It is demonstrated that in the theory presented inflationary scenarios appear quite naturally even in the dust-filled Universe without any additional matter sources. Finally, we construct an inflationary model in one of the simplest representation of the theory, calculate the main inflationary parameters and find that it may be in quite good agreement with observations.
Highlights
According to current knowledge, based on experimental data, there were two different epochs of dynamical evolution of our Universe when the key role was played dark energy (DE): an inflationary stage at the early times of evolution and a late time acceleration (l.t.a.) stage, which started recently and continues till modern time
Substituting Eq (40) into (37) we find and this expression provides us with the relation between ρ0 and the parameters of the theory, which is quite natural because ρ0 is an integration constant which must be determined from the equations
In this paper we discuss the possibility of a further generalization of f (R, T )-gravity by incorporating higher derivative terms T in the action
Summary
According to current knowledge, based on experimental data, there were (at least) two different epochs of dynamical evolution of our Universe when the key role was played dark energy (DE): an inflationary stage at the early times of evolution and a late time acceleration (l.t.a.) stage, which started recently (on cosmological scales) and continues till modern time. The number of different approaches in this way is huge and we only mention here examples such as f (R)-gravity [12,13,14], Horndeski theory [15], unimodular gravity [16], teleparallel gravity [17], theories with non-minimal kinetic coupling [18]; see [19] There is another possibility to solve DE problem: we can introduce some exotic matter or modify the right hand side (matter sector) of the equations. This paper is organized as follows: in Sect. 2 we derive general equations and discuss stability conditions; in Sect. 3 we study a few concrete examples of functions and find some cosmological solutions; in Sect. 4 we estimate inflationary parameters for one of the simplest shapes of the function; and in Sect. 5 we give some concluding remarks
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