Testing modified gravity at cosmological distances with LISA standard sirens (1906.01593v2)

Abstract: Modifications of General Relativity leave their imprint both on the cosmic expansion history through a non-trivial dark energy equation of state, and on the evolution of cosmological perturbations in the scalar and in the tensor sectors. In particular, the modification in the tensor sector gives rise to a notion of gravitational-wave (GW) luminosity distance, different from the standard electromagnetic luminosity distance, that can be studied with standard sirens at GW detectors such as LISA or third-generation ground based experiments. We discuss the predictions for modified GW propagation from some of the best studied theories of modified gravity, such as Horndeski or the more general degenerate higher order scalar-tensor (DHOST) theories, non-local infrared modifications of gravity, bigravity theories and the corresponding phenomenon of GW oscillation, as well as theories with extra or varying dimensions. We show that modified GW propagation is a completely generic phenomenon in modified gravity. We then use a simple parametrization of the effect in terms of two parameters $(\Xi_0,n)$, that is shown to fit well the results from a large class of models, to study the prospects of observing modified GW propagation using supermassive black hole binaries as standard sirens with LISA. We construct mock source catalogs and perform detailed Markov Chain Monte Carlo studies of the likelihood obtained from LISA standard sirens alone, as well as by combining them with CMB, BAO and SNe data to reduce the degeneracies between cosmological parameters. We find that the combination of LISA with the other cosmological datasets allows one to measure the parameter $\Xi_0$ that characterizes modified GW propagation to the percent level accuracy, sufficient to test several modified gravity theories. [Abridged]

• The paper demonstrates LISA’s ability to test modified gravity theories through observations of gravitational wave standard sirens.
• It details how modifications in GW luminosity distances via a revised friction term are parameterized by (Ξ0, n) to identify deviations from General Relativity.
• Results indicate that LISA, combined with electromagnetic data, can constrain modified gravity parameters to around 1% precision to advance dark energy research.

Evaluating Modified Gravity Theories with LISA Standard Sirens

This paper explores the potential of the Laser Interferometer Space Antenna (LISA) to test theories of modified gravity at cosmological distances by using gravitational wave (GW) standard sirens. Utilized here is the unique feature of gravitational wave propagation that can offer insights into the dynamics of the universe and test deviations from General Relativity (GR). These deviations manifest as changes in cosmological distances known as GW luminosity distances, which differ from the standard electromagnetic luminosity distance.

The paper focuses on detecting gravitational waves emitted by massive black hole binaries (MBHBs) using LISA. Gravitational waves from these sources can propagate through modified gravity fields over cosmological distances, and their observation could reveal significant insights into the nature of dark energy and the evolution of the universe.

Core Components Analyzed

1. Theories of Modified Gravity:
   • The paper explores various modified gravity theories including prominent ones like Horndeski and DHOST theories, which extend standard scalar-tensor gravity theories that are currently some of the most studied alternatives to GR.
   • It examines non-local gravity models which incorporate corrections to GR that become significant at cosmological scales. These models incorporate terms with inverse d’Alembertian operators, seeking to capture IR effects.
2. Gravitational Wave Luminosity Distance:
   • It is illustrated how a modified friction term in the evolution equation for GW tensor modes can modify the GW luminosity distance.
   • The paper utilizes the parameterization $(\Xi_0, n)$, initially proposed in past works, which efficiently encapsulates modifications over a broad range of models by predicting a scaling law for the GW luminosity distance.
3. Bigravity and Extra Dimensions:
   • The use of bigravity models is investigated. These support oscillation effects during GW propagation, analogous to the phenomenon of neutrino oscillations. Such features within these models could potentially be detectable with LISA’s sensitivity.
   • The paper also touches upon models involving extra dimensions and the implications of dimensional flow in scenarios of quantum gravity.

Implications and Prospective Insights

The ability of LISA to detect and characterize GWs from cosmological distances provides unique opportunities for testing theories beyond GR. The results indicate that gravitational and electromagnetic luminosity distances will offer a way to distinguish between GR and modified gravity theories and to investigate the dynamics of dark energy.

Quantitative Forecasts

The paper suggests that LISA, alongside other cosmological data such as CMB, SNe, and BAO, could constrain the parameters of modified gravity with enhanced precision. The parameter $\Xi_0$ could be measured with an accuracy potentially reaching 1% or better, which is significant when testing the predictions of various dark energy models.

In conclusion, this paper delineates how LISA’s ability to measure GWs from standard sirens introduces a new frontier in testing gravity and dark energy at cosmological scales. It makes a case for the instrument’s capacity not only to compliment current cosmological datasets but also significantly enrich our understanding of the universe’s fundamental forces. Future research is anticipated to refine these methods and broaden their applicability across other GW sources detectable by LISA.