We present an analysis of the Hubble diagram for 12 Type Ia supernovae (SNe
Ia) observed in the near-infrared J and H bands. We select SNe exclusively from
the redshift range 0.03 < z < 0.09 to reduce uncertainties coming from peculiar
velocities while remaining in a cosmologically well-understood region. All of
the SNe in our sample exhibit no spectral or B-band light-curve peculiarities
and lie in the B-band stretch range of 0.8-1.15. Our results suggest that SNe
Ia observed in the near-infrared (NIR) are the best known standard candles. We
fit previously determined NIR light-curve templates to new high-precision data
to derive peak magnitudes and to determine the scatter about the Hubble line.
Photometry of the 12 SNe is presented in the natural system. Using a standard
cosmology of (H_0, Omega_m, Lambda) = (70,0.27,0.73) we find a median J-band
absolute magnitude of M_J = -18.39 with a scatter of 0.116 and a median H-band
absolute magnitude of M_H = -18.36 with a scatter of 0.085. The scatter in the
H band is the smallest yet measured. We search for correlations between
residuals in the J- and H-band Hubble diagrams and SN properties, such as SN
colour, B-band stretch and the projected distance from host-galaxy centre. The
only significant correlation is between the J-band Hubble residual and the J-H
pseudo-colour. We also examine how the scatter changes when fewer points in the
near-infrared are used to constrain the light curve. With a single point in the
H band taken anywhere from 10 days before to 15 days after B-band maximum light
and a prior on the date of H-band maximum set from the date of B-band maximum,
we find that we can measure distances to an accuracy of 6%. The precision of
SNe Ia in the NIR provides new opportunities for precision measurements of both
the expansion history of the universe and peculiar velocities of nearby
galaxies.Comment: 6 pages, 2 figures. Accepted for publication in MNRA