I am studying this very interesting paper that appeared on the archive in October,
I am usually a factor [tex]\pi[/tex] months late with the respect to new posts so I apologize for being late, but I am very much puzzled and maybe someone in the forum may
light on.
In section VII (first paragraph at the bottom of the column), the authors state:
I found this very confusing, shouldn't be exactly the opposite? At least in the case [tex]w>-1[/tex], the acceleration starts earlier for [tex]w\rightarrow -1[/tex],The above discussion assumes that the acceleration is due to a cosmological constant.....For [tex]w>-1[/tex], the ISW signal is enhanced, increasing the best fit value of [tex]\Omega_M[/tex] relative to the [tex]w=-1[/tex] case, while [tex]w<-1[/tex] reduces the signal, allowing for even lower values of [tex]\Omega_M[/tex].
hence the expansion rate starts deviating from the Matter Dominated behaviour earlier and consequently produces a larger ISW signal.
In particular if we limit to models with [tex]w>-1[/tex] the LCDM has the largest signal and I think there is pretty much consensus on this as it has been found in a number of papers. For models with [tex]w<-1[/tex] the ISW is actually enanced and not suppressed.
I tried to check their plot in Fig.12, so using their galaxy window function I have computed the cross-correlation power spectrum [tex]X_l[/tex] for different values of constant [tex]w[/tex] and keept the cosmological parameters fixed to the values of Fig.12.
However I cannot reproduce their trend, where the ratio [tex]x=\frac{X_l(w)}{X_l(-1)}[/tex] increases as function of [tex]w=-1.3 \rightarrow -0.7[/tex]. In agreement with the previous argument I found exactly the opposite.
In the case with no dark energy perturbations, such that the ISW is entirely caused by the background expansion, I found [tex]x \rightarrow 0[/tex] for [tex]w \rightarrow 0[/tex], as can been seen here
While accounting for the dark energy perturbations slightly modify this behaviour since they can affects the late time evolution of the gravitational potentials,
in particular I found that [tex]x[/tex] increases up to [tex]w=-0.8[/tex] and then decreases for [tex]w>-0.8[/tex].
Comments are welcome I wish to understand the cause of the discrepancy.
All the best,
Pier-Stefano