Information carrying capacity of a cosmological constant

We analyze the exchange of information in different cosmological backgrounds when sender and receiver are timelike separated and communicate through massless fields (without the exchange of light signals). Remarkably, we show that the dominance of a cosmological constant makes the amount of recoverable information imprinted in the field by the sender extremely resilient: it does not decay in time or with the spatial separation of the sender and receiver, and it actually increases with the rate of expansion of the Universe. This is in stark contrast with the information carried by conventional light signals and with previous results on timelike communication through massless fields in matter-dominated cosmologies.

Figure 1

The five possible causal relationships between the switching periods of Alice’s and Bob’s detectors. In conformal time $\eta$ and comoving distance $R$, the boundaries of the light cones (diagonal lines) have slopes of $c=1$.

Figure 2

Scale factors governing the expansion of the matter- ($w=0$) and cosmological constant-dominated ($w=-1$) universes, plotted as functions of time. The four rightmost vertical lines show the earliest times $T_{i\mathrm{B}}$ for which Alice and Bob are strictly timelike separated, while keeping constant their spatial separation. When comoving separation is held constant, $R=1/2$, and when proper separation is approximated as constant, $P(T_{i\mathrm{B}})=1/2$. Here, $T_{i\mathrm{A}}=2/3$, $\mathrm{\Delta }=1/100$, ${\kappa }_1=1/4$, ${\kappa }_2=\exp (-2/3)$, and $\sqrt{|\mathrm{\Lambda }|}=1$.

Figure 3

Variations of the channel capacity with the instant $T_{i\mathrm{B}}$ when Bob’s detector is switched on in a universe dominated by a) matter and b) a cosmological constant. We study the case when the detectors are strictly timelike separated; the vertical lines indicate the earliest $T_{i\mathrm{B}}$ for which this occurs, while the proper/comoving separation is kept constant. Notice that the plots only show the correct channel capacity for values of $T_{i\mathrm{B}}$ that ensure timelike separation (to the right of each dashed vertical line) since (36) and (42) are only valid for timelike separation between Alice and Bob. Here, $T_{i\mathrm{A}}=2/3$, $\mathrm{\Delta }=1/100$, ${\kappa }_1=1/4$, ${\kappa }_2=\exp (-2/3)$, and $\sqrt{|\mathrm{\Lambda }|}=1$. When comoving separation is held constant, $R=1/2$. When proper separation is approximated as constant, $P(T_{i\mathrm{B}})=1/2$. Various values of the detectors’ energy gap $\mathrm{\Omega }$ are considered.