Session U15: Alternate Theories of Gravity

Spontaneous Scalarization of Massive Fields

Spontaneous scalarization is a phenomenon in certain scalar-tensor theories where large deviations from general relativity can be observed inside compact stars, while the known observational bounds can also be satisfied far away. This scenario has been investigated for massless scalars and binary neutron stars using numerical relativity, but the parameter space for such theories have been severely restricted by recent observations. Here, we present our results on the spontaneous scalarization of massive scalars. We simulate cases with different equations of state and scalar field parameters, and comment on the detectability of the scalar field effects from the gravitational wave signal.   

Bursty Gravitational Waves

Compact objects in highly elliptical binaries, unlike their circular counterparts, emit most of their gravitational radiation during pericenter passage. Such events would look like a sequence of bursts in time-frequency space, which would be difficult to extract with a matched filtering approach. However, if we could predict the time and frequency of the next burst, we could then search over that region of time-frequency space until the next burst is detected and then stack the power of the bursts to create an enhanced data product. We here present a proof of concept burst model, where we treat the bursts as boxes in time-frequency space and model the evolution of the system to Newtonian order. From this, we develop an algorithm to determine the mapping between boxes. We study the accuracy of the model by comparing the burst model to numerical solutions of the system under Newtonian order radiation reaction and by studying the strength of the 1PN corrections to the energy and angular momentum flux. Finally, we explain how this model can be used to test General Relativity and alternative theories of gravity.   

Applicability of the Newman-Janis Algorithm to Modified Gravity Theories

The Newman-Janis algorithm is an appealing method to generate rotating black hole metrics from non-rotating ones. In this talk, I investigate the applicability of this algorithm in modified gravity theories, concentrating on quadratic gravity. We find that this algorithm leads to a metric that does not agree with slowly-rotating solutions in this theory, and in fact, does not even satisfy the modified vacuum field equations. I will also show that associating the latter with a stress-energy tensor implies the existence of naked singularities in the spacetime. This suggests that the Newman-Janis algorithm is not well-suited to generate rotating black hole solutions in modified gravity theories.   

Gravitational radiation from compact binaries in scalar-tensor gravity

General relativity (GR) has been extensively tested in the solar system and in binary pulsars, but never in the strong-field, dynamical regime. Soon, gravitational-wave (GW) detectors like Advanced LIGO will be able to probe this regime by measuring GWs from inspiraling and merging compact binaries. One particularly interesting alternative to GR is scalar-tensor gravity. We present the calculation of second post-Newtonian (2PN) gravitational waveforms for inspiraling compact binaries in a general class of scalar-tensor theories. The waveforms are constructed using a standard GR method known as ``Direct Integration of the Relaxed Einstein equations,'' appropriately adapted to the scalar-tensor case. We find that differences from general relativity can be characterized by a reasonably small number of parameters. Among the differences are new hereditary terms which depend on the past history of the source. In one special case, mixed black hole-neutron star systems, all differences from GR can be characterized by only a single parameter. In another, binary black hole systems, we find that the waveform is indistinguishable from that of general relativity.   

Dynamical scalarization of neutron stars in scalar-tensor gravity theories

We present a framework to study generic neutron-star binaries in scalar-tensor theories of gravity. Our formalism achieves this goal by suitably interfacing a post-Newtonian orbital evolution with a set of non-linear algebraic equations to describe the scalar charge of each binary's component along the evolution in terms of isolated-star data. We validate this semi-analytical procedure by comparing its results to those of fully general-relativistic simulations, and use it to investigate the behavior of binary systems in large portions of the parameter space of scalar-tensor theories. This allows us to shed further light on the phenomena of ``dynamical scalarization,'' which takes place in tight binaries even for stars that have exactly zero scalar charge in isolation. Finally, we discuss the extent to which deviations from General Relativity can be detected, either directly by the emitted gravitational waves, or by their electromagnetic counterparts.   

Is Quadratic Gravity Stable?

As the advanced gravitational wave detector era approaches it is vital to understand and analytically test the wide range of alternative theories to General Relativity. An important analytical test is a stability analysis as any instabilities arising due to perturbations suggest the theory to be invalid. In this talk I present our results of a stability analysis of dynamical, quadratic gravity to linear order in the perturbation and coupling constant in the high-frequency, geometric optics approximation. This analysis is based on a study of gravitational and scalar modes propagating on spherically-symmetric and axially-symmetric, vacuum solutions of the theory. We find dispersion relations that do not lead to exponential growth of the propagating modes, suggesting the theory is linearly stable on these backgrounds. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry.   

Dark matter as an integral part of an alternative gravity model

The purpose of this paper is to reconcile observations of dark matter effects on the galactic and cosmological scales with the null results of astroparticle physics observations such as CDMS and ANTARES. This paper will also provide a candidate unified and simpler mathematical formulation for the Lambda CDM model. Unification is achieved by a combination of the f(R) approach, with the standard LCDM approach and inflationary models. It is postulated that dark matter-energy fields depend on the Ricci curvature R. Standard methods of classical and quantum field theory on curved space time are applied. When this model is treated as a quantum field theory in curved space-time, the dark matter-dark matter fermion annihilation cross section grows as the square of the Ricci scalar. It is proposed and mathematically demonstrated that in this model dark matter particles could have shorter lifetimes in regions of relatively strong gravity such as near the sun, near the Earth, or any other large mass. The unexpected difficulties in directly observing fermionic particles of dark matter in Earth based observatories are explained by this theory. The gravitational field of the Sun and Earth may effect them in ways the standard WIMP models would never predict.