Nucleosynthesis in alternative theories of gravity

Abstract

Big Bang nucleosynthesis (BBN) is one of the most reliable tools for testing standard model cosmology, as well as alternative models, well-known models are Brans-Dicke's theory of gravity, quintessence models, and higher-dimensional models. Standard BBN employs general relativity and the standard model of particle physics, thus, relying solely on one adjustable parameter; the baryon number density. Predicted primordial abundances based on SBBN are calculated with the help of BBN codes that contain well-established thermonuclear reactions network involved during the early evolution of the universe and presented as a function of the baryon number density. Observations from CMB and large-scale structure distributions indicate that the baryon number density can be restricted to a small range, allowing us to derive the basic relationship between predicted primordial abundances and new parameters emerging from alternative models of cosmology. All modifications to SBBN enforce the expansion rate of the early evolution of the universe to change, resulting in new relic abundances that differ from element abundances predicted by SBBN. Hence, we can parameterize the deviations from SBBN by introducing the $S$ parameter as $S\equiv H'/H $ where $H'$ is the modified Hubble parameter, $H$ is the Hubble parameter in the first Friedmann equation derived from the Einstein equation inserting the FRW metric. $S$ is constrained with the range of $0.85 \leq S \leq 1.15$ to obtain the simple relations between relic abundances and free parameters of the alternative models. Therefore, with this range of $S$, we can bound for free parameters of non-standard cosmological models. This thesis focuses on two models; Brans-Dicke's theory of gravity and its extensions with self-coupling potentials, and five-dimensional pure gravity which has an extra curled and compact dimension. Both theories have two free parameters. For the five-dimensional pure gravity, the parameters are the scale factor of the extra dimension, $b(t)$, and the length of the extra dimension, $l_c$ whereas the Brans-Dicke theory has parameters $w$ and $\beta$ that comes from the evolution function of the scalar field as $\phi(t) = \phi_i e^{-\beta(t-t_i)}$. To constrain these parameters, we used predicted primordial element abundances, leftover in the first three minutes of the universe, as a function of the number baryon density and expansion rate factor, $S$. In our five-dimensional model, the scale factor $b$ and the length of the extra dimension, $l_c$, directly impact on the synthesis of light elements. Since the range of $S$ is kept limited, that is, the deviation from SBBN is minimal, it is anticipated that its effect decreases as time passes. Therefore, first, it is assumed that the evolution of an extra dimension is $b(t)=b_0e^{-\beta t}$. In that case, predicted $^4 {He}$ mass fraction $Y_p$, $De$ abundance, $y_D$ and $Li$ abundance as a function of $\beta$ and $l_c$ can be obtained and compared with the data inferred from observations. The Big Bang Nucleosynthesis (BBN) bounds on the parameters of the five-dimensional theory of gravity as $\beta \sim 2$x$10^{-2}$, $10^{-7} \lesssim l_c \lesssim 10^{-2}$. It can be seen that $\beta$ works only in a limited range while $l_c$ is suitable in an extensive range. Our motivation for an extra dimension comes from the string theory, which suggests that the extra dimension should be too small to be not detected in a large scale. Hence, it can be concluded that our results are compatible with our motivation. Also, we investigate another possibility that the evolution of the scale factor of an extra dimension as $b=b_0 t^{-p}$. In that case, $p$ is restricted on $p\sim 0.5$ while the broad range of $l_c$ satisfies the theory, $10^{-7} \lesssim l_c \lesssim 10^{-2}$. For Brans-Dicke theory of gravity, first, we studied the effects of the BD scalar field in the absence of potential, $V(\phi)$, on Big Bang Nucleosynthesis. Inserting the FRW metric to the Brans-Dicke field equation, we obtained the modified Hubble parameter of the theory, which depends on various parameters $(\phi,\Dot{\phi},w,\rho)$. Therefore, these parameters can directly alter the synthesis of primordial elements. Within the allowed range of $S$, it is assumed that the effects of a scalar field diminish over time as $\phi(t)=\phi_i e^{-\beta(t-t_i)}$, where $t_i$ is the initial cosmic time. These parameters can be constrained by using $^4 {He}$ mass fraction, $De$, and $Li$ abundances. It is found that $\beta$ is limited in the range of $10^{-5}-10^{-6}$, and for $w$ is $10^{-3}-10^{-2}$. Also, we have obtained the initial value of a scalar field extremely large value as $\phi_i = 1.3$x$10^7$. Next, we looked for alternative models which include scalar field potential, $V(\phi)$, to be compatible with data from BBN. The scalar field potential is taken polynomial function as $V(\phi) = V_0 \phi^n$. In all cases, from $n=-1$ to $n=3$, the same conclusion as the previous model without scalar field potential has been achieved; the theory is highly dependent on the initial condition of the scalar field and requires a considerably large value of $\phi_i$.