Hubble speed from first principles

We introduce a way of measuring $H_0$ from a combination of independent geometrical data sets, without the need for calibration or the choice of a cosmological model. We build on the distance duality relation, which sets the ratio of the luminosity and angular diameter distance to a fixed scaling in redshift for any metric theory of gravity with standard photon propagation and constitutes a founding block of any theory describing our Universe. Our method allows us to determine $H_0$ from first principles, unleashing the measurement of this fundamental constant from calibration and the assumption of a cosmological model. We find $H_0=69.5\pm 1.7\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ at 68% C.L., showing that the Hubble constant can be constrained at the percent level with minimal assumptions.

Figure 1

GP interpolations of the CCH (upper panel) and SNIa (bottom panel) data with different kernels from the Matern family [Eq. (a3)] as well as with the RatQ kernel [Eq. (a2)]. The fits are shown against the data (black dots), which in the SNIa case are the binned Pantheon data. Different colors correspond to different kernels, as shown in the legend. For each kernel, the solid line represents the mean, and the three corresponding shaded regions represent the $1\sigma$ level.

Figure 2

Top panel: angular diameter distance reconstructed from BAO and CC data, and corresponding residual. The points with error bars correspond to the data reconstructed via the GPMC applied to the BAO and CC measurements; the solid blue curve is the GP fit to the data points. Bottom panel: GP fit to the luminosity distance from SNIa (Pantheon) data. In both panels, the dashed black curve shows the $\mathrm{\Lambda }\mathrm{CDM}$ model predictions corresponding to our best-fit $H_0$ and ${\mathrm{\Omega }}_m=0.3$, with respect to which the residuals are calculated.

Figure 3

Top panel: PDFs for the Hubble parameter obtained from Eq. (6), at the seven redshift points of BAO data (shaded curves). The solid black line represents the combined PDF (full result). Bottom panel: PDF for $H_0$ corresponding to our full result (solid black curve) and conservative result (solid blue line), along with recent constraints from SH0ES [2], TRGB [23], and Planck [5]; shaded regions represent the $1\sigma$ interval.