Dark Energy

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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.

thanks

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

Hello Friends

I have a critical problem that I wish to solve it with maple

suppose we have a list like following: y_obs=(2,4,8,7,9,52,35,478,52) and corresponding variance σy=(.2,.3,.5,.87,.1.2,.22,.78,.99,1.5)
we know y as the function of x described such as y_theoric=x+p and minimizing X is

X=Sigma [(y_theoric-y_obs)^2]/σy which includes the sum of nine numbers...

the question is:

How we can find p from likelihood function and plot general behavior of y versus of x through two above series?

for example this solution used in article under the names Hubble parameter data constraints on dark energy by Yun Chen and Bhatra Ratra (Physics Letters B)

Thank you

 

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