Dark Energy

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These are questions asked by Dark Energy


I want to find abs(psi)^2 for below psi

psi=int(int(exp(-a*(mu-b)^2)*exp(-c*(V-d)^2)*exp(I*(Q*u-(5/3*Q)*v^(mu/V)-3/16*(v^(4/V)/Q)))*v^((1/2)*(1-V)/V), mu = 0 .. 2), V = -15 .. 15) when mu=0..2 and V=-15..15 for Q:=3, a=10, c=5, b=3 and d=0.

unfortunatelly, I write above psi in maple 18 but it does not work, please tell me how to calculate (abs(psi))^2 for above wave equation (psi).

with the best regard.

Hi guys

I want to solve the following differential equation but I can not. please help me in this way

diff(phi((8*R^(3/2)-W)*sqrt(2)/(24*sqrt(M))), W$2)=lambda*phi((8*R^(3/2)-W)*sqrt(2)/(24*sqrt(M)))


with the best regard

Hello my friends

I want to solve first order non-linear differential equation by maple 2018 but it does not give me the explicit form for a(t) as the function of time t.

this is my equation where z,k,c, and w are non zero constants 

3*a(t)-a(t)^2-3*z*(diff(a(t), t))^2+k*c*a(t)+w/a(t) = 0

please guide me.

with the best regard

Hello guys

I have a simple but crucial question about variation, especially in cosmology and gravity. suppose we have the action such as

S=int(sqrt(-g)*F(R,RµναβRµναβ),d^4x) where g is determinant metric gµν and d^4x is space in 4D and F is an arbitrary function of R (Ricci scalar) and scalar which created by Riemann tensor. How we can define this action in the maple 18 and take variation with respect to the metric.


Hello my friends

I have some problems with maple 18. I try to consider and extract some things about tensor such as contraction.

for instance, suppose we have metric=-exp(alpha(r))*(dt^2)+exp(beta(r))*(dr^2)+r^2*(dtheta^2)+r^2*(sin(theta)^2)*(dphi^2). how we can find all Riemann tensor and corresponding contraction, Ricci tensor and its contraction and even Weyl tensor and its contraction. unfortunately, I attempt to find them by using some other examples on the net but they don't help me to calculate them when time is the first element in coordinate, not last ( t,r,theta,phi) not (r,theta,phi)

thanks with the best regard

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