Mapping the inhomogeneous Universe with Standard Sirens: Degeneracy between inhomogeneity and modified gravity theories. (arXiv:2007.15020v1 [astro-ph.CO])

<a href="http://arxiv.org/find/astro-ph/1/au:+Kalomenopoulos_M/0/1/0/all/0/1">Marios Kalomenopoulos</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Khochfar_S/0/1/0/all/0/1">Sadegh Khochfar</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Gair_J/0/1/0/all/0/1">Jonathan Gair</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Arai_S/0/1/0/all/0/1">Shun Arai</a>

The detection of gravitational waves (GWs) and an accompanying

electromagnetic (E/M) counterpart have been suggested as a future probe for

cosmology and theories of gravity. In this paper, we present calculations of

the luminosity distance of sources taking into account inhomogeneities in the

matter distribution that are predicted in numerical simulations of structure

formation. We assume mock GWs sources, with known redshift, based on binary

population synthesis models, between redshifts $z=0$ and $z=5$. We show that

present systematic limits of observations allow for a wide range of effective

inhomogeneous models to be consistent with a homogeneous and isotropic

Friedman-Lema{^i}tre-Robertson-Walker background model. Increasing the number

of standard sirens from $150$ to $350$ and up to $z=5$ helps shrink the

confidence contours $(68% rm{C.L.})$ by $sim 35 %$, but still leaving the

inhomogeneity parameters loosely constrained. In addition, we show that

inhomogeneities resulting from clustering of matter can mimic certain classes

of modified gravity theories, or other effects that dampen GW amplitudes, and

deviations larger than $delta nu sim mathcal{O}(0.1) (99% rm{C.L.})$ to

the extra friction term $nu$, from zero, would be necessary to distinguish

them. This limit is determined by observational errors (signal-to-noise ratio)

and to improve on this constraint by an order of magnitude, one would need to

reduce systematic observational errors to about one-fifth of their current

values.

The detection of gravitational waves (GWs) and an accompanying

electromagnetic (E/M) counterpart have been suggested as a future probe for

cosmology and theories of gravity. In this paper, we present calculations of

the luminosity distance of sources taking into account inhomogeneities in the

matter distribution that are predicted in numerical simulations of structure

formation. We assume mock GWs sources, with known redshift, based on binary

population synthesis models, between redshifts $z=0$ and $z=5$. We show that

present systematic limits of observations allow for a wide range of effective

inhomogeneous models to be consistent with a homogeneous and isotropic

Friedman-Lema{^i}tre-Robertson-Walker background model. Increasing the number

of standard sirens from $150$ to $350$ and up to $z=5$ helps shrink the

confidence contours $(68% rm{C.L.})$ by $sim 35 %$, but still leaving the

inhomogeneity parameters loosely constrained. In addition, we show that

inhomogeneities resulting from clustering of matter can mimic certain classes

of modified gravity theories, or other effects that dampen GW amplitudes, and

deviations larger than $delta nu sim mathcal{O}(0.1) (99% rm{C.L.})$ to

the extra friction term $nu$, from zero, would be necessary to distinguish

them. This limit is determined by observational errors (signal-to-noise ratio)

and to improve on this constraint by an order of magnitude, one would need to

reduce systematic observational errors to about one-fifth of their current

values.

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