Piret Kuusk

Bio: Piret Kuusk is an academic researcher from University of Tartu. The author has contributed to research in topics: Scalar field & General relativity. The author has an hindex of 17, co-authored 52 publications receiving 819 citations.

Invariant quantities in the scalar-tensor theories of gravitation

Abstract: We consider the general scalar-tensor gravity without derivative couplings. By rescaling of the metric and reparametrization of the scalar field, the theory can be presented in different conformal frames and parametrizations. In this work we argue that while due to the freedom to transform the metric and the scalar field, the scalar field itself does not carry a physical meaning (in a generic parametrization), there are functions of the scalar field and its derivatives which remain invariant under the transformations. We put forward a scheme to construct these invariants, discuss how to formulate the theory in terms of the invariants, and show how the observables like parametrized post-Newtonian parameters and characteristics of the cosmological solutions can be neatly expressed in terms of the invariants. In particular, we describe the scalar field solutions in Friedmann-Lemaitre-Robertson-Walker cosmology in Einstein and Jordan frames and explain their correspondence despite the approximate equations turning out to be linear and nonlinear in different frames.

Post-Newtonian parameters gamma and beta of scalar-tensor gravity with a general potential

Abstract: We calculate the parametrized post-Newtonian parameters $\ensuremath{\gamma}$ and $\ensuremath{\beta}$ for scalar-tensor gravity with a generic coupling function $\ensuremath{\omega}$ and scalar potential $V$ in the Jordan conformal frame in the case of a static spherically symmetric source. Since the potential generally introduces a radial dependence to the effective gravitational constant as well as to $\ensuremath{\gamma}$ and $\ensuremath{\beta}$, we discuss the issue of defining these parametrized post-Newtonian parameters and compare our expressions with previous calculations in simpler cases. We confront our results with current observational constraints on the values of $\ensuremath{\gamma}$ and $\ensuremath{\beta}$ and thus draw restrictions on the form of the functions $\ensuremath{\omega}$ and $V$ around their asymptotic background values.

Invariant slow-roll parameters in scalar-tensor theories

Abstract: A general scalar-tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan frames using quantities that are invariant under the conformal rescaling of the metric and transform as scalar functions under the reparametrization of the scalar field. By comparing spectral indices, calculated up to second order, we find that the frames are equivalent up to this order, due to the underlying assumptions.

f(R) theories

Abstract: 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.

Variational Principles in Mechanics

Abstract: The recognition that minimizing an integral function through variational methods (as in the last chapters) leads to the second-order differential equations of Euler-Lagrange for the minimizing function made it natural for mathematicians of the eighteenth century to ask for an integral quantity whose minimization would result in Newton’s equations of motion. With such a quantity, a new principle through which the universe acts would be obtained. The belief that “something” should be minimized was in fact a long-standing conviction of natural philosophers who felt that God had constructed the universe to operate in the most efficient manner—but how that efficiency was to be assessed was subject to interpretation. However, Fermat (1657) had already invoked such a principle successfully in declaring that light travels through a medium along the path of least time of transit. Indeed, it was by recognizing that the brachistochrone should give the least time of transit for light in an appropriate medium that Johann Bernoulli “proved” that it should be a cycloid in 1697. (See Problem 1.1.) And it was Johann Bernoulli who in 1717 suggested that static equilibrium might be characterized through requiring that the work done by the external forces during a small displacement from equilibrium should vanish. This “principle of virtual work” marked a departure from other minimizing principles in that it incorporated stationarity—even local stationarity—(tacitly) in its formulation. Efforts were made by Leibniz, by Euler, and most notably, by Lagrange to define a principle of least action (kinetic energy), but it was not until the last century that a truly satisfactory principle emerged, namely, Hamilton’s principle of stationary action (c. 1835) which was foreshadowed by Poisson (1809) and polished by Jacobi (1848) and his successors into an enduring landmark of human intellect, one, moreover, which has survived transition to both relativity and quantum mechanics. (See [L], [Fu] and Problems 8.11 8.12.)