I'm having trouble deriving the amount of dimming expected of standard candles (eg. type 1a supernovae) as a result of dark energy. Without the presence of dark energy, the standard GR solution (matter-only, at critical density) is that the absolute bolometric brightness of a standard candle varies with redshift z as 1/(1+z - [1+z]1/2)2. This expression is the product of two terms: 1/DL2 multiplied by 1/(1+z)2. Here DL is the "luminosity distance", which is the expected dimming of light due to geometry. As it turns out, DL is a function of z so that the product simplifies to 1/(1+z - [1+z]1/2)2. Suppose that recent stretching of space due to dark energy is by a factor of b (b>1). Obviously this would change the redshift, replacing 1+z with b(1+z) for a given distant object. (This factor b is the extra stretch that occurred between the time when a given distant object emitted a photon and the present when the photon is received.) How would the factor b change the geometric distance term? The observed luminosity at z=1 is only about half of the value 1/(1+z - [1+z]1/2)2. If one simply replaces 1+z with b(1+z), luminosity vs. redshift curve remains the same instead of reducing to about half at z=1.