Ultimate fate and age of the universe Hubble's law

the age , ultimate fate of universe can determined measuring hubble constant today , extrapolating observed value of deceleration parameter, uniquely characterized values of density parameters (Ωm matter , ΩΛ dark energy). closed universe Ωm > 1 , ΩΛ = 0 comes end in big crunch , considerably younger hubble age. open universe Ωm ≤ 1 , ΩΛ = 0 expands forever , has age closer hubble age. accelerating universe nonzero ΩΛ inhabit, age of universe coincidentally close hubble age.

the value of hubble parameter changes on time, either increasing or decreasing depending on value of so-called deceleration parameter



q


{\displaystyle q}

, defined by

q
=
−

(
1
+




h
˙



h

2




)

.


{\displaystyle q=-\left(1+{\frac {\dot {h}}{h^{2}}}\right).}

in universe deceleration parameter equal zero, follows h = 1/t, t time since big bang. non-zero, time-dependent value of



q


{\displaystyle q}

requires integration of friedmann equations backwards present time time when comoving horizon size zero.

it long thought q positive, indicating expansion slowing down due gravitational attraction. imply age of universe less 1/h (which 14 billion years). instance, value q of 1/2 (once favoured theorists) give age of universe 2/(3h). discovery in 1998 q apparently negative means universe older 1/h. however, estimates of age of universe close 1/h.