The cosmological constant as a zero action boundary

ABSTRACT The cosmological constant Λ is usually interpreted as Dark Energy (DE) or modified gravity (MG). Here, we propose instead that Λ corresponds to a boundary term in the action of classical General Relativity. The action is zero for a perfect fluid solution and this fixes Λ to the average density ρ and pressure p inside a primordial causal boundary: Λ = 4πG <ρ+3p >. This explains both why the observed value of Λ is related to the matter density today and also why other contributions to Λ, such as DE or MG, do not produce cosmic expansion. Cosmic acceleration results from the repulsive boundary force that occurs when the expansion reaches the causal horizon. This universe is similar to the ΛCDM universe, except on the largest observable scales, where we expect departures from homogeneity/isotropy, such as CMB anomalies and variations in cosmological parameters indicated by recent observations.

The Bayesian stance: Equations for ‘as-if’ sensorimotor agency

The verb ‘to do’ plays a vital part in our understanding of the world, and it goes hand-in-hand with words such as active, action and agent. But the physical sciences describe only mechanical happenings, not acts. Their theoretical language is, in essence, a strict mathematical formalism applied to the description of variables (usually quantitative ones) that can – at least in principle – be measured by mechanical instruments. In such a language, what is the definition of an agent? Of an act? In contrast to previous approaches, which attempt to discriminate between agent and non-agent systems, we pursue a more Dennettian approach that attempts only to characterise the explanatory logic of intentional (agentive) interpretations of a physical system; we wish to do so purely in terms of the formal relations that hold between variables in a dynamical system or stochastic process. Our approach is straightforward: we use Pearl’s causal formalism to identify physical variables at the causal boundary between ‘agent’ and ‘environment’, and identify these with variables in Bayesian decision theory; this provides a rigorous bridge between mathematical models of physics and mathematical models of rational decision-making.