There might be some extra bits feel free to remove ClearAll["Global`*"]; n = 4; coord = {t, x, y, z}; (*For raising/lowering latin indices like a, b, ...*) \[Eta] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}; \[Eta] // MatrixForm; inveta = Inverse[\[Eta]]; inveta // MatrixForm; (*"e-Metric";*) e = {{\[ScriptCapitalN][t], 0, 0, 0}, {0, \[ScriptA][t], 0, 0}, {0, 0, \[ScriptA][t], 0}, {0, 0, 0, \[ScriptA][t]}}; \[ScriptCapitalN][t] = -1; e // MatrixForm; dete = Det[e]; (*Inverse e-Metric*) inve = Inverse[e]; inve // MatrixForm; detinve = Det[inve]; g := g = Simplify[Table[ ParallelSum[ \[Eta][[a, b]]*e[[a, \[Mu]]]*e[[b, \[Nu]]] , {a, 1, n}, {b, 1, n}] , {\[Mu], 1, n}, {\[Nu], 1, n}]] g // MatrixForm; (*g is used to LOWER indices for Greek indices \[Mu], \[Nu]*) invg = Inverse[g]; invg // MatrixForm; (*invg is used to RAISE indices for Greek indices \[Mu], \[Nu]*) (* In the form \[CapitalGamma]^{x}_{xx}*) affine := affine = Simplify[Table[(1/2)*Sum[(invg[[i, s]])* (D[g[[s, j]], coord[[k]] ] + D[g[[s, k]], coord[[j]] ] - D[g[[j, k]], coord[[s]] ]), {s, 1, n}], {i, 1, n}, {j, 1, n}, {k, 1, n}] ]; listaffine := Table[If[UnsameQ[affine[[i, j, k]], 0], {ToString[\[CapitalGamma][i, j, k]], affine[[i, j, k]]}] , {i, 1, n}, {j, 1, n}, {k, 1, j}]; TableForm[Partition[DeleteCases[Flatten[listaffine], Null], 2], TableSpacing -> {2, 2}]; (* In the form R^{x}_{xxx} *) riemann := riemann = Simplify[Table[ D[affine[[i, j, l]], coord[[k]] ] - D[affine[[i, j, k]], coord[[l]] ] + Sum[ affine[[s, j, l]] affine[[i, k, s]] - affine[[s, j, k]] affine[[i, l, s]], {s, 1, n}], {i, 1, n}, {j, 1, n}, {k, 1, n}, {l, 1, n}] ]; listriemann := Table[If[UnsameQ[riemann[[i, j, k, l]], 0], {ToString[R[i, j, k, l]], riemann[[i, j, k, l]]}] , {i, 1, n}, {j, 1, n}, {k, 1, n}, {l, 1, k - 1}] TableForm[Partition[DeleteCases[Flatten[listriemann], Null], 2], TableSpacing -> {2, 2}]; (* In the form R_{xxxx} *) riemann1 := riemann1 = Simplify[Table[ Sum[ g[[\[Mu], \[Mu]1]]*riemann[[\[Mu]1, \[Nu], \[Rho], \[Sigma]]] , {\[Mu]1, 1, n}] , {\[Mu], 1, n}, {\[Nu], 1, n}, {\[Rho], 1, n}, {\[Sigma], 1, n}]] listriemann1 := Table[If[UnsameQ[riemann1[[\[Mu], \[Nu], \[Rho], \[Sigma]]], 0], {ToString[R1[\[Mu], \[Nu], \[Rho], \[Sigma]]], riemann1[[\[Mu], \[Nu], \[Rho], \[Sigma]]]}] , {\[Mu], 1, n}, {\[Nu], 1, n}, {\[Rho], 1, n}, {\[Sigma], 1, \[Rho] - 1}]; TableForm[Partition[DeleteCases[Flatten[listriemann1], Null], 2], TableSpacing -> {2, 2}]; (* In the form R^{xxxx} *) riemann2 := riemann2 = Simplify[Table[ Sum[ Sum[ Sum[ invg[[\[Nu]1, \[Nu]]]*invg[[\[Rho]1, \[Rho]]]* invg[[\[Sigma]1, \[Sigma]]]* riemann[[\[Mu], \[Nu]1, \[Rho]1, \[Sigma]1]] , {\[Nu]1, 1, n}] , {\[Rho]1, 1, n}] , {\[Sigma]1, 1, n}] , {\[Mu], 1, n}, {\[Nu], 1, n}, {\[Rho], 1, n}, {\[Sigma], 1, n}]] listriemann2 := Table[If[UnsameQ[riemann2[[\[Mu], \[Nu], \[Rho], \[Sigma]]], 0], {ToString[R2[\[Mu], \[Nu], \[Rho], \[Sigma]]], riemann2[[\[Mu], \[Nu], \[Rho], \[Sigma]]]}] , {\[Mu], 1, n}, {\[Nu], 1, n}, {\[Rho], 1, n}, {\[Sigma], 1, \[Rho] - 1}]; TableForm[Partition[DeleteCases[Flatten[listriemann2], Null], 2], TableSpacing -> {2, 2}]; KretschmannScalar = Simplify[ Sum[riemann1[[a, b, c, d]]*riemann2[[a, b, c, d]], {a, 1, n}, {b, 1, n}, {c, 1, n}, {d, 1, n}]] With that input metric I got this answer: $\frac{12 \left(\mathit{a}(t)^2 \mathit{a}''(t)^2+\mathit{a}'(t)^4\right)}{\mathit{a}(t)^4}$