We re-investigated the use of the Hubble diagram to measure the cosmological constant (Λ) and the mass density of the Universe (ΩM). We find an important focusing effect in Λ for redshifts of about 3. This effect implies that the apparent magnitude of a standard candle at redshifts z=2–3 has almost no dependence on Λ for ΩM>0.2. This means that ΩM can be measured independently of ΩΛ by targeting the redshift range according to an estimate of the value of ΩM.
We explore the evidence in support of the suggestion that extreme starburst galaxies, also known as H ii galaxies, can be used as distance estimators over a wide range of redshifts and reaching very high values. We have compiled literature data of H ii galaxies up to z∼3 and found a good correlation between their luminosity and velocity dispersion measured from their strong emission lines, thus confirming the correlation already known to exist for H ii galaxies in the nearby Universe. Several systematic effects, such as age, extinction, kinematics and metallicity, are discussed, as well as the effects of different cosmologies.