Preprint Article Version 1 This version is not peer-reviewed

On the Expansion of Space and How to Measure It

Version 1 : Received: 25 February 2018 / Approved: 27 February 2018 / Online: 27 February 2018 (03:41:54 CET)

How to cite: Oliveira, F.J. On the Expansion of Space and How to Measure It. Preprints 2018, 2018020170 (doi: 10.20944/preprints201802.0170.v1). Oliveira, F.J. On the Expansion of Space and How to Measure It. Preprints 2018, 2018020170 (doi: 10.20944/preprints201802.0170.v1).

Abstract

We describe the effect of the expansion of space on the wavelength of the light beam in a Fabry-Pérot interferometer. For an instrument such as the Laser Interferometer Gravitational-Wave Observatory (LIGO), which has high sensitivity and a long period of light storage, the wavelength λ L of laser photons are redshifted due to the expansion of space in each cavity by an amount δ λ given by δ λ / λ L = H 0 τ s 8 . 8 × 10 - 21 , where H 0 2 . 2 × 10 - 18 s - 1 is the Hubble constant and τ s 4 ms is the light storage time for the cavity. Since τ s is based on the cavity finesse F which depends on the laser beam full width at half maximum (FWHM) δ ω of each cavity, we show that a difference in finesses between the LIGO arm cavities produces a signal h H ( t ) at the anti-symmetric output port given by h H t = 2 a 1 H 0 1 δ ω X t - 1 δ ω Y t , where δ ω X ( t ) and δ ω Y ( t ) are the beam FWHM at time t, respectively, for the X and Y arm cavities and a 1 is a beam proportionality constant to be determined expermentally. Assuming a 1 1 , then for cavity beams FWHM of δ ω ( t ) ( 523 . 2 ± 31 ) rad . s - 1 the output signal has the range h H ( t ) 1 × 10 - 21 , which is detectable by advanced LIGO.

Subject Areas

universe expansion; Hubble constant; cavity finesse; cosmological redshift; strain

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