F(R) gravity and the Hubble parameter

In summary, the conversation discusses the use of Einstein field equations to obtain the Friedman equations and Hubble parameter, as well as the complications that arise when using f(R) models. The equations involve the fourth order of the scale factor and it is unclear if they can be solved in the matter dominated era. The use of the FRW metric is also mentioned, along with a question about the change of Hubble parameter with f(R) and possible approximations.
  • #1
shadishacker
30
0
Dear all,

Considering Einstein Hilbert lagrangian, by using Einstein field equations one can get the form of Friedman equations and consequently the Hubble parameter.
I know that in f(R) models, Einstein equations get modified. However, what happens to the Friedman equation and the Hubble parameter?
I tried to solve them and get to the form of H, but it seems such a complicated equation.

Using the (00) component, I get
\begin{equation}
H^2=\frac{8\pi G}{3}\rho -\frac{6\alpha}{c^2}(\frac{\ddot{a}^2}{a^2} + H^4)
\end{equation}
What should I do with the
\begin{equation} \ddot{a}^2\end{equation}
in the first equation?!
The (11) component just makes everything more complicated!
I really appreciate any help or idea.
BTW, I am using FRW metric.
 
Last edited:
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  • #2
I just realized that the equations consist the forth order of the scale factor (a(t)).
Are these solvable in the matter dominated era? when
\begin{equation}
\rho(z)=\rho_m a^{-3}
\end{equation}
 
  • #3
Has anybody seen any paper on the change of Hubble parameter with f(R)? Is there at least any approximation?
 

1. What is F(R) gravity and how does it differ from Einstein's theory of general relativity?

F(R) gravity is a modified theory of gravity that incorporates an additional term, denoted by F(R), into Einstein's equations of general relativity. This term accounts for the effects of higher-order curvature terms on the gravitational field, allowing for a different description of the relationship between matter and space-time.

2. How does F(R) gravity affect the Hubble parameter, and what implications does this have for our understanding of the universe?

In F(R) gravity, the Hubble parameter, which describes the rate at which the universe is expanding, is modified by the additional F(R) term. This can lead to a different interpretation of the expansion rate and potentially affect our understanding of the evolution of the universe and its ultimate fate.

3. Can F(R) gravity explain the observed accelerated expansion of the universe?

F(R) gravity has been proposed as a possible explanation for the accelerated expansion of the universe, which was first discovered through observations of distant supernovae. However, more research is needed to determine if F(R) gravity can fully account for this phenomenon or if additional factors are at play.

4. How do scientists test and validate F(R) gravity as a theory?

Scientists use a variety of methods to test and validate F(R) gravity, including comparing its predictions to observations of the universe on both small and large scales. They also study the effects of F(R) gravity on gravitational waves, galaxy clusters, and other astronomical objects to further understand its implications and potential limitations.

5. What are some potential implications of F(R) gravity for our current understanding of gravity and the laws of physics?

F(R) gravity challenges our current understanding of gravity and the laws of physics by introducing a new term into Einstein's equations. It also has implications for the concept of dark energy, which is thought to drive the accelerated expansion of the universe. Further research on F(R) gravity may lead to a better understanding of these fundamental concepts and potentially revolutionize our understanding of the universe.

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