# FindFit and Integration errors

First off, appologies for what may sound like a newbie question, as I am very new to using Mathematica.

I am trying to find a way to get Mathematica to give me an expression that would describe the data I get from my code, but I'm not sure how. I've played around with FindFit and can't seem to get it to work. Also, I have an integral whose integrand relies on two variables, but I'd only like to integrate with respect to one and keep the other constant. I can do this at the "defining a function" stage but am unsure as to how to display the information thereafter. Any help would be much appreciated! Here is my code

a := 3.24077*10^-20 (* km \[Rule] Mpc *)
b := 3.16888*10^-14 (* s \[Rule] MYear *)
c := a/b*(2.99792*10^5) (*Mpc/ MYear*)
H0 := a/b*71 (*1/MYear*)
G := a^3/b^2*6.67398*10^-20 (*Mpc^3/(Kg*MYear^2)*)
\[CapitalOmega]M := 0.27
\[CapitalOmega]\[Gamma] := 8.24*10^-4
\[CapitalOmega]\[CapitalLambda] := 0.73
f := 1*10^-4
y := 100
\[Lambda] := (1/(a^2)) 1*(10^-58)(*1/Mpc^2*)
H[z_] := H0 Sqrt[\[CapitalOmega]M (1 +
z)^3 + \[CapitalOmega]\[Gamma] (1 +
z)^4 + \[CapitalOmega]\[CapitalLambda]]
\[Rho]crit := 3/(8 \[Pi]*G)*(H0)^2
\[Rho]Pert[r_] := \[CapitalOmega]M*\[Rho]crit*(1 + f*Exp[-(r/y)^2])
M1[r_] := 4 \[Pi] Integrate[\[Rho]Pert[r]*r^2, r]
E1[r_] :=
1/2*((H[999]*r)/(c*(1000)))^2 - ((G*M1[r]*(1000))/(
c^2*(r))) - (\[Lambda]*r^2)/(3 (1000)^2)
ScaleFactor =
NDSolveValue[
SetPrecision[{(Sqrt[R[r, t]] (D[R[r, t], t])) == Sqrt[
2*G*M1[r] + 2*c^2*E1[r]*R[r, t] + (2 c^2 \[Lambda]*R[r, t]^3)/
3], R[r, 0] == r/1000}, 200], R, {r, 1, 20000}, {t, 1, 15000}];
Plot3D[Re[ScaleFactor[r, t]], {r, 1, 20000}, {t, 1, 15000},
PlotRange -> Automatic, Axes -> True,
AxesLabel -> {"Comoving Radius (Mpc)", "Time (MegaYears)"},
LabelStyle -> Directive[Bold, Black]]
FindFit[ScaleFactor[r,
t], \[Alpha]*r^n + \[Beta]*t^m, {\[Alpha], \[Beta], n, m}, {r, t}]
ParticleHorizon[r_, t_] :=
c*Integrate[Sqrt[1 + 2*E1[r]]/D[ScaleFactor[r, t], r], t]

-
As currently posted, this strikes me as a "can you debug my code" question. –  m_goldberg Mar 11 at 14:20

sample=Join @@ Table[{r, t, ScaleFactor[r, t]}, {r, 1, 20000, 200}, {t, 1, 15000,  150}];

Thanks alot, that works great for the FindFit! However, I still get an error when I try to do a ParallelTable for ParticleHorizon, which is defined as follows: ParticleHorizondata = ParallelTable[ ParticleHorizon[r, t], {r, 1, 10}, {t, 1, 10}] –  Gokotai Mar 11 at 14:23