**Stephen Adler**

*Institute for Advanced Study, Princeton, USA*

## Incorporating Gravity Into Trace Dynamics: the Induced Gravitational Action

I study the incorporation of gravity into trace dynamics, which I have proposed as a pre-quantum theory from which quantum mechanics emerges as a thermodynamic approximation. In order for the determinant of the metric times dV to define an invariant volume element, the metric must be introduced as a classical, not a matrix-valued field. I study corrections to the classical gravitational action induced by the ensemble average of the trace dynamics matter fields. Using constraints from global Weyl scaling and three-space general coordinate invariance, I deduce constraints on the structure of the induced gravitational action. For the Robertson-Walker metric, this action exactly reduced to a cosmological term, but for the Schwarzschild metric it has a very different form, and modifies the horizon and large distance behavior.

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