Graviton creation by small scale factor oscillations in an expanding universe

We treat quantum creation of gravitons by small scale factor oscillations around the average of an expanding universe. Such oscillations can arise in standard general relativity due to oscillations of a homogeneous, minimally coupled scalar field. They can also arise in modified gravity theories with a term proportional to the square of the Ricci scalar in the gravitational action. The graviton wave equation is different in the two cases, leading to somewhat different creation rates. Both cases are treated using a perturbative method due to Birrell and Davies, involving an expansion in a conformal coupling parameter to calculate the number density and energy density of the created gravitons. Cosmological constraints on the present graviton energy density and the dimensionless amplitude of the oscillations are discussed. We also discuss decoherence of quantum systems produced by the spacetime geometry fluctuations due to such a graviton bath.

Figure 1

Oscillatory part of the scale factor in a radiation dominated universe is illustrated in the GRSF model and in $f(R)$ gravity. Here $\delta a(t{)}_{\mathrm{norm}}$ is $\delta a(t)$ expressed in units where $\delta a(t{)}_{\mathrm{norm}}=1$ at an initial time given by $\omega t=1$.

Figure 2

Observational data for $H(z)$ and their errors (see Ref. [28]) are plotted. The solid line gives the fiducial cosmology, which assumes no gravitons with $h_0=0.673$, ${\mathrm{\Omega }}_{r,0}=4.15\times {10}^{-5}{h}_0^{-2}$, ${\mathrm{\Omega }}_{m,0}=0.315$, and ${\mathrm{\Omega }}_{\mathrm{\Lambda }}=1-({\mathrm{\Omega }}_{r,0}+{\mathrm{\Omega }}_{m,0})$. The dashed line is a best fit using the least squares method with nonzero ${\mathrm{\Omega }}_{g,0}$. The boundaries of the regions associated with confidence levels of ${\sigma }_H(z;{\mathrm{\Omega }}_{g,0}^{*})$ and of $3{\sigma }_H(z;{\mathrm{\Omega }}_{g,0}^{*})$ are also illustrated.

Figure 3

The field potential $V(\varphi )$, Eq. (b8), for the model $f(R)=R+(a_2/2)R^2$.