Early universe constraints on time variation of fundamental constants

We study the time variation of fundamental constants in the early Universe. Using data from primordial light nuclei abundances, cosmic microwave background, and the 2dFGRS power spectrum, we put constraints on the time variation of the fine structure constant $\alpha$ and the Higgs vacuum expectation value $⟨v⟩$ without assuming any theoretical framework. A variation in $⟨v⟩$ leads to a variation in the electron mass, among other effects. Along the same line, we study the variation of $\alpha$ and the electron mass $m_e$. In a purely phenomenological fashion, we derive a relationship between both variations.

Figure 1

$N_A⟨\sigma v⟩$ (in units of ${10}^7{\mathrm{cm}}^3{\mathrm{s}}^{-1}{\mathrm{g}}^{-1}$) for the reaction $d+d\to p+t$, as a function of the temperature (in units of ${10}^9\mathrm{K}$), when $\frac{\Delta \alpha }{{\alpha }_0}=-0.1$ (solid line), $\frac{\Delta \alpha }{{\alpha }_0}=0.0$ (dashed line), and $\frac{\Delta \alpha }{{\alpha }_0}=0.1$ (dotted line).

Figure 2

Left figure: Likelihood contours for $\frac{\Delta \alpha }{{\alpha }_0}$, $\frac{\Delta ⟨v⟩}{⟨v{⟩}_0}$, and ${\eta }_B$ (in units of ${10}^{-10}$) and one-dimensional likelihood (using $\frac{\Delta {ϵ}_D}{({ϵ}_D{)}_0}=-6.230\frac{\Delta ⟨v⟩}{⟨v{⟩}_0}$). Right figure: Likelihood contours for $\frac{\Delta \alpha }{{\alpha }_0}$, $\frac{\Delta m_e}{(m_e{)}_0}$, and ${\eta }_B$ (in units of ${10}^{-10}$) and one-dimensional likelihood.

Figure 3

Likelihood contours for $\frac{\Delta \alpha }{{\alpha }_0}$ vs $\frac{\Delta ⟨v⟩}{⟨v{⟩}_0}$ and one-dimensional likelihood. Left figure: $\mathrm{D}+{}^7\mathrm{Li}$ data; right figure: $\mathrm{D}+{}^4\mathrm{He}$. The figures were obtained using $\frac{\Delta {ϵ}_D}{({ϵ}_D{)}_0}=-6.230\frac{\Delta ⟨v⟩}{⟨v{⟩}_0}$.

Figure 4

Likelihood contours for $\frac{\Delta \alpha }{{\alpha }_0}$ vs $\frac{\Delta m_e}{(m_e{)}_0}$ and one-dimensional likelihood. Left figure: $\mathrm{D}+{}^4\mathrm{He}+{}^7\mathrm{Li}$ data; right figure: $\mathrm{D}+{}^4\mathrm{He}$.

Figure 5

Ionization history as a function of redshift, for different values of $\alpha$ (left panel) and $m_e$ (right panel) at recombination time.

Figure 6

Visibility function as a function of conformal time in Mpc, for different values of $\alpha$ (left panel) and $m_e$ (right panel).

Figure 7

The spectrum of CMB fluctuations for different values of $\alpha$ (left panel) and $m_e$ (right panel).

Figure 8

Marginalized posterior distributions obtained with CMB data, including the WMAP 3-year data release plus 2dFGRS power spectrum. The diagonal shows the posterior distributions for individual parameters, the other panels show the 2D contours for pairs of parameters, marginalizing over the others.

Figure 9

$1\sigma$ and $2\sigma$ contour levels. Dotted line: variation of $\alpha$ and $⟨v⟩$; solid line: only $\alpha$ variation. The cosmological parameters are free to vary in both cases.

Figure 10

$1\sigma$ and $2\sigma$ contour levels. Dotted line: variation of $\alpha$ and $⟨v⟩$; solid line: only $⟨v⟩$ variation. The cosmological parameters are free to vary in both cases.

Figure 11

2D contour levels for variation of $\alpha$ and $⟨v⟩$ from BBN (solid line) and CMB (dotted line) data.

Figure 12

2D contour levels for variation of $\alpha$ and $m_e$ from BBN (solid line) and CMB (dotted line) data.