Modified Gravity and Cosmology

Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

f(R) theories

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

Extended Theories of Gravity

We construct consistent theories of multiple interacting spin-2 fields in arbitrary spacetime dimensions using a vielbein formulation. We show that these theories have the additional primary constraints needed to eliminate potential ghosts, to all orders in the fields, and to all orders beyond any decoupling limit. We postulate that the number of spin-2 fields interacting at a single vertex is limited by the number of spacetime dimensions. We then show that, for the case of two spin-2 fields, the vielbein theory is equivalent to the recently proposed theories of ghost-free massive gravity and bi-metric gravity. The vielbein formulation greatly simplifies the proof that these theories have an extra primary constraint which eliminates the Boulware-Deser ghost.

Interacting spin-2 fields

The symmetron is a scalar field associated with the dark sector whose coupling to matter depends on the ambient matter density The symmetron is decoupled and screened in regions of high density, thereby satisfying local constraints from tests of gravity, but couples with gravitational strength in regions of low density, such as the cosmos In this paper we derive the cosmological expansion history in the presence of a symmetron field, tracking the evolution through the inflationary, radiation- and matter-dominated epochs, using a combination of analytical approximations and numerical integration For a broad range of initial conditions at the onset of inflation, the scalar field reaches its symmetry-breaking vacuum by the present epoch, as assumed in the local analysis of spherically-symmetric solutions and tests of gravity For the simplest form of the potential, the energy scale is too small for the symmetron to act as dark energy, hence we must add a cosmological constant to drive late-time cosmic acceleration We briefly discuss a class of generalized, non-renormalizable potentials that can have a greater impact on the late-time cosmology, though cosmic acceleration requires a delicate tuning of parameters in this case

Symmetron Cosmology

Interacting Spin-2 Fields

We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate N+1-point correlation functions with a soft-momentum scalar or tensor mode to a symmetry transformation on N-point correlation functions of hard-momentum modes. We derive these consistency relations from Ward identities for an infinite tower of non-linearly realized global symmetries governing scalar and tensor perturbations. These symmetries can be labeled by an integer n. At each order n, the consistency relations constrain — completely for n = 0,1, and partially for n ≥ 2 — the q{sup n} behavior of the soft limits. The identities at n = 0 recover Maldacena's original consistency relations for a soft scalar and tensor mode, n = 1 gives the recently-discovered conformal consistency relations, and the identities for n ≥ 2 are new. As a check, we verify directly that the n = 2 identity is satisfied by known correlation functions in slow-roll inflation.

https://iopscience.iop.org/article/10.1088/1475-7516/2014/01/039/pdf

An infinite set of Ward identities for adiabatic modes in cosmology

We discuss the criteria that must be satisfied by a well-posed variational principle. We clarify the role of Gibbons-Hawking-York type boundary terms in the actions of higher derivative models of gravity, such as F(R) gravity, and argue that the correct boundary terms are the naive ones obtained through the correspondence with scalar-tensor theory, despite the fact that variations of normal derivatives of the metric must be fixed on the boundary. We show in the case of F(R) gravity that these boundary terms reproduce the correct Arnowitt-Deser-Misner energy in the Hamiltonian formalism, and the correct entropy for black holes in the semiclassical approximation.

Kurt Hinterbichler

Papers

Interacting spin-2 fields

Symmetron Cosmology

Interacting Spin-2 Fields

An infinite set of Ward identities for adiabatic modes in cosmology

Boundary Terms, Variational Principles and Higher Derivative Modified Gravity