Saving the universe with finite volume effects

Setting aside anthropic arguments, there is no reason why the Universe should initially favor a net expanding phase rather than one experiencing a net contraction. However, a collapsing universe containing “normal” matter will end at a singularity in a finite time. We point out that there is a mechanism, derived from nonperturbative effects in quantum field theory in a finite volume, which may provide a bias toward expansion when the spacetime volume shrinks, by dynamically violating the null energy condition, without the need for modified gravity or exotic matter. We describe a scalar field component subjected to this nonperturbative effect in a cosmological background and consider its impact on a contracting phase. We discuss how this could dynamically generate the necessary initial conditions for inflation to get started, or form part of the mechanism for a nonsingular cosmological bounce.

Figure 1

Illustration of finite volume effects on a concave bare potential. Symmetry is restored by tunneling between the two bare minima, which results in a negative energy density in the ground state.

Figure 2

An illustration of the evolution of the scale factor $a$ and Hubble constant $H$ as a function of time $t$ for the cases of (a) initial contraction and (b) initial expansion in our toy model. We see in the collapsing case that the convection field provides the necessary bounce to transition to a period of exponential expansion. If the initial condition is already expanding, the effect of the convection is quickly diluted away.