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Stochastic Cosmological Background Study with 3G Gravitational Wave Detectors : Probing the Very Early Universe Second Year PhD Progress Report Ashish Sharma , , 1 Gran Sasso Science

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Ashish Sharma𝟐,πŸ‘π›π¨πž πŠπ›π¨ πˆπ›π¬π§π­πŸ,πŸ‘

1Gran Sasso Science Institute (GSSI), Iβˆ’67100 LAquila, Italy 2INFN, Laboratori Nazionali del Gran Sasso, Iβˆ’67100 Assergi, Italy

Stochastic Cosmological Background Study with 3G Gravitational Wave Detectors : Probing the Very Early Universe

Second Year PhD Progress Report

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Outline

  • Motivation
  • Stochastic background
  • Cosmological source of GWs
  • Best-fit subtraction
  • Projection method
  • Results
  • Conclusion

10/10/19 Ashish Sharma 2

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Motivation

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  • A GW stochastic background may be next

class signal detected.

  • It would be a statistical detection, confidence

level will grow with the observation time.

  • Produced very shortly after big bang.
  • Carry Information to study early universe

phenomenon not accessible by EM ways.

  • signals

will help us to understand the characteristics of the primordial signals, the fundamental physics and the evolution of the Universe.

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Stochastic Background

  • An incoherent superposition of large number of resolved and unresolved sources defined by

statistical properties, isotropic, unpolarized, stationary and Gaussian. Ξ©/0 𝑔 = 3

45 6478 6 9: ;

, 𝜍= = > =?@A

?

BC/

  • Uncorrelated gravitational wave sources can be of astrophysical or cosmological sources.
  • Cosmological: Signal of Early Universe
  • Inflationary epoch
  • Phase transitions
  • Cosmic Strings
  • Astrophysical
  • Supernovae
  • Magnetars
  • Binary Objects (BH, NS)

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Energy Spectra of SCGW Backgrounds

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LVC, Nature 460, 990-994 (2009)

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BBH Background Spectrum

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LVC, PRL 119, 029901 (2017)

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  • T. Regimbau et al, PRL 118 (2017) 15, 151105

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Sensitivity Level for GW Detectors

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Luminosity Distance and Binary mass Distribution

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Subtraction- Noise Projection Method

  • 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.

  • How we used this method
  • Injections: Generated a frequency domain strain containing the instrumental noise and

signal for 1000 binary black-holes (BH).

  • Subtraction: Performing the parameter estimation to best-fit waveform, which will give

us residual noise data after subtraction

  • 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.

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Fisher Matrix : Signal Model and It’s derivatives

Ξ“EF = πœ–Eπ‘ˆI πœ–Fπ‘ˆI Ξ“EF = 2 J

K L

𝑒𝑔 𝑆𝑓(πœ–Eπ‘ˆI 𝑔 πœ–Fπ‘ˆIβˆ— 𝑔 ) 𝑇T(𝑔)

  • π‘ˆI represent the signal model depending on πœ‡E parameters used to analyse the data.
  • Fisher matrix defined the manifold of all physical waveform of binary objects.
  • Normalized Fisher matrix and Inverse Fisher matrix are computed to define the

subtraction noise projection operator.

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Projection operator 𝑄 = 1 βˆ’ Ξ“EF πœ–E𝐼 βŸ¨πœ–F𝐼 | Projected data stream π‘„π‘ˆ[\]^6_`a(𝑔) = π‘ˆ[\]^6_`a(𝑔) βˆ’ Ξ“EF πœ–Fπ‘ˆI π‘ˆ[\]^6_`a πœ–Eπ‘ˆI(𝑔)

Projection of Subtraction Errors

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Overlap Reduction Function And Optimal Filter

  • Quantify the instrumental influence on the

correlation strength of detector outputs. Ξ³xy f = 5 8Ο€ }

~

J dβ€’ Ξ©exβ‚¬β€’β€šβ€’

Ζ’ .βˆ†β€¦ † F3 ~(β€’

Ξ©)F€

~(β€’

Ω) 𝐺

^ ‰ β€’

Ξ© = 𝑓`Ε 

‰

  • Ξ© dx

β€ΉΕ’ = eβ€ΉΕ’ ~

  • Ξ© 1

2 π‘Œ^

`π‘Œ^ Ε  βˆ’ 𝑍 ^ `𝑍 ^ Ε 

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  • The choice of filter depends upon the statistical

properties of stochastic background and location and orientation of detectors. 𝑅^β€’(𝑔) = β€˜ ; Ζ’78(;)@A

?

;’ β€œβ€(;)β€œβ€’(;)

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Detector Sensitivity After Subtraction-Noise Projection

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Conclusion

  • Subtraction noise projection method is effective in reducing the

residual noise data.

  • Geometrical

Interpretation

  • f

matched filtering and parameter estimation easy and realistic approach for such a method.

  • Increasing the possibility of detecting a cosmological background

signal with third generation gravitational wave detectors.

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Plan for Following Year

  • Testing efficiency of projection method on low-SNR CBC signals.
  • Check compatibility of subtraction-noise projection methods with arbitrary waveforms and

compare the dependence of the subtraction and projection on the model for search.

  • 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.

  • Comparing the projection method with alternative approaches (computationally expensive full

Bayesian analysis of a CBC foreground + primordial background).

  • Implementing the projection pipeline in existing LIGO/Virgo codes.

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