Constraining power of cosmological observables: blind redshift spots and optimal ranges. (arXiv:1812.05356v1 [astro-ph.CO])

Constraining power of cosmological observables: blind redshift spots and optimal ranges. (arXiv:1812.05356v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Kazantzidis_L/0/1/0/all/0/1">L. Kazantzidis</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Perivolaropoulos_L/0/1/0/all/0/1">L. Perivolaropoulos</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Skara_F/0/1/0/all/0/1">F. Skara</a>

A cosmological observable measured in a range of redshifts can be used as a
probe of a set cosmological parameters. Given the cosmological observable and
the cosmological parameter, there is an optimum range of redshifts where the
observable can constrain the parameter in the most effective manner. For other
redshift ranges the observable values may be degenerate with respect to the
cosmological parameter values and thus inefficient in constraining the given
parameter. These are blind redshift ranges. We determine the optimum and the
blind redshift ranges of basic cosmological observables with respect to three
cosmological parameters: the matter density parameter $Omega_m$, the equation
of state parameter $w$ and a modified gravity parameter $g_a$ which
parametrizes the evolution of an effective Newton’s constant. We consider the
observables: growth rate of matter density perturbations expressed through
$f(z)$ and $fsigma_8$, the distance modulus $mu(z)$, Baryon Acoustic
Oscillation observables $D_V(z) times frac{r_s^{fid}}{r_s}$, $H times
frac{r_s}{r_s^{fid}}$ and $D_A times frac{r_s^{fid}}{r_s}$, $H(z)$
measurements and the gravitational wave luminosity distance. We introduce a new
statistic $S_P^O(z)equiv frac{delta O}{delta P}(z)$ as a measure of the
constraining power of a given observable $O$ with respect to a cosmological
parameter $P$ as a function of redshift $z$. We find blind redshift spots $z_b$
($S_P^O(z_b)simeq 0$) and optimal redshift spots $z_s$ ($S_P^O(z_s)simeq
max$) for the above observables with respect to the parameters $Omega_m$, $w$
and $g_a$. For example for $O=fsigma_8$ and $P=(Omega_{m},w,g_a)$ we find
blind spots at $z_bsimeq(1,2,2.7)$ respectively and optimal (sweet) spots at
$z_s=(0,0.5,0.5)$. Thus probing higher redshifts may in some cases be less
effective than probing lower redshifts with higher accuracy.

A cosmological observable measured in a range of redshifts can be used as a
probe of a set cosmological parameters. Given the cosmological observable and
the cosmological parameter, there is an optimum range of redshifts where the
observable can constrain the parameter in the most effective manner. For other
redshift ranges the observable values may be degenerate with respect to the
cosmological parameter values and thus inefficient in constraining the given
parameter. These are blind redshift ranges. We determine the optimum and the
blind redshift ranges of basic cosmological observables with respect to three
cosmological parameters: the matter density parameter $Omega_m$, the equation
of state parameter $w$ and a modified gravity parameter $g_a$ which
parametrizes the evolution of an effective Newton’s constant. We consider the
observables: growth rate of matter density perturbations expressed through
$f(z)$ and $fsigma_8$, the distance modulus $mu(z)$, Baryon Acoustic
Oscillation observables $D_V(z) times frac{r_s^{fid}}{r_s}$, $H times
frac{r_s}{r_s^{fid}}$ and $D_A times frac{r_s^{fid}}{r_s}$, $H(z)$
measurements and the gravitational wave luminosity distance. We introduce a new
statistic $S_P^O(z)equiv frac{delta O}{delta P}(z)$ as a measure of the
constraining power of a given observable $O$ with respect to a cosmological
parameter $P$ as a function of redshift $z$. We find blind redshift spots $z_b$
($S_P^O(z_b)simeq 0$) and optimal redshift spots $z_s$ ($S_P^O(z_s)simeq
max$) for the above observables with respect to the parameters $Omega_m$, $w$
and $g_a$. For example for $O=fsigma_8$ and $P=(Omega_{m},w,g_a)$ we find
blind spots at $z_bsimeq(1,2,2.7)$ respectively and optimal (sweet) spots at
$z_s=(0,0.5,0.5)$. Thus probing higher redshifts may in some cases be less
effective than probing lower redshifts with higher accuracy.

http://arxiv.org/icons/sfx.gif