Modified Gravity

A modified gravity-type cage, developed by SADCO Shelf Ltd., was examined using numerical and physical models to determine if the cage and mooring system is suitable for an exposed site south of the Isles of Shoals, NH. The 3000-m3 SADCO Shelf Submersible Fish Cage has angled stays between the upper framework and the ballasted bottom rim (in addition to net)

In this paper we review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating Universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

There is a distinct possibility that current and future cosmological data can be used to constrain Einstein's theory of gravity on the very largest scales. To be able to do this in a model-independent way, it makes sense to work with a general parameterization of modified gravity. Such an approach would be analogous to the Parameterized Post-Newtonian (PPN) approach which is used on the scale of the Solar System. A few such parameterizations have been proposed and preliminary constraints have been obtained. We show that the majority of such parameterizations are only exactly applicable in the quasistatic regime. On larger scales they fail to encapsulate the full behaviour of typical models currently under consideration. We suggest that it may be possible to capture the additions to the `Parameterized Post-Friedmann' (PPF) formalism by treating them akin to fluid perturbations.

In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergrav-ity, extra dimensional theory, modified gravity etc.), which are equivalently described by soft attractors in the effective field theory framework. In this description we have restricted our analysis for two scalar fields-dilaton and Higgsotic fields minimally coupled with Einstein gravity, which can be generalized for any arbitrary number of scalar field contents with generalized non-canonical and non-minimal interactions. We have explicitly used R 2 gravity, from which we have studied the attractor and non-attractor phase by exactly computing two point, three point and four point correlation functions from scalar fluctuations using In-In (Schwinger-Keldysh) and δN formalism. We have also presented theoretical bounds on the amplitude, tilt and running of the primordial power spectrum, various shapes (equilateral, squeezed, folded kite or counter collinear) of the amplitude as obtained from three and four point scalar functions, which are consistent with observed data. Also the results from two point tensor fluctuations and field excursion formula are explicitly presented for attractor and non-attractor phase. Further, reheating constraints, scale dependent behaviour of the couplings and the dynamical solution for the dilaton and Higgsotic fields are also presented. New sets of consistency relations between two, three and four point observables are also presented, which shows significant deviation from canonical slow roll models. Additionally, three possible theoretical proposals have presented to overcome the tachyonic instability at the time of late time acceleration. Finally, we have also provided the bulk interpretation from the three and four point scalar correlation functions for completeness.

Edmund J. Copeland,1 M. Sami,2, 3 and Shinji Tsujikawa4 1School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom Email:ed.copeland@nottingham.ac.uk 2Centre for Theoretical Physics, Jamia Millia ...

We have studied primordial non-Gaussian features from a model of potential driven single field DBI Galileon inflation. We have computed the bispectrum from the three point correlation function considering all possible cross correlation between scalar and tensor modes from the proposed setup. Further, we have computed the trispectrum from four point correlation function considering the contribution from contact interaction, scalar and graviton exchange diagrams in the in-in picture. Finally we have obtained the non-Gaussian consistency conditions from the four point correlator, which results in partial violation of the Suyama-Yamaguchi four-point consistency relation. This further leads to the conclusion that sufficient primordial non-Gaussianities can be obtained from DBI Galileon inflation.

The equivalence between metric and Palatini formalisms in f(R)-gravity can be achieved in the general context of theories with divergence free current. This equivalence is a necessary result of a symmetry which is included in a particular conservation equation of the current. In fact the conservation equation, by an appropriate redefinition of the introduced auxiliary field, may be encoded in a massless scalar field equation.

In the framework of a cosmological model of the Universe filled with a nonrelativistic particle soup, we easily reproduce inflation due to the quantum potential. The lightest particles in the soup serve as a driving force of this simple, natural and promising mechanism. It is explicitly demonstrated that the appropriate choice of their mass and fraction leads to reasonable numbers of e-folds. Thus, the direct introduction of the quantum potential into cosmology of the earliest Universe gives ample opportunities of successful reconsideration of the modern inflationary theory.

A geometrical explanation of Dark Matter and Dark Energy is easy to develop. It makes testable predictions and is thus completely falsifiable. The theory is based on a macroscopically extended fourth dimension of space, yielding a five-dimensional space-time structure. In this structure, the four-dimensional space-time of relativity is extrinsically curved in the higher spatial dimension. Dark Matter is curvature in the higher dimension that is not directly associated with local matter, but instead a result of the interaction between local matter or curvature and the global curvature due to all matter in the universe. However, criticisms have been leveled that the theory is not mathematical, i.e., there were no algebraic equations to describe the geometrical structure. Indeed, it seemed that no mathematical equations were even suggested by the geometry.  However, a simple algebraic equation that describes and explains the geometry of the four-dimensional structure of space has since been derived by considering the particulate source of the DM halo. Although the algebraic equation appears to be Newtonian, it implies a five-dimensional unification of the gravitational and electromagnetic fields such as that accomplished by Kaluza in 1921 and extended by Einstein and his colleagues in the late 1930s. The new equation also shows how gravity can be quantized on the basis of relativity without hypothesizing the discrete nature of matter, i.e., without the existence of specific ‘particles’ of gravity as is inherent in quantum gravity theories, the Standard  and other quantum models.

Key Words: galactic rotation problem, halo, Dark Matter, CDM, Dark Energy, General Relativity, electromagnetism, Einstein, Kaluza, five-dimensional, fourth dimension, four-dimensional space, space-time, positive curvature, extrinsic curvature, compactification, unification

We use dynamical system methods to explore the general behaviour of f (T) cosmol-ogy. In contrast to the standard applications of dynamical analysis, we present a way to transform the equations into a one-dimensional autonomous system, taking advantage of the crucial property that the torsion scalar in flat FRW geometry is just a function of the Hubble function, thus the field equations include only up to first derivatives of it, and therefore in a general f (T) cosmological scenario every quantity is expressed only in terms of the Hubble function. The great advantage is that for one-dimensional systems it is easy to construct the phase space portraits, and thus extract information and explore in detail the features and possible behaviours of f (T) cosmology. We utilize the phase space portraits and we show that f (T) cosmology can describe the universe evolution in agreement with observations, namely starting from a Big Bang singularity, evolving into the subsequent thermal history and the matter domination, entering into a late-time accelerated expansion, and resulting to the de Sitter phase in the far future. Nevertheless, f (T) cosmology can present a rich class of more exotic behaviours, such as the cosmological bounce and turnaround, the phantom-divide crossing, the Big Brake and the Big Crunch, and it may exhibit various singu-larities, including the non-harmful ones of type II and type IV. We study the phase space of three specific viable f (T) models offering a complete picture. Moreover, we present a new model of f (T) gravity that can lead to a universe in agreement with observations, free of perturbative instabilities, and applying the Om(z) diagnostic test we confirm that it is in agreement with the combination of SNIa, BAO and CMB data at 1σ confidence level.

Abstract: BigBOSS is a Stage IV ground-based dark energy experiment to study baryon acoustic oscillations (BAO) and the growth of structure with a wide-area galaxy and quasar redshift survey over 14,000 square degrees. It has been conditionally accepted by NOAO in response to a call for major new instrumentation and a high-impact science program for the 4-m Mayall telescope at Kitt Peak.

We develop the gradient expansion formalism for shift-symmetric Galileon-type actions. We focus on backgrounds that undergo inflation, work in the synchronous gauge, and obtain a general solution up to second order without imposing extra conditions at first order. The solution simplifies during the late stages of inflation. We also define a curvature perturbation conserved up to first order.

In this paper we investigate the cosmological effects of modified gravity with string curvature corrections added to Einstein-Hilbert action in the presence of a dynamically evolving scalar field coupled to Riemann invariants. The scenario exhibits several features of cosmological interest for late universe. It is shown that higher order stringy corrections can lead to a class of dark energy models consistent with recent observations. The model can give rise to quintessence, deSitter or phantom dark energy, in last case without recourse to negative kinetic energy field. The detailed treatment of reconstruction program for general scalar-Gauss-Bonnet gravity is presented for any given cosmology. The explicit examples of reconstructed scalar potentials are given for accelerated (quintessence, cosmological constant or phantom) universe. Finally, the relation with modified $F(G)$ gravity is established on classical level and is extended to include third order terms on curvature.

We show that in modified f(R) type gravity models with nonminimal coupling between matter and geometry, both the matter Lagrangian and the energy-momentum tensor are completely and uniquely determined by the form of the coupling. This result is obtained by using the variational formulation for the derivation of the equations of motion in the modified gravity models with geometry-matter coupling,

Motivated by the work of Yang et al. (Mod. Phys.
Lett. A 26:191, 2011), we report on a study of the new
holographic dark energy (NHDE) model with energy density
given by ρD = 3φ2
4ω (μH2 +νH˙) in the framework of
chameleon Brans–Dicke cosmology. We have studied the
correspondence between the quintessence, the DBI-essence,
and the tachyon scalar-field models with the NHDE model
in the framework of chameleon Brans–Dicke cosmology.
Deriving an expression of the Hubble parameter H and,
accordingly, ρD in the context of chameleon Brans–Dicke
chameleon cosmology, we have reconstructed the potentials
and dynamics for these scalar-field models. Furthermore, we
have examined the stability for the obtained solutions of the
crossing of the phantom divide under a quantum correction of
massless conformally invariant fields, and we have seen that
the quantum correction could be small when the phantom
crossing occurs and the obtained solutions of the phantom
crossing could be stable under the quantum correction. It has
also been noted that the potential increases as the matter–
chameleon coupling gets stronger with the evolution of the
universe.

In this paper we study scalar perturbations of the metric for nonlinear $f(R)$ models. We consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. We investigate the astrophysical approach in the case of Minkowski spacetime background and two cases in the cosmological approach, the large scalaron mass approximation and the quasi-static approximation, getting explicit expressions for scalar perturbations for both these cases. In the most interesting quasi-static approximation, the scalar perturbation functions depend on both the nonlinearity function $f(R)$ and the scale factor $a$. Hence, we can study the dynamical behavior of the inhomogeneities (e.g., galaxies and dwarf galaxies) including into consideration their gravitational attraction and the cosmological expansion, and also taking into account the effects of nonlinearity. Our investigation is valid for functions $f(R)$ which have stable de Sitter points in future with respect to the present time, that is typical for the most popular $f(R)$ models.

In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, scalar-tensor, Einstein-æther, and Bimetric theories, as well as TeVeS, f(R), general higher-order theories, Hořava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

This paper proposes a strong variant of ER=EPR conjecture (svEEC) based on Planck wormholes (PWs) (and partially assuming Einstein’s General Relativity), which svEEC helps redefining both big G and Planck constant, potentially explaining both the accelerated expansion of our universe (OU) and the highly variable experimental values of big G. This paper continues (from alternative angles of view!) the work of other past articles/preprints of the same author.
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The gravitational phase shift of neutrino oscillation can be discussed in the framework of f(R)-gravity. We show that the shift of quantum mechanical phase can depend on the given f(R)-theory that we choose. This fact is general and could constitute a fundamental test to discriminate among the various alternative relativistic theories of gravity. Estimations of ratio between the gravitational phase shift and the standard phase are carried out for the electronic Solar neutrinos.