A new type of isotropic cosmological models without singularity

Modified Gravity and Cosmology

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

/pdf/cosmology-and-fundamental-physics-with-the-euclid-satellite-1pi37a138r.pdf

Cosmology and Fundamental Physics with the Euclid Satellite

https://cds.cern.ch/record/134600/files/198110088.pdf

Stability of gravity with a cosmological constant

For higher-derivative f(R) gravity, where R is the Ricci scalar, a class of models is proposed, which produce viable cosmology different from the ACDM at recent times and satisfy cosmological, Solar System, and laboratory tests. These models have both flat and de Sitter spacetimes as particular solutions in the absence of matter. Thus, a cosmological constant is zero in a flat spacetime, but appears effectively in a curved one for sufficiently large R. A “smoking gun” for these models would be a small discrepancy in the values of the slope of the primordial perturbation power spectrum determined from galaxy surveys and CMB fluctuations. On the other hand, a new problem for dark energy models based on f(R) gravity is pointed out, which is connected with the possible overproduction of new massive scalar particles (scalarons) arising in this theory in the very early Universe.

Disappearing cosmological constant in f(R) gravity

In view of an equal qualification of Brans and Dicke's gravitational theory to Einstein's general theory of relativity on an experimental level, the problem of Mach's principle, fun­ damental in the former theory, is studied by the use of the retarded bi-~calar Green's func­ tion for their inertial field ifJ in a homogeneous and isotropic universe. After deriving con­ cretely the relevant Green's function, we show that Brans and Dicke's cosmology is compatible with their stipulation of Mach's principle, with some proviso about the radiation universe in which the trace of the energy-momentum tensor is vanishing. Four dimensional Green's functions play an essential role in the treatment of the propagation of action, not only in the Minkowski space-time, but also in a curved space-time. As regards a massless scalar field and. the electromagnetic field, a formal procedure to derive the Green's functions of these fields in any Riemannian space-time has been given by De Witt and Brehme/) but it is in general difficult to find their exact expressions by means of that procedure. Several years ago, however, the author and Kimura 2 ),*) derived concretely the Green's functions in a homogeneous and isotropic universe .to deal with the quantum nature of gravitons and photons in the universe. On the other hand, the recent discovery3) of the cosmic background radia­ tion of T= 3°K provides us with a renewal of inter~st in the worl9. models with the big-bang origin. Among various cosmological theories permitting the big­ bang models, the most interesting will be the a-/1-r-theory4) based on general relativity and Brans and Dicke's theory5) based on their gravitational theory with variable gravitation "constant". The reason is that, according to' Dicke,6) the two gravitational theories alone can reasonably explain the so-called three crucial tests and give results which are in accord with astrophysical observations ex­ amined in the light of modern stellar evolutionary theory. The underlying philosophy of Brans and Dicke's gravitational theory IS, however, considerably different from that of Einstein's, because they have con­ sidered that the E6tv6s experiment gives an experimental support of the" weak

On the Green's Function in an Expanding Universe and Its Role in the Problem of Mach's Principle

/pdf/hamiltonian-approach-to-the-dynamics-of-expanding-3ofjy4xuz5.pdf

Hamiltonian approach to the dynamics of expanding homogeneous universes in the Brans-Dicke cosmology

On the Removal of Initial Singularity in a Big-Bang Universe in Terms of a Renormalized Theory of Gravitation. II : Criteria for Obtaining a Physically Reasonable Model

Hidekazu Nariai

Papers

On the Green's Function in an Expanding Universe and Its Role in the Problem of Mach's Principle

Hamiltonian approach to the dynamics of expanding homogeneous universes in the Brans-Dicke cosmology

On the Removal of Initial Singularity in a Big-Bang Universe in Terms of a Renormalized Theory of Gravitation. II : Criteria for Obtaining a Physically Reasonable Model

Gravitational Instability in the Brans-Dicke Cosmology

Gravitational Instability of Regular Model-Universes in a Modified Theory of General Relativity