Return to Answer

Please note that the model of the universe corresponding to ΩR=ΩNR=Ωk=0, ΩΛ=1 has no matter and no radiation and no curvature. This is an empty Euclidean universe with no expansion. Therefore Ho and a are and H0 are both constants. Since da/dt = 0, then Ho = 0. The integral of da/a is ln a, which is infinity. Since H0 has units 1/t, this means T = infinity.

Please note that the model of the universe corresponding to ΩR=ΩNR=Ωk=0, ΩΛ=1 has no matter and no radiation and no curvature. This is an empty Euclidean universe with no expansion. Therefore Ho and a are and both constants. Since da/dt = 0, then Ho = 0. If a was a variable rather than a constant, then the integral of da/a is ln a, which is infinity. For da = 0, this integral is zero. Since H0 has units 1/t, T = can be chosen as any constant with a time unit.

Please note that the model of the universe corresponding to ΩR=ΩNR=Ωk=0, ΩΛ=1 has no matter and no radiation and no curvature. This is an empty Euclidean universe, and H0 is an arbitrary constant. Since da/dt = 0, Ho = 0. The integral of da/a is ln a, which is infinity. Since H0 has units 1/t, this means T = infinity.

Please note that the model of the universe corresponding to ΩR=ΩNR=Ωk=0, ΩΛ=1 has no matter and no radiation and no curvature. This is an empty Euclidean universe with no expansion. Therefore Ho and a are and H0 are both constants. Since da/dt = 0, then Ho = 0. The integral of da/a is ln a, which is infinity. Since H0 has units 1/t, this means T = infinity.

Please note that the model of the universe corresponding to ΩR=ΩNR=Ωk=0, ΩΛ=1 has no matter and no radiation and no curvature. This is an empty Euclidean universe, and H0 = 0. Since H0 has units 1/t, this means T = infinity. The integral of da/a is ln a, which is also infinity.

Please note that the model of the universe corresponding to ΩR=ΩNR=Ωk=0, ΩΛ=1 has no matter and no radiation and no curvature. This is an empty Euclidean universe, and H0 is an arbitrary constant. Since da/dt = 0, Ho = 0. The integral of da/a is ln a, which is infinity. Since H0 has units 1/t, this means T = infinity.