General Class Of Scalar-tensor Theories Research Articles

Jointly fitting weak lensing, x-ray, and Sunyaev-Zel’dovich data to constrain scalar-tensor theories with clusters of galaxies

Degenerate higher-order scalar-tensor (DHOST) theories are considered the most general class of scalar-tensor theories so that any constraints on them apply to the full set of scalar-tensor models. DHOST theories modify the laws of gravity even at galaxy clusters scale hence affecting the weak lensing (WL), X-ray and Sunyaev-Zel'dovich observables. We derive the theoretical expression for the lensing convergence $\kappa$, and the pressure profile $P$, of clusters in the framework of DHOST theories, and quantify how much they deviate from their General Relativity (GR) counterparts. We argue that combined measurements of $\kappa$, $P$, and of the electron number density, $n_e$, can constrain both the cluster and DHOST theory parameters. We carry on a Fisher matrix forecasts analysis to investigate whether this is indeed the case considering different scenarios for the spatial resolution and errors on the measured quantities.

Higher derivative scalar-tensor theory through a non-dynamical scalar field

We propose a new class of higher derivative scalar-tensor theories without the Ostrogradsky's ghost instabilities. The construction of our theory is originally motivated by a scalar field with spacelike gradient, which enables us to fix a gauge in which the scalar field appears to be non-dynamical. We dub such a gauge as the spatial gauge. Though the scalar field loses its dynamics, the spatial gauge fixing breaks the time diffeomorphism invariance and thus excites a scalar mode in the gravity sector. We generalize this idea and construct a general class of scalar-tensor theories through a non-dynamical scalar field, which preserves only spatial covariance. We perform a Hamiltonian analysis and confirm that there are at most three (two tensors and one scalar) dynamical degrees of freedom, which ensures the absence of a degree of freedom due to higher derivatives. Our construction opens a new branch of scalar-tensor theories with higher derivatives.

Galilean creation of the inflationary universe

It has been pointed out that the null energy condition can be violated stably in some non-canonical scalar-field theories. This allows us to consider the Galilean Genesis scenario in which the universe starts expanding from Minkowski spacetime and hence is free from the initial singularity. We use this scenario to study the early-time completion of inflation, pushing forward the recent idea of Pirtskhalava et al. We present a generic form of the Lagrangian governing the background and perturbation dynamics in the Genesis phase, the subsequent inflationary phase, and the graceful exit from inflation, as opposed to employing the effective field theory approach. Our Lagrangian belongs to a more general class of scalar-tensor theories than the Horndeski theory and Gleyzes-Langlois-Piazza-Vernizzi generalization, but still has the same number of the propagating degrees of freedom, and thus can avoid Ostrogradski instabilities. We investigate the generation and evolution of primordial perturbations in this scenario and show that one can indeed construct a stable model of inflation preceded by (generalized) Galilean Genesis.

Compact binary systems in scalar-tensor gravity. III. Scalar waves and energy flux

We derive the scalar waveform generated by a binary of nonspinning compact objects (black holes or neutron stars) in a general class of scalar-tensor theories of gravity. The waveform is accurate to 1.5 post-Newtonian order [$O((v/c)^3)$] beyond the leading-order tensor gravitational waves (the "Newtonian quadrupole"). To solve the scalar-tensor field equations, we adapt the direct integration of the relaxed Einstein equations formalism developed by Will, Wiseman, and Pati. The internal gravity of the compact objects is treated with an approach developed by Eardley. We find that the scalar waves are described by the same small set of parameters which describes the equations of motion and tensor waves. For black hole--black hole binaries, the scalar waveform vanishes, as expected from previous results which show that these systems in scalar-tensor theory are indistinguishable from their general relativistic counterparts. For black hole--neutron star binaries, the scalar waveform simplifies considerably from the generic case, essentially depending on only a single parameter up to first post-Newtonian order. With both the tensor and scalar waveforms in hand, we calculate the total energy flux carried by the outgoing waves. This quantity is computed to first post-Newtonian order relative to the "quadrupole formula" and agrees with previous, lower order calculations.

Bounce conditions for FRW models in modified gravity theories

In this paper, we have derived the minimal conditions for a bounce to occur in FRW cosmologies for the theories like Hoyle-Narlikar creation field theory, Lyra geometry, Brans-Dicke theory, general class of Scalar-Tensor theories, Einstein’s theory with variable cosmological term, with bulk viscosity and Finslerian cosmology. We derive the model-independent minimal necessary conditions for non-singular bounce and show that there is an open temporal region surrounding the bounce over which the strong energy condition (SEC) must be violated. Null energy condition is also violated in some of the modified gravity theories.

Compact binary systems in scalar-tensor gravity. II. Tensor gravitational waves to second post-Newtonian order

We derive the tensor gravitational waveform generated by a binary of nonspinning compact objects (black holes or neutron stars) in a general class of scalar-tensor theories of gravity. The waveform is accurate to second post-Newtonian order beyond the leading order quadrupole approximation. We use the direct integration of the relaxed Einstein equations formalism, appropriately adapted to scalar-tensor theories, along with previous results for the equations of motion in these theories. The self-gravity of the compact objects is treated with an approach developed by Eardley. The scalar field causes deviations from the general relativistic waveform that depend only on a small number of parameters. Among the effects of the scalar field are new hereditary terms which depend on the past history of the source. One of these, a dipole-dipole coupling, produces a zero-frequency "gravitational-wave memory" equivalent to the Christodoulou memory of general relativity. In the special case of two black holes, the waveform reduces to the general relativistic waveform. For a mixed (black hole-neutron star) system, the waveform is identical to that of Einstein's theory to first post-Newtonian order, with deviations at higher order depending only on a single parameter. The behavior in these cases matches that found for the equations of motion.

Compact binary systems in scalar-tensor gravity: Equations of motion to 2.5 post-Newtonian order

We calculate the explicit equations of motion for non-spinning compact objects to 2.5 post-Newtonian order, or O(v/c)^5 beyond Newtonian gravity, in a general class of scalar-tensor theories of gravity. We use the formalism of the Direct Integration of the Relaxed Einstein Equations (DIRE), adapted to scalar-tensor theory, coupled with an approach pioneered by Eardley for incorporating the internal gravity of compact, self-gravitating bodies. For the conservative part of the motion, we obtain the two-body Lagrangian and conserved energy and momentum through second post-Newtonian order. We find the 1.5 post-Newtonian and 2.5 post-Newtonian contributions to gravitational radiation reaction, the former corresponding to the effects of dipole gravitational radiation, and verify that the resulting energy loss agrees with earlier calculations of the energy flux. For binary black holes we show that the motion through 2.5 post-Newtonian order is observationally identical to that predicted by general relativity. For mixed black-hole neutron-star binary systems, the motion is identical to that in general relativity through the first post-Newtonian order, but deviates from general relativity beginning at 1.5 post-Newtonian order, in part through the onset of dipole gravitational radiation. But through 2.5 post-Newtonian order, those deviations in the motion of a mixed system are governed by a single parameter dependent only upon the scalar-tensor coupling constant and the structure of the neutron star, and are formally the same for a general class of scalar-tensor theories as they are for pure Brans-Dicke theory.

Constraints on the variation ofGfrom primordial nucleosynthesis

We study here the effect of a varying G on the evolution of the early Universe and, in particular, on primordial nucleosynthesis. This variation of G is modelled using the Brans-Dicke theory as well as a more general class of scalar-tensor theories. Modified nucleosynthesis codes are used to investigate this effect and the results obtained are used to constrain the parameters of the theories. We extend previous studies of primordial nucleosynthesis in scalar-tensor theories by including effects which can cause a slow variation of G during radiation domination and by including a late-time accelerating phase to the Universe's history. We include a brief discussion on the epoch of matter-radiation equality in Brans-Dicke theory, which is also of interest for determining the positions of the cosmic microwave background power-spectrum peaks.

Scalar-tensor gravity and conformal continuations

Global properties of vacuum static, spherically symmetric configurations are studied in a general class of scalar-tensor theories (STTs) of gravity in various dimensions. The conformal mapping between the Jordan and Einstein frames is used as a tool. Necessary and sufficient conditions are found for the existence of solutions admitting a conformal continuation (CC). The latter means that a singularity in the Einstein-frame manifold maps to a regular surface Strans in the Jordan frame, and the solution is then continued beyond this surface. Strans can be an ordinary regular sphere or a horizon. In the second case, Strans connect two epochs of a Kantowski-Sachs type cosmology. It is shown that the list of possible types of global causal structure of vacuum space–times in any STT, with any potential function U(φ), is the same as in general relativity with a cosmological constant. This is even true for conformally continued solutions. A traversable wormhole is shown to be one of the generic structures created as a result of CC. Two explicit examples are presented: the known solution for a conformal field in general relativity, illustrating the emergence of singularities and wormholes due to CC, and a nonsingular three-dimensional model with an infinite sequence of CCs.

Gravitational equation of motion of spherical extended bodies.

The gravitational equation of motion of the nonrotating, spherically symmetric, extended celestial body is calculated explicitly to $\frac{1}{{c}^{2}}$ order within the general class of scalar-tensor theories of gravity. Corrections to the motion proportional to spherical extension are generally nonzero in such theories; but when both PPN coefficients $\ensuremath{\gamma}$ and $\ensuremath{\beta}$ separately take their general relativistic values, the extension-dependent corrections to the motion vanish. Starting from the rather unique $\frac{1}{{c}^{2}}$ order expression obtained for the extended body equation of motion in this perturbative, but otherwise general, case, an educated guess can be made for the fully covariant variational principle with resulting tensor equation of motion of a rigid, spherically symmetric, extended body. Such bodies couple their spherical extension to the Ricci tensor of the metric field rather than the full curvature tensor, and hence such coupling vanishes in general relativity.

GENERAL CLASS OF SCALAR-TENSOR THEORIES: A REVIEW

The general class of scalar-tensor theories is discussed in which, in contrast to Brans-Dicke theory, the coupling parameter ω is not a constant but a function of the scalar field ϕ. Some other generalizations of the Brans-Dicke theory have also been discussed in brief. The physical aspects of these theories have been dealt. The cosmological models in scalar-tensor theories have been discussed in detail. Finally some open problems in these theories have been pointed out.

Static gravitational fields in a general class of scalar–tensor theories

The static field equations are investigated within the framework of a general class of scalar-tensor theories of gravitation proposed by Nordtvedt. In the Brans-Dicke and Barker theories, it is shown that in vacuum g00 is functionally related to the scaler field. Two families of exact solutions are also obtained for a static spherically symmetric gravitational field in Barker theory.

On Birkhoff's theorem in a general class of scalar-tensor theories

For a general class of scalar-tensor theories of gravitation proposed by Nordtvedt (1970) it is shown that Birkhoff's theorem (1923) holds both in vacuum as well as in the presence of an electromagnetic field when the scalar field is time independent.