Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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. Oliveira, F.J. On the Expansion of Space and How to Measure It. Preprints 2018, 2018020170.


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.


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


Physical Sciences, Astronomy and Astrophysics

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