Its the Friedmann Equation. trying to add adjustable sliders any ideas would be helpful..
% Define the parameters
Omega_M = .31; % Assign the actual value for matter density parameter
Omega_A = .70; % Assign the actual value for dark energy density parameter
% Define the initial conditions
R0 = 1; % Initial value of R at t = t0
dRdt0 = 1; % Initial value of dR/dt at t = t0
% Define the time span for the solution
t0 = 0; % Start time
tf = 1; % End time
% Solve the system of ODEs using ode45
options = odeset('RelTol',1e-8,'AbsTol',1e-10); % Set tolerances if needed
[t, Y] = ode45(@(t, Y) cosmologyODEs(t, Y, Omega_M, Omega_A), [t0 tf], [R0; dRdt0], options);
% Extract the solution for R and dR/dt
R_solution = Y(:, 1);
dRdt_solution = Y(:, 2);
% Plot the solution for R as a function of time
plot(t, R_solution);
xlabel('Time');
ylabel('R(t)');
title('Evolution of R over time');
% Define the system of ODEs as a function
function dYdt = cosmologyODEs(t, Y, Omega_M, Omega_A)
R = Y(1);
dRdt = Y(2);
% First derivative of R
dRdt1 = dRdt;
% Second derivative of R
dRdt2 = -Omega_M/(2 * R^2) + Omega_A * R;
dYdt = [dRdt1; dRdt2];
end
