The general-purpose mortality logmu falls back on where one is needed and none was given, and a reasonable thing to reach for whenever a broadly sensible pensioner basis will do:
$$\log\mu_{xt} = -3.8 + 0.1\,(x - 75) - 0.01\,(t - 2020)$$
It sits about midway between S4PMA and S4PFA at age 75, with a shallower slope to allow for higher mortality at younger ages and for plateauing at higher ones.
Details
Its main use is as the test mortality that sets the \(Z\) scale of a
log-likelihood, which is why fit() and compare_models() default
test_mortality to it. Only slope_x materially matters there, so a single
fixed choice is enough and a shared one is better than a good one: \(Z\) is
the yardstick that makes a difference of one in the penalised log-likelihood
mean one parameter's worth, so two analyses that used different test
mortalities are not on one scale.
It takes no arguments deliberately. Vary it and it is no longer the default
mortality but a Gompertz law of your own, which is what
gompertz_mortality() is for.
It is named logmu default, which is how it appears wherever a mortality is
printed, as in the header of a fit() or a compare_models().
Examples
default_mortality()
#> <mortality_expr: logmu default> ((-3.8 - (0.1 * (.i$birth - 1945-01-01.0))) + (0.09 * (.t - 2020-01-01.0)))
name(default_mortality())
#> [1] "logmu default"
# It is exactly the no-argument Gompertz, given a name.
identical(default_mortality(), gompertz_mortality(name = "logmu default"))
#> [1] TRUE