Spatial curvature in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity

Abstract

In this work, we consider four $f(R)$ gravity models---the Hu-Sawicki, Starobinsky, Exponential and Tsujikawa models---and use a range of cosmological data, together with Markov Chain Monte Carlo sampling techniques, to constrain the associated model parameters. Our main aim is to compare the results we get when ${\mathrm{\ensuremath{\Omega}}}_{k,0}$ is treated as a free parameter with their counterparts in a spatially flat scenario. The bounds we obtain for ${\mathrm{\ensuremath{\Omega}}}_{k,0}$ in the former case are compatible with a flat geometry. It appears, however, that a higher value of the Hubble constant ${H}_{0}$ allows for more curvature. Indeed, upon including in our analysis a Gaussian likelihood constructed from the local measurement of ${H}_{0}$, we find that the results favor an open universe at a little over $1\ensuremath{\sigma}$. This is perhaps not statistically significant, but it underlines the important implications of the Hubble tension for the assumptions commonly made about spatial curvature. We note that the late-time deviation of the Hubble parameter from its $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ equivalent is comparable across all four models, especially in the nonflat case. When ${\mathrm{\ensuremath{\Omega}}}_{k,0}=0$, the Hu-Sawicki model admits a smaller mean value for ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{cdm},0}{h}^{2}$, which increases the said deviation at redshifts higher than unity. We also study the effect of a change in scale by evaluating the growth rate at two different wave numbers ${k}_{\ifmmode\dagger\else\textdagger\fi{}}$. Any changes are, on the whole, negligible, although a smaller ${k}_{\ifmmode\dagger\else\textdagger\fi{}}$ does result in a slightly larger average value for the deviation parameter $b$.

Topics & Concepts