Shinʼichi Nojiri

Models for Little Rip Dark Energy

Abstract We examine in more detail specific models which yield a little rip cosmology, i.e., a universe in which the dark energy density increases without bound but the universe never reaches a finite time singularity. We derive the conditions for the little rip in terms of the inertial force in the expanding universe and present two representative models to illustrate in more detail the difference between little rip models and those which are asymptotically de Sitter. We derive conditions on the equation of state parameter of the dark energy to distinguish between the two types of models. We show that coupling between dark matter and dark energy with a little rip equation of state can alter the evolution, changing the little rip into an asymptotic de Sitter expansion. We give conditions on minimally coupled phantom scalar field models and on scalar-tensor models that indicate whether or not they correspond to a little rip expansion. We show that, counterintuitively, despite local instability, a little rip cosmology has an infinite lifetime.

Phantom Cosmology without Big Rip Singularity

Abstract We construct phantom energy models with the equation of state parameter w which is less than −1, w − 1 , but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time (“phantom energy” without “Big Rip” singularity) and (ii) energy density tends to constant value with time (“cosmological constant” with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun–Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.

Time-dependent matter instability and star singularity in F(R) gravity

Abstract We investigate a curvature singularity appearing in the star collapse process in F ( R ) gravity. In particular, we propose an understanding of the mechanism to produce the curvature singularity. Moreover, we explicitly demonstrate that R α ( 1 α ⩽ 2 ) term addition could cure the curvature singularity and viable F ( R ) gravity models could become free of such a singularity. Furthermore, we discuss the realization process of the curvature singularity and estimate the time scale of its appearance. For exponential gravity, it is shown that in case of the star collapse, the time scale is much shorter than the age of the universe, whereas in cosmological circumstances, it is as long as the cosmological time.

Unifying inflation with dark energy in modified F(R) Hořava–Lifshitz gravity

We study FRW cosmology for a non-linear modified F(R) Hořava–Lifshitz gravity which has a viable convenient counterpart. A unified description of early-time inflation and late-time acceleration is possible in this theory, but the cosmological dynamic details are generically different from the ones of the convenient viable F(R) model. Remarkably, for some specific choice of parameters they do coincide. The emergence of finite-time future singularities is investigated in detail. It is shown that these singularities can be cured by adding an extra, higher-derivative term, which turns out to be qualitatively different when compared with the corresponding one of the convenient F(R) theory.

Ghost-free

Abstract We propose a bigravity analogue of the F ( R ) gravity. Our construction is based on recent ghost-free massive bigravity where additional scalar fields are added and the corresponding conformal transformation is implemented. It turns out that F ( R ) bigravity is easier to formulate in terms of the auxiliary scalars as the explicit presentation in terms of F ( R ) is quite cumbersome. The consistent cosmological reconstruction scheme of F ( R ) bigravity is developed in detail, showing the possibility to realize nearly arbitrary physical universe evolution with consistent solution for second metric. The examples of accelerating universe which includes phantom, quintessence and ΛCDM acceleration are worked out in detail and their physical properties are briefly discussed.

F(R)

Abstract We explore the four-dimensional effective F ( T ) gravity with T the torsion scalar in teleparallelism originating from higher-dimensional space–time theories, in particular the Kaluza–Klein (KK) and Randall–Sundrum (RS) theories. First, through the KK dimensional reduction from the five-dimensional space–time, we obtain the four-dimensional effective theory of F ( T ) gravity with its coupling to a scalar field. Second, taking the RS type-II model in which there exist the five-dimensional Anti-de Sitter (AdS) space–time with four-dimensional Friedmann–Lemaitre–Robertson–Walker (FLRW) brane, we find that there will appear the contribution of F ( T ) gravity on the four-dimensional FLRW brane. It is demonstrated that inflation and the dark energy dominated stage can be realized in the KK and RS models, respectively, due to the effect of only the torsion in teleparallelism without that of the curvature.

bigravity and accelerating cosmology

Abstract We explore the possibility of further gravitational wave modes in F ( T ) gravity, where T is the torsion scalar in teleparallelism. It is explicitly demonstrated that gravitational wave modes in F ( T ) gravity are equivalent to those in General Relativity. This result is achieved by calculating the Minkowskian limit for a class of analytic function of F ( T ) . This consequence is also confirmed by the preservative analysis around the flat background in the weak field limit with the scalar–tensor representation of F ( T ) gravity.

Effective

Abstract Dark energy models with various scenarios of evolution are considered from the viewpoint of the formalism for the equation of state. It is shown that these models are compatible with current astronomical data. Some of the models presented here evolve arbitrarily close to ΛCDM up to the present, but diverge in the future into a number of different possible asymptotic states, including asymptotic de Sitter (pseudo-rip) evolution, little rips with disintegration of bound structures, and various forms of finite-time future singularities. Therefore it is impossible from observational data to determine whether the universe will end in a future singularity or not. We demonstrate that the models under consideration are stable for a long period of time (billions of years) before entering a Little Rip/Pseudo-Rip induced dissolution of bound structures or before entering a soft finite-time future singularity. Finally, the physical consequences of Little Rip, Types II, III and Big Crush singularities are briefly compared.

F(T)

Abstract We propose new version of massive F ( R ) gravity which is natural generalization of convenient massive ghost-free gravity. Its Hamiltonian formulation in scalar-tensor frame is developed. We show that such F ( R ) theory is ghost-free. The cosmological evolution of such theory is investigated. Despite the strong Bianchi identity constraint the possibility of cosmic acceleration (especially, in the presence of cold dark matter) is established. Ghost-free massive F ( R , T ) gravity is also proposed.

gravity from the higher-dimensional Kaluza-Klein and Randall-Sundrum theories

This paper is devoted to the study of various aspects of projectable F(R) Hořava–Lifshitz (HL) gravity. We show that some versions of F(R) HL gravity may have stable de Sitter solution and unstable flat-space solution. In this case, the problem of scalar graviton does not appear because flat space is not vacuum state. Generalizing the U(1) HL theory proposed in arXiv:1007.2410, we formulate U(1) extension of scalar theory and of F(R) Hořava–Lifshitz gravity. The Hamiltonian approach for such the theory is developed in full detail. It is demonstrated that its Hamiltonian structure is the same as for the non-relativistic covariant HL gravity. The spectrum analysis performed around the flat background indicates the consistency of the theory because it contains a graviton with only transverse polarization. Finally, we analyze the spatially flat FRW equations for U(1) invariant F(R) Hořava–Lifshitz gravity.