A nontrivial footprint of standard cosmology in the future observations of low-frequency gravitational waves
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A nontrivial footprint of standard cosmology in the future observations of low-frequency gravitational waves Jorge Alfaro1
· Mauricio Gamonal1
Received: 20 January 2020 / Accepted: 19 November 2020 © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2020
Abstract Recent research shows that the cosmological components of the Universe should influence on the propagation of Gravitational Waves (GWs) and even it has been proposed a new way to measure the cosmological constant using Pulsar Timing Arrays (PTAs). However, these results have considered very particular cases (e.g. a de Sitter Universe or a mixing with non-relativistic matter). In this work we propose an extension of these results, using the Hubble constant as the natural parameter that includes all the cosmological information and studying its effect on the propagation of GWs. Using linearized gravity we considered a mixture of perfect fluids permeating the spacetime and studied the propagation of GWs within the context of the CDM model. We found from numerical simulations that the timing residual of local pulsars should present a distinguishable peak depending on the local value of the Hubble constant. As a consequence, when assuming the standard CDM model, our result predicts that the region of maximum timing residual is determined by the redshift of the source. This framework represents an alternative test for the standard cosmological model, and it can be used to facilitate the measurements of gravitational waves by ongoing PTAs projects. Keywords Gravitational waves · Pulsar timing arrays · Cosmology
Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Gravitational waves in an expanding universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Linearized theory of general relativity and standard cosmology . . . . . . . . . . . . . . . . . .
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Jorge Alfaro [email protected] Mauricio Gamonal [email protected]
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Instituto de Física, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna, Santiago 4860, Chile 0123456789().: V,-vol
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2.2 Coordinate transformation and an application to the CDM model . . . . . . . . 2.3 The effect of the cosmological expansion on the waveform of low-frequency GWs 3 Pulsar timing arrays and timing residual . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Timing residual of pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Including the CDM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Effects of the Hubble constant on the timing residual . . . . . . . . . . . . . . . . . . 4.1 Simulation of the timing residual of an individual pulsar . . . . . . . . . . . . . . 4.2 A relationship between PTA observables and the Hubble constant . . . . . . . . . 5 Statistical significance and signal-to-noise ratios . . . . . . . . . . . . . . . . . . . . 5.1 Estimates of statistical significance in th
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