Localized particle states and dynamic gravitational effects

Scalar particles—i.e., scalar-field excitations—in de Sitter space exhibit behavior unlike either classical particles in expanding space or quantum particles in flat spacetime. Their energies oscillate forever, and their interactions are spread out in energy. Here it is shown that these features characterize not only normal-mode excitations spread out over all space, but localized particles or wave packets as well. Both one-particle and coherent states of a massive, minimally coupled scalar field in de Sitter space, associated with classical wave packets, are constructed explicitly. Their energy expectation values and corresponding Unruh-DeWitt detector response functions are calculated. Numerical evaluation of these quantities for a simple set of classical wave packets clearly displays these novel features. Hence, given the observed accelerating expansion of the Universe, it is possible that observation of an ultralow-mass scalar particle could yield direct confirmation of distinct predictions of quantum field theory in curved spacetime.

Figure 1

Evolution of a spherically symmetric, initially Gaussian scalar wave packet in de Sitter space, centered on the “north pole” (${\theta }_1=0$). The (angular) width of the initial Gaussian here is $\sigma \doteq 0.1414$. The field $\Phi$ is rescaled by ${cosh}^{3/2}(t/a)$ to compensate for the physical expansion of the space.

Figure 2

Excitation energies ${\mathcal{E}}_c$ of coherent (Glauber) field states corresponding to initially Gaussian classical wave packets. The energy for the initially pointlike ($\sigma \to 0$) wave packet decreases monotonically from a value of $80.4133a^{-1}$ at $t=0$ to the region shown here.

Figure 3

Detector response functions ${\mathcal{F}}_c$ for coherent field states corresponding to initially Gaussian wave packets, above the Euclidean-vacuum contribution (“dark current”). The detector is comoving at the “north pole” ${\theta }_1=0$. Responses for smeared one-particle states corresponding to the same wave packets are indistinguishable from these on this scale.

Figure 4

Detector response functions ${\mathcal{F}}_1$ and ${\mathcal{F}}_c$ for smeared one-particle and coherent states corresponding to an initially Gaussian wave packet with $\sigma =0.2236$. Here the detector is comoving at the “equator” (${\theta }_1=\pi /2$).

Figure 5

Detector responses ${\mathcal{F}}_1$ for smeared one-particle states corresponding to initially Gaussian wave packets. Here the detector is comoving at the “south pole” (${\theta }_1=\pi$). Responses for coherent states for the same wave packets, for this detector position, are negligible on the scale of this graph (and below the resolution of the calculation).