# Brans-Dicke's model: how to shift to the left the curve of scale factor to get a standard age for universe?

Using a MCMC code that implements the Brans-Dicke's model with all the modified equations of field.

Finally, I get this curve that represents the scale factor versus cosmic time:

with the following expression:

and we get finally:

What should I do for priors in my MCMC code to produce an older universe since on this attached ?, the universe is young compared to the LCDM model.

Have I got to play with $$tc$$ or constants $$C1$$ and $$C2$$ in this expression :

?

All I want is to have an older universe (at least -10 Gy from the present).

Any remark/track/clue are welcome.

## Edit:

1. Some precisions for @buzz about the first answer that I got.

Yes, $$\Omega_k\equiv\Omega_K$$ and $$\Omega_{de}=\Omega_{\Lambda}$$ ($$de$$ for Dark Energy).

You are right when you say that I didn't take into account of radiation $$\Omega_{r}$$. Actually, if I include it in the computation of $$\Omega_k=1-\Omega_{m}-\Omega_{\Lambda}-\Omega_{r}, this doesn't seem to have an impact on the young age of universe that I get by computing scale factor$$a(t)$. In my MCMC code, I have put the following priors on cosmological parameters : variables = {$$Omega_m$$,\Omega_k,H0,\Phi_0,d\Phi_0,\Omega_{BD}}; priors={{0.27,0.33},{-0.01,0.01}, {64,76}, {0,4}, {0., 0.01}, {0,1000}};  I get the follwing estimations after an MCMC run : {Ωm, Ωk, Ωde, H0, ϕ0, dϕ0, ωBD, tc} -> {0.270023, 0.00311401, 0.726863, 64.0442, 2.66395, 0.000218655, 907.375, 0.449043}  1. Intuitively, by making decrease the Hubble constant $$H_0$$ (let say $$H_0=60$$, I make universe older with the following curve : I manage to reach over the 8 Gyr instead of 6 in my first attempt. This coould be explained by the fact that age of universe is classical kind of : $$t_{age}=\dfrac{1}{H_0}$$ , so if I take a lower $$H_0$$, I will have an older universe. But the problem is that $$H_0$$ is larger (with Planck, $$H_0=67 km/s/Mpc$$ and with Riess, $$H0=72 km/s/Mpc$$). How to find a way into Brans-Dicke's model to compensate the low estimation of $$H_0=64$$ that I get with MCMC by another parameter (Maybe "$$t_c$$" or $$\omega_{BD}$$) ? The ideal would be to have an estimation close to Planck and have in the same time an older universe ## Edit 2: I have got an interesting result (by playing on H0, omega_BD, phi0 and dphi0) : $$\Omega_r=10^{-4};\\ \Omega_m=0.270023;\\ \Omega_{de}=\Omega_{\Lambda}=0.726863;\\ \Omega_k=1.0-\Omega_m-\Omega_{de}-\Omega_r;\\ H0=67;\\ \Phi_0=0.66395\\ tc=0.0001;\\$$ you can see a first part with decellerated expansion and after an accelerated expansion. Now, I have to make universe older (only 4 Gyrs on my figure) but I don't know how to make it older : I must notify this result is a fine-tuned result by playing with all parameters ## 1 Answer I have been working on a similar problem. https://www.physicsforums.com/threads/seeking-reference-for-math-related-to-the-age-of-recombination.1015331/ I would like to help your problem, but I do not understand your symbols. I get Ω_m and H_0, but I'm not sure about Ω_de and Ω_k. I guess Ω_de is what I call Ω_Lambda. Regarding Ω_k, this is a more accurate value. See http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/denpar.html for the value Ω_k = 8.24 x 10^-5. I am also interested where you got Ω_m = 0.240303 since the value in the reference above is 0.27 . You seem to ignore Ω_r (radiation density). You also seem to ignore the Friedmann equation in If you can clarify my confusion, I will try to help you. • Thanks for your answer. I have put in Edit morre precisons on what I have done. For the scale factor, I use Runge-Kutta 4 applied on modified Friedmann's equations of Brans-Dicke's models (slightly different from LCDM but implying$\omega_{BD}$and$\phi\$ potential). Best regards
– ACat
May 29 at 5:57
• I apologize @ACat . I looked at en.wikipedia.org/wiki/Brans%E2%80%93Dicke_theory. I found that I am completely not able to understand the related mathematics. I would appreciate it you posted a comment with references for the values you included in your post: Ω_m = 0.240303, ΩΛ=0.726863, Ωr=10−4. Also, the equation t = 1/H_0 is wrong. The correct equation is derived from en.wikipedia.org/wiki/Friedmann_equations#Detailed_derivation
– Buzz
May 30 at 18:49
• The correct equation under the above heading is the integral (it has the form below). t H_0 = INTEGRAL(0,a) SQRT("sum of four Omega terms") da.
– Buzz
May 30 at 18:58
• The SQRT should be 1/SQRT.
– Buzz
May 30 at 23:38