Stochastic Cosmological Background Study with 3G Gravitational Wave Detectors : Probing the Very Early Universe Second Year PhD Progress Report Ashish Sharma π,π ππ¨π πππ¨ πππ¬π§π π,π 1 Gran Sasso Science Institute (GSSI), Iβ67100 LAquila, Italy 2 INFN, Laboratori Nazionali del Gran Sasso, Iβ67100 Assergi, Italy
Outline β’ Motivation β’ Stochastic background β’ Cosmological source of GWs β’ Best-fit subtraction β’ Projection method β’ Results β’ Conclusion 10/10/19 Ashish Sharma 2
Motivation β’ A GW stochastic background may be next class signal detected. β’ It would be a statistical detection, confidence level will grow with the observation time. β’ Produced very shortly after big bang. β’ Carry Information to study early universe phenomenon not accessible by EM ways. β’ signals will help us to understand the characteristics of the primordial signals, the fundamental physics and the evolution of the Universe. 10/10/19 Ashish Sharma 3
Stochastic Background β’ An incoherent superposition of large number of resolved and unresolved sources defined by statistical properties, isotropic, unpolarized, stationary and Gaussian. ? , π = = > = ? @ A Ξ© /0 π = 3 64 78 4 5 6 9: ; BC/ β’ Uncorrelated gravitational wave sources can be of astrophysical or cosmological sources. β’ Cosmological: Signal of Early Universe β’ Inflationary epoch β’ Phase transitions β’ Cosmic Strings β’ Astrophysical β’ Supernovae β’ Magnetars β’ Binary Objects (BH, NS) 10/10/19 Ashish Sharma 4
Energy Spectra of SCGW Backgrounds LVC, Nature 460 , 990-994 (2009) 10/10/19 Ashish Sharma 5
BBH Background Spectrum LVC, PRL 119, 029901 (2017) 10/10/19 Ashish Sharma 6
Sensitivity Level for GW Detectors T. Regimbau et al, PRL 118 (2017) 15, 151105 10/10/19 Ashish Sharma 7
Luminosity Distance and Binary mass Distribution 10/10/19 Ashish Sharma 8
Subtraction- Noise Projection Method β’ This method is based on a geometrical interpretation of matched filtering and allows to access the weak signals like a stochastic GW background, irrespective of the residual noise in the data. β’ How we used this method β’ Injections: Generated a frequency domain strain containing the instrumental noise and signal for 1000 binary black-holes (BH). β’ Subtraction: Performing the parameter estimation to best-fit waveform, which will give us residual noise data after subtraction β’ Projections: Using residual noise data and Fisher matrix to perform the projection method to project out the residual noise data and search for stochastic background. 10/10/19 Ashish Sharma 9
Fisher Matrix : Signal Model and Itβs derivatives Ξ EF = π E π I π F π I ππ ππ(π E π I π π F π Iβ π ) L Ξ EF = 2 J π T (π) K β’ π I represent the signal model depending on π E parameters used to analyse the data. β’ Fisher matrix defined the manifold of all physical waveform of binary objects. β’ Normalized Fisher matrix and Inverse Fisher matrix are computed to define the subtraction noise projection operator. 10/10/19 Ashish Sharma 10
Projection of Subtraction Errors π = 1 β Ξ EF π E πΌ β¨π F πΌ | Projection operator Projected data stream ππ [\]^6_`a (π) = π [\]^6_`a (π) β Ξ EF π F π I π [\]^6_`a π E π I (π) 10/10/19 Ashish Sharma 11
Overlap Reduction Function And Optimal Filter β’ Quantify the instrumental influence on the correlation strength of detector outputs. Ξ³ xy f = 5 Ξ©e xβ¬β’ββ’ Ζ . ββ¦ J dβ’ ~ (β’ ~ (β’ β F 3 8Ο } Ξ©)F β¬ Ξ©) ~ Ξ© 1 β° β’ βΉΕ = e βΉΕ Ε β π β’ β’ β° ~ ` π ^ ` π Ε πΊ Ξ© = π `Ε Ξ© d x 2 π ^ ^ ^ ^ β’ The choice of filter depends upon the statistical properties of stochastic background and location and orientation of detectors. ? π ^β’ (π) = β ; Ζ 78 (;)@ A ; β β β (;)β β’ (;) 12 10/10/19 Ashish Sharma
Detector Sensitivity After Subtraction-Noise Projection 10/10/19 Ashish Sharma 13
Conclusion β’ Subtraction noise projection method is effective in reducing the residual noise data. β’ Geometrical Interpretation of matched filtering and parameter estimation easy and realistic approach for such a method. β’ Increasing the possibility of detecting a cosmological background signal with third generation gravitational wave detectors. 10/10/19 Ashish Sharma 14
Plan for Following Year β’ Testing efficiency of projection method on low-SNR CBC signals. β’ Check compatibility of subtraction-noise projection methods with arbitrary waveforms and compare the dependence of the subtraction and projection on the model for search. β’ Injection of different types of primordial backgrounds into data and assess their detectability with 3G networks, sensitivity of 3G detectors network towards stochastic backgrounds with and without the projection. β’ Comparing the projection method with alternative approaches (computationally expensive full Bayesian analysis of a CBC foreground + primordial background). β’ Implementing the projection pipeline in existing LIGO/Virgo codes. 10/10/19 Ashish Sharma 15
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